Generation of Digital Terrain Models using polarimetric

Generation of Digital Terrain Models using polarimetric SAR

interferometry

Mounira Souissi Ouarzeddine March, 2002

Generation Of Digital Terrain Models Using

Polarimetric SAR Interferometry

by

Mounira Souissi Ouarzeddine

Thesis submitted to the International Institute for Geo-information Science and Earth Obser-vation in partial fulfillment of the requirements for the degree of Master of Science in Geo-informatics. Supervisors: Mr. G.C.Huurneman Dr. M.Brandfass Dr. K.Tempfli

International Institute for Geo-information Science and Earth Observation

Disclaimer This document describes work undertaken as part of a programme of study at the International Institute for Aerospace Survey and Earth Sciences. All views and opinions expressed therein re-main the sole responsibility of the author, and do not necessarily represent those of the institute.

I

Abstract

There is a requirement in many fields of earth science for accurate knowledge of terrain topography. Radar interferometry is a technique that makes a significant contribution to the topography mapping. The Digital Terrain Model (DTM) generation from interferometry SAR (InSAR) as a technique is not a new one, but getting a better DTM from polarimetric radar data is a new field of research. In this the-sis we describe two issues, i) The technique of DTM generation using two co-registered radar Single Look Complex (SLC) images acquired in a non polarimetric mode, this is what is called the conven-tional interferometric SAR; and ii) The mathematical formulation for the use of fully polarimetric ra-dar data, which is used to improve the interferometric coherence.

The InSAR concept has been studied and is implemented in this work. From two SLC radar images we are able to extract the phase content for each pixel, which is included in the process of DTM genera-tion. The novelty of this study is that we are using the SLC radar images acquired in polarimetric mode and include the properties of this polarimetry in the DTM generation to realise a higher quality.

The airborne radar data are acquired in repeat pass fully polarimetric mode and are provided by Aero-sensing RadarSysteme GmbH Company (Munich, Germany). The wavelength is in the P band. The P band wavelengths are able to penetrate the forest canopy. The study area is located in the Tapa-jós National Forest, Brazil.

Before DTM generation, coherence maps from non-polarimetric data and from fully polarimetric data using the optimisation theory have been generated. The coherence map gives an indication about the correlation between the couple of co-registered radar images and is related with the quality of the in-terferogram. Comparison between the singular interferometric coherence obtained from conventional interferometry and the optimised coherence obtained from fully polarimetric data, using histograms, reveal that the optimisation applied in this study brought significant improvement to the quality of the coherence. In our case coherence optimisation is indeed a reliable tool to improve the quality of the interferogram, and generally if we have access to fully polarimetric data, the coherence optimisation is a better solu-tion. Results given in this research study are generated using IDL language software; this language seems to be very suited for satellite image processing.

II

Acknowledgments

I would like to express my deepest and most sincere thanks to all who contributed in the graduate study ending to this work. I would like to thank the Nuffic fellowship and the Netherlands Government for funding me for the completion of this MSc degree. I am especially grateful to the Aero-Sensing Radarsysteme GmbH Company (Munich, Germany) who gave me the opportunity to deal with radar processing in near range and for all the stuff who accepted to receive me in a critical busy time. I am further grateful for the company for supplying me with a rare data: the fully polarimetric SLC radar data. Mr Gerrit Huurneman was my principal supervisor in this subject, and his mentorship, support and comprehension have been very useful to finalise the results presented in this work. Thank you so much. Dr. Michael Brandfass acted as my second supervisor but his help was more than that. I am very grate-ful to him for his support when I have been to Aero-Sensing Radarsysteme GmbH Company, as well as far from there via my daily bunch of e-mails, in the programming part and in the technical part of the subject. My thanks also go to Dr. Klaus Tempfli for his very good suggestions and critical reading. I would like to thank the examiners professor Martien Molenaar and Ramon Hanssen for agreeing to evaluate this work. Likewise, Mr. H.Van Oosten, Mr. W. Bakker from ITC offered me fresh insights and new tricks in IDL programming. My thanks also go to Mr G. Reinink and Mr A. Blenke for their technical support. My special thanks to Dr. M. Hellmann from DLR and A. Reigber for the very nice published site, “ep-silon.nought.de”, that contains some IDL programs on polarimetry and Interferometry SAR, from where I could get some ideas. Thanks to Mrs Tea De kluijver for her mental support during my difficult times and to Mrs. Marion Pereik for her comprehension when my sister passed away and during my mother illness. I want to thank all my classmates GFM2 2000 for their friendship, support and cooperation, my family especially my husband because he allowed me to be abroad for this long time and my eldest sister for taking care of Meriem Mey. I will not forget my friends in Algeria for their understanding and support especially Nadia and Assia.

III

Table of contents

Abstract ................................................................................................................................................... i Acknowledgments.................................................................................................................................. ii Table of contents................................................................................................................................... iii List of Figures ....................................................................................................................................... vi List of tables......................................................................................................................................... vii List of symbols and acronyms ........................................................................................................... viii Chapter 1.................................................................................................................................................1 1. Introduction to DTM generation using InSAR........................................................................1

1.1. Introduction ..............................................................................................................................1 1.2. Historical review ......................................................................................................................1 1.3. What is interferometry?............................................................................................................2 1.4. What is polarimetry and for what it is used?............................................................................3 1.5. Current stage.............................................................................................................................3 1.6. Radar data.................................................................................................................................3 1.7. Research objective....................................................................................................................4 1.8. Description of the research method..........................................................................................4 1.9. Structure of the thesis ...............................................................................................................5

Chapter 2.................................................................................................................................................7 2. SAR interferometry:Concepts and Basics................................................................................7

2.1. Principle of SAR ......................................................................................................................7 2.2. Principle of InSAR ...................................................................................................................8 2.3. InSAR geometry problems.......................................................................................................9

2.3.1. Foreshortening....................................................................................................................9 2.3.2. Layover.............................................................................................................................10 2.3.3. Shadowing ........................................................................................................................10 2.3.4. The Methods for Acquiring SAR data for Interferometry................................................10 2.3.5. Repeat pass interferometry ...............................................................................................11

2.4. The Processing of Interferometric Data..................................................................................11 2.4.1. Calibration ........................................................................................................................11 2.4.2. Co-registration ..................................................................................................................11 2.4.3. Generation of an interferogram ........................................................................................12 2.4.4. Flat Earth Removal...........................................................................................................12 2.4.5. Phase unwrapping.............................................................................................................12 2.4.6. Geocoding.........................................................................................................................16

2.5. Quality of an interferogram....................................................................................................17 2.6. Coherence...............................................................................................................................17

IV

2.7. A comparison between airborne and spaceborne InSAR ...................................................... 18 2.8. Conclusion............................................................................................................................. 19

Chapter 3.............................................................................................................................................. 21 3. Polarimetry InSAR...................................................................................................................... 21

3.1. Background of radar polarimetry .......................................................................................... 21 3.2. Polarization............................................................................................................................ 21

3.2.1. Definition of polarization ................................................................................................ 21 3.2.2. Wave polarization............................................................................................................ 22 3.2.3. Antenna role in polarization ............................................................................................ 23

3.3. Polarization in remote sensing............................................................................................... 23 3.3.1. What is polarization useful for?....................................................................................... 23 3.3.2. Polarimetric interferometry.............................................................................................. 24 3.3.3. Scattering matrix.............................................................................................................. 24

3.4. Limitations in PolSAR........................................................................................................... 25 3.5. Data used ............................................................................................................................... 25

3.5.1. Study site and data ........................................................................................................... 25 3.5.2. Radar data ........................................................................................................................ 26

3.6. Airborne polarimetry hardware ............................................................................................. 27 3.6.1. System requirements in airborne polarimetry.................................................................. 27 3.6.2. Overview of the AeS-1 SAR System............................................................................... 27

3.7. Conclusion............................................................................................................................. 28 Chapter 4.............................................................................................................................................. 29 4. Mathematical formulation of the optimised coherence........................................................ 29

4.1. Coherence optimisation using Polarimetry............................................................................ 29 4.1.1. Data representation in polarimetric interferometry.......................................................... 29 4.1.2. The vectorial representation using the Pauli basis matrix ............................................... 30 4.1.3. Vectorial complex representation .................................................................................... 31

4.2. Conclusion............................................................................................................................. 35 Chapter 5.............................................................................................................................................. 37 5. Implementation, Results and Discussion ............................................................................... 37

5.1. Results ................................................................................................................................... 38 5.1.1. Interferogram generation ................................................................................................. 38 5.1.2. Phase flat-earth removal .................................................................................................. 39 5.1.3. Phase Unwrapping ........................................................................................................... 40 5.1.4. Height estimation............................................................................................................. 42

5.2. Generation of coherence maps............................................................................................... 45 5.2.1. Coherence map from non polarimetric data..................................................................... 45 5.2.2. Optimised coherence........................................................................................................ 47

5.3. Programming part .................................................................................................................. 50 5.3.1. IDL Language.................................................................................................................. 50 5.3.2. Handling SAR data .......................................................................................................... 50 5.3.3. Phase flat removal............................................................................................................ 50

V

5.4. Conclusion..............................................................................................................................51 Chapter 6...............................................................................................................................................53 6. Conclusions and recommendations.............................................................................................53 References .............................................................................................................................................55 Appendices .............................................................................................................................................A

The AES-1 System provided with X band ..........................................................................................A Doppler centroid Frequency: DCF......................................................................................................C Eigenvalue Problems........................................................................................................................... E IDL programming example ................................................................................................................. F

VI

List of Figures

Figure 1.1: Representation of the workflow of DTM generation............................................................ 2 Figure 1.2: Representation of the workflow of the research objectives .................................................. 5 Figure 2.1: Principal of SAR Adapted from URL1................................................................................. 7 Figure 2.2: Interferometric geometry (Adapted From Zebker and Goldstein, 1986)......................................... 8 Figure 2.3: Different distortions encountered in SAR geometry........................................................... 10 Figure 2.4: Wrapped phase and Unwrapped phase ............................................................................... 12 Figure 2.5: Mirror Function................................................................................................................... 14 Figure 2.6: simplified flowchart for the computation of jkρ ............................................................... 15

Figure 3.1: Propagation of an electromagnetic wave in the space ........................................................ 22 Figure 3.2: Representation of an elliptical polarization ........................................................................ 22 Figure 3.3: Polarization of a wave using filters (From URL1)) ............................................................ 23 Figure 3.4: map of the location of the Tapajós National Forest ............................................................ 26 Figure 4.1: Methodology of calculation of the optimised coherence .................................................... 34 Figure 5.1: Magnitude of the co-registered SLC airborne radar images: SLC1HH (a), SLC1HV (b) . 37 Figure 5.2: Filtered interferograms related respectively to HHHH (a), VVVV (b) and HVHV (c)

polarizations (528*4112 pixels). Time difference between the two acquisitions is 13 minutes ... 38 Figure 5.3: Flat-earth phase (a) and the Wrapped flat-earth phase....................................................... 39 Figure 5.4: Interferogram before(a) and after the correction for the flat-earth phase effect (b)............ 40 Figure 5.5: Unwrapped phase (a) The wrapping of the unwrapped phase (b) and error phase map (c) 41 Figure 5.6: The Etna mountain: the magnitude of the master image (a) the unwrapped phase (b), the

height map of the DTM (c) and the DTM given in a shaded view using the IDL function Shad_surf (d) ................................................................................................................................. 43

Figure 5.7: DTM generated from an unwrapped phase not added to the flat earth phase ..................... 44 Figure 5.8 : DTM generated with wrong orbital parameters ................................................................. 44 Figure 5.9: Coherence maps calculated from the original images........................................................ 45 Figure 5.10:: Coherence maps calculated from small images ............................................................. 46 Figure 5.11: First optimised coherence (a), second optimised coherence (b) and third optimised

coherence (c) ................................................................................................................................. 47 Figure 5.12: First optimised coherence (a), coherence map of the HH-HH polarization (b) ................ 48 Figure 5.13:Histograms of the singular coherence maps (a) and of the optimised coherence maps (b)

Values are multiplied by 1000 for better visualisation.................................................................. 49

VII

List of tables

Table 3.1: Radar Data Used ...................................................................................................................26 Table 3.2: Orbital data ...............................................................................................................................27 Table 3.3: Information concerning the AeS-1 SAR System ..................................................................27 Table 5.1: Coherence statistics from a small image ...............................................................................46

VIII

List of symbols and acronyms

Symbol Definition * Conjugate function of a complex variable <> Ensemble average T Matrix transposition 3-D Three-dimensional 4-D Four-dimensional a Semi-major ellipsoid axis A1 Position for antenna 1 A2 Position for Antenna 2

2,1A&r

Derivatives with respect to time

AeS-1 Aerosensing SAR system No. 1 Atan The Arc-tangent function in IDL b Semi-minor ellipsoid axis. B Baseline C1 Constant C2 Constant

DEM. Digital elevation model DT Digital Terrain Model DGPS Differential Global Positioning System DLR Deutches Zentrum für luft-und Raumfahrt EM Electromagnetic EXP Exponential FFT Fast Fourier Transform

2,1DCf Doppler centroid frequency

H Horizontal polarization h Aircraft height above the geoid or flight height hh-vv Co-polarization hh-hv Cross-polarization I Interferogram IDL Interactive Data Language IMU Inertial Measuring Unit INS Inertial navigation System InSAR Interferometry SAR j Row indice J Hermitian semidefinite matrix k Column indice

IX

1kr

Scattering vector (3-D)

2kr

Scattering vector (3-D)

L Lagrangian function Lidar Light Detection and Ranging M Size of rows window N Size of columns window

p Illuminated object pv Object position vector

P Radar Microwave =0.72cm xp x coordinate of the object in the ellipsoid

yp y coordinate of the object in the ellipsoid

zp z coordinate of the object in the ellipsoid

mnP Two-dimensional Fourier transforms of jkρ

p&v Derivative of the object position with respect to time

POLSAR Polarimetry SAR PRF Pulse Repetition Frequency r Distance or slant range to the target r1 Range distance of master image pixel Radar Radio detection and ranging S Scattering matrix S1 Scattering matrix of an SLC1 or SLC1 S2 Scattering matrix of an SLC2 or SLC2

hhS 2,1 SLC 1 or 2 in the hh polarization

vvS 2,1 SLC 1 or 2 in the vv polarization

vhS 2,1 SLC 1 or 2 in the vh polarization

hvS 2,1 SLC 1 or 2 in the hv polarization

SAR Synthetic Aperture Radar SLC Single Look Complex SNR Signal to Noise t0 Begin time for illumination t1 End time for illumination [T11] 3*3 complex matrices composed as follow [T22] 3*3 complex matrices composed as follow

[T6] 6x6 Hermitian positive semidefinite matrix x Subscript refer to difference in the i indice y Subscript refer to difference in the k indice

z Pixel height above the geoid V Vertical polarization π 3.1415927

β Angle defining the ellipticity parameter

X

α The tilt angle or the angle with the horizontal baseline θ The look angle or the incidence angle at the target location θ’ The baseline angle with respect to the horizontal δr Difference in range between the echoes from the two antennas

xkj ,∆ Row wrapped phase differences

ykj ,∆ Column wrapped phase differences

φ or φ∆ The pixel’s interferometric phase ϕm: Wrapped phase

mnΦ Two-dimensional Fourier transforms of jkφ~

jkφ Unwrapped phase associated to the j, k pixel

jkφ~ Periodic function jkφ

jkψ Wrapped function on a discrete grid of points

jkψ~ Periodic function jkψ

[ ]12Ω 3*3 complex matrices composed as follow

γ Coherence γ Coherence magnitude

intγ Coherence due to scalar interferometry

maxγ Maximum coherence

polγ Coherence due to polarimetric effect

λ Radar wavelength λ1 Lagrangian multiplier λ2 Lagrangian multiplier

ijρ Periodic function

µ Angle of the orientation of the ellipse

1µ Scattering coefficient

2µ Scattering coefficient ν Eigenvalue

maxν Maximum eigenvalue

pΨ The set of 2x2 orthogonal complex Pauli basis matrices

1wr Normalised complex vector

2wr Normalised complex vector

max1wr First maximum eigenvector

max2wr Second maximum eigenvector

optw1r

First optimum scattering mechanism

optw2r

Second optimum scattering mechanism

1

Chapter 1

1. Introduction to DTM generation using InSAR

1.1. Introduction

Digital Terrain Models (DTMs) are used in many applications in the context of earth sciences. The required quality (accuracy and reliability) of them is dependent on the application. The production costs of a DTM are strongly correlated with that quality. Since projects are most often lacking money, people are looking for useful products for the lowest price. DTMs can be created from data that is ac-quired with airborne or spaceborne sensors operating in the optical and microwave part of the spec-trum or by ground based methods e.g. levelling. The quality of DTM’s that are created using data from space are at a relative low range in price when large areas have to be covered, but also in quality. The ground-based method can result in a high quality DTM but they are very expensive (manpower). In between these, the DTM creation by airborne sensors like aerial cameras, multi-spectral sensors, lidar and radar can be found. At this moment, many researchers are looking for the quality improvement of the DTM produced by methods that are based on the different datasets. In this study the creation of a DTM from radar data using interferometry will be described.

1.2. Historical review

Radar interferometry is a technique to extract 3D information of the earth surface by using the phase content of the radar signal. Graham was the first to introduce synthetic aperture radar (SAR) for topographic mapping in 1974 using data supplied by the first civilian remote sensing satellite SeaSAT. Zebker and Goldstein pre-sented the first results with side looking airborne in 1986 (Zebker and Goldstein, 1986). They mounted two SAR antennas on an aircraft with 11.1m from each other. Since that time many Interferometric SAR (InSAR) systems were designed and constructed. Numerous papers have been published since the European Space Agency (ESA) launched the ERS-1 satellite in July 1991. But the spaceborne interferometry was given a good opportunity when the ESA launched in 1995 the ERS-2, giving the chance to the collection of data acquired just one day apart in what they called the Tandem mission. The interferometry that has been used for long time was dealing with non polarimetric data, i-e one wave polarization in transmitting and also one in receiving. Having fully polarimetric data, i-e a radar image that is acquired in different polarizations was difficult because of the electronics and the hard-ware, which have to be installed on the platform to handle that big amount of data. Nowdays and with the development of technology polarimetric radar data are available, and the investigations of interfer-ometry polarimetric SAR are initiated.

Chapter 1: Introduction to DTM generation using InSAR

1.3. What is interferometry?

Radar interferometry is a technique for extracting three-dimensional information of the earth’s surface by using the phase content of the radar signal. Phase information is calculated from two images S1 and S2 acquired on the same area and co-registered very accurately. Measurements in three-dimensions can be made by SAR interferometry with a side looking geometry from both airborne and spaceborne SAR sensors (Gens and Genderen, 1996) , (Lin et al., 1994). The technique more suited for airborne SAR is the Across-track interferometry, which requires two SAR antennas mounted on the same platform for simultaneous data acquisition. Another option is the repeat pass interferometry creating two images in different orbits or flight passes. The phase and magnitude of the return signal is recorded and used to calculate the height of the terrain. Many authors have published papers on this process (Gens and Genderen, 1996), (Massonet, 1997). The illustration of the principle of calculating height, using interferometry SAR will be given in chap-ter 2.

The most important steps in DTM generation using interferometry InSAR are: • Generation of coherence map • Calculation of the interferogram (wrapped phase) • Phase unwrapping which is the conversion of the phase contained in the interval (-π,π] to its

real value which can be more that just π radian • Generation of the DTM’s using geo-coding

In the following, the general flowchart of DTM generation is given.

SLC1 SLC2

2

Figure 1.1: Representation of the workflow of DTM generation

flat-earthphase

wrapping

calculate theinterferogram

wrapped phase

Phase unwrapping

Filtering

Ge-coding

DTM

flight-passdata


3

1.4. What is polarimetry and for what it is used?

Polarization is the term used to describe the way in which an electromagnetic wave oscillates as it trav-els. For most SAR systems, only one polarization can be transmitted or received at a time. The transmitting antenna determines the polarization of the emitted wave, and the receiving antenna deter-mines which polarization of the returned signal will be recorded. Polarimetry deals with the full vector nature of polarized electromagnetic waves through the frequency spectrum. By full polarimetry we mean that radar waves are transmitted and received in both horizon-tal (H) and vertical (V) polarization for a wavelength. The data products resulting from polarimetry SAR data are in slant-range projection. When the wave passes through a medium of changing index of refraction, or when it strikes an object such as a radar target and /or a scattering surface and it is reflected, then characteristic information about the reflectivity of the object can be obtained using polarization. Different polarization modes are VV, HH, HV and VH. The first letter refers to the transmitting channel and the second one to the re-ceiving channel (Boerner and Yamagushi, 2000). These polarization modes give more information about several themes such as vegetation layer height and biomass. The aim of the present investigation is to utilise polarized data to estimate a better coherence in order to generate a more accurate SAR in-terferogram.

1.5. Current stage

The development of radar polarimetry and radar interferometry is advancing rapidly. Due to recent advances in SAR polarimetry, interferometric Synthetic Aperture Radar (InSAR) sensors are currently gaining a wider recognition. It is used in the field of forest and crop classification, geological mapping, terrain analysis and digital elevation model generation. With fully polarized radar data the textural fine structure, target orientation, symmetries and material constituents can be recovered with considerable improvement above that of single polarization (Boerner and Yamagushi, 2000).

1.6. Radar data

The analysis of different images acquired with different polarizations has the capability to provide a broader set of useful information (Helmann and Krätzschmar,1998). Also the different wavelengths such as in the X, C, L and P-band are useful since they show different interactions with scatterers. In this study, the P-band is used. This wavelength is capable of penetrating the vegetation coverage and thus it offers the possibility to retrieve information about the phase and magnitude of the signal return-ing from the ground surface. The correlation between two data sets that are acquired from slightly different position can be com-puted and the derived coherence map is a measure of the equality of the data. A high coherence is re-quired to create a good DTM. The de-correlation, which results in a low coherence, is the result of a number of disturbing effects. One of them is the baseline de-correlation. Recent studies have revealed that the de-correlation between the image pair, which is related to base-line de-correlation, can be reduced if fully polarized SAR data are used (Sagnés et al., 2000). It is expected that coherence maps retrieved from the fully polarized SAR data can give a better esti-mation of the terrain height.


4

1.7. Research objective

The main objective of this research is to investigate a novel approach to generate DTMs using po-larimetry InSAR airborne data acquired in the P band. We will generate different coherence maps and assess the usefulness of fully polarized data compared to single-polarized data in improving the quality of this important output. For this aim, programs in IDL language will be written.

Research questions, which have to be answered in this subject, are: • Why using P band? • Which combination of polarization is suited for the DTM creation? • Why repeat-pass and not single-pass mode is used? • Have the data, which will be provided by the Aerosensing RadarSysteme GmbH Company

undergone some processing steps? If yes what are these steps? • What is the mathematical formulation, which is behind the generation of a DTM using po-

larimetry InSAR? • Is IDL programming language a good choice for this research? • How will the accuracy of the output be evaluated?

1.8. Description of the research method

AeroSensing RadarSysteme GmbH Company has provided data for this study. We will generate DTM’s from co-registered SLC images, using the IDL programming language and analyse our find-ings. We will

• Review the InSAR concept • Collect polarimetric radar data acquired in P band. • Write IDL programs for

Visualisation of SAR images in different polarizations Generation of Coherence maps and interferograms Flat earth phase wrapping and phase flat removal of the interferogram Unwrapping phase Geocoding of the unwrapped phase

• Conduct a comparative evaluation of the coherences and DTMs from single-polarized and from fully polarized data.

In this research only a relative comparison can be done since we do not have any reference data about the study area (Tapajós National Forest). The following flowchart gives a general overview of the work that must be done.


5

Fullypolarimetric

data

Optmizedcoherence

DTM

Comparison

Coherence from HH-HH polarization

SingularinterferometricCoherences

Figure 1.2: Representation of the workflow of the research objectives

1.9. Structure of the thesis

In chapter 2 we will provide the principle of radar imaging and the method of DTM generation using interferometry and in chapter 3, information about the test area and radar data will be given as well as the principle and the usefulness of fully polarized data. A brief overview on the current results of In-SAR and fully polarized InSAR in the radar community is also given. Chapter 4 will be focused on the mathematical formulation of the coherence optimisation. Results are covered and discussed in chapter 5. The thesis ends with some suggestion for future work. Program examples written in IDL language can be found in the appendix D.

Chapter 2

2. SAR interferometry:Concepts and Basics

2.1. Principle of SAR

The term Synthetic Aperture Radar, or SAR refers to the technique used to simulate a long antenna by combining signals (echoes) received by the sensor as it moves along a particular flight track. In gen-eral the larger the antenna, the more unique information you can obtain about a particular viewed ob-ject and hence the better the resolution. With more information, you can create a better image of that object.

A SAR antenna transmits radar pulses very rapidly. In fact, the SAR is generally able to transmit sev-eral hundred pulses while the aircraft or the spacecraft passes over a particular object. Many backscat-tered radar responses are therefore obtained for that object. SAR technology was developed to allow a small antenna to gather high-resolution data. It uses the "Doppler history" of radar echoes generated by the forward motion of the platform to synthesize a large antenna.

After intensive signal processing, all of those echoes can be manipulated such that the resulting image looks like the data were obtained from a big, stationary antenna. The "length" of the synthetic aper-ture, is the distance travelled by the spacecraft while the radar antenna collected information about the object. This technique is represented in Figure 2.1. A detailed description of the theory of SAR operation is complex and beyond the scope of this thesis. For more detail see (Lillesand and Kiefer, 1999).

7

Figure 2.1: Principal of SAR Adapted from URL1

Chapter 2: SAR Interferometry: Concepts and Basics

8

Where θ : The look angle. h : the flight height p : the object illuminated T0 : begin time for illumination Tn : end time for illumination

2.2. Principle of InSAR

InSAR is a relatively new technique in radar remote sensing that allows pairs of radar images to be processed to form accurate elevation models, or DTMs. For InSAR a pair of images is acquired from two antenna positions, spatially separated by a distance, referred to as baseline. Because the images are acquired from different views, the corresponding im-ages do not overlap perfectly; hence a co-registration is needed, before any further processing step can be done. Two antennas may be mounted on the same platform, it is what we call single pass mode or the area may be flown at different times by the same antenna, it is then what we call the repeat pass mode. Fig-ure 2.2 represents the principle of InSAR.

Figure 2.2: Interferometric geometry (Adapted From Zebker and Goldstein, 1986) The difference in range can be given by:

( )αθ +=− cos' Brr

While the height h is ( )αsinrh = (2.1)

α

α

θ’

r

r-r’r’

B

h

Antenna 2

Antenna 1


9

The measured phase φ of the interferogram is expressed as

( )λπδρ

λπφ 22' =−= rr (2.2)

h is the aircraft altitude r is the distance or slant range to the target. θ’ is the baseline angle with respect to the horizontal. α: the depression angle B: the baseline λ: the wavelength of the microwave δρ: the difference in range from the object to the two antenna positions If we combine the three equations given above (Zebker and Goldstein, 1986), we get

−= − '

2cossin 1 θ

Brh

πφλ

2.3

This phase difference is also called the interferometric phase. Derivation of a DTM from InSAR data is not a simple task; the two acquired images must be proc-essed as was depicted in Figure 1.1. In the next paragraph we will discuss the geometric problems en-countered in collecting radar data.

2.3. InSAR geometry problems

When a radar sensor acquires the images, it measures the time that the microwave takes when it is emitted from the radar, interacts with the ground and comes back to its origin. This time is then con-verted to a distance on the ground. Obviously ground parts, which are in higher elevations or facing towards the sensor or facing away from it are displaced, compressed or extended. Such distortions are known as Foreshortening, Layover, and Shadowing and they will be explained in the following.

2.3.1. Foreshortening

Foreshortening is a special case of elevation displacement. When the radar beam reaches the slope of a tall feature e.g. a mountain, at the same moment, the foreshortening will occur. In Figure (2.3.a) the slope (a to b) will appear compressed and the length of the slope will be represented incorrectly (a' to b'). The severity of foreshortening will vary depending on the angle of the mountain slope in relation to the incidence angle of the radar beam. Maximum foreshortening occurs when the radar beam is per-pendicular to the slope such that the slope, the base, and the top are imaged simultaneously. The length of the slope will be reduced to an effective length of zero in slant range (c'd'). The slopes that face to-wards the sensor appear bright, while slopes facing away from sensor appear darker. The effect is more pronounced for steeper slopes, and for radars that use steeper incidence angles.


10

2.3.2. Layover

When the reflected energy from the upper portion of a feature is received by the satellite sensors, be-fore that from the lower portion of the feature, the effect Layover happens. We can also explain the effect saying that this occurs when the radar beam reaches the top of a tall feature (b) before it reaches the base (b). Figure (2.3.b) gives an illustration of the effect. The return signal from the top of the fea-ture will be received before the signal from the bottom. As a result, the top of the feature is displaced towards the radar from its true position on the ground, and "lays over" the base of the feature (b' to a'). Layover is most severe for small incidence angles as with foreshortening effect (Zebker and Lu 1998). Furthermore when layover effects occur several areas of the earth’s surface can disappear from the SAR image (Rocca et al., 1998).

2.3.3. Shadowing

Radar shadow occurs when the radar beam is not able to illuminate the ground surface. Shadows occur behind vertical features or slopes with steep sides. Since the radar beam does not illuminate the sur-face, shadowed regions will appear dark on an image, as no energy is available to be backscattered. As incidence angle increases from near to far range, so will shadow effects as the radar beam looks more and more obliquely at the surface. Figure (2.3.c) explains the process that is responsible for shadow appearing on one image. Shadowing is provoked also when a slope is steeper than the incidence of the radar beam.

(a) (b) (c)

Figure 2.3: Different distortions encountered in SAR geometry

Foreshortening, Layover, and Shadowing are more pronounced in rugged terrain. Such distortions af-fect mainly the accuracy of the phase to height conversion and contribute in the decorrelation effect.

2.3.4. The Methods for Acquiring SAR data for Interferometry

In SAR Interferometry there are three main ways to gather data. These are across track interferometry, along track interferometry and repeat track (also called repeat-pass or multi-pass) interferometry (Gens and Genderen, 1996). Each method is developed to explore the strengths of the sensor as well as the application for which the data is required. The single pass modes, are only employed on airborne sys-tems, as they require two SAR antenna systems mounted on one platform. This is not yet possible on

Region of Shadow

Sar antenna

aa a

b b b

c

a’ a’

b’ b’ b’

a’

d

Sar antenna Sar antenna


11

satellites due to technical limitations. Both, airborne and spaceborne radar systems can be used in the repeat pass mode.

In this study, the repeat pass interferometry data is used and an overview of it is given in the next para-graph.

2.3.5. Repeat pass interferometry

Repeat pass interferometry requires only one antenna and hence is the method more suited to space-borne SAR sensors. This is also because for this method precise location of the flight path is required. Satellites typically have precise and stable orbital paths in the absence of the atmosphere.

In the repeat pass case each track has its own motion which makes interferometry much more sensitive to the performance of motion compensation. Corresponding errors have to be corrected during data processing.

2.4. The Processing of Interferometric Data

An interferogram is defined as the product of the complex SAR values of the first image referred to as master image with the complex conjugate of the second image referred to as slave image; i.e. the cor-responding amplitudes have to be averaged and the corresponding phases have to be differenced at each point in the image (Gens and Genderen, 1996). The interferogram is then filtered to perform qual-ity analysis as well as interferogram enhancement. The following essential steps can be recognised in the DTM generation.

2.4.1. Calibration

Due to the spatial separation of the antennas (baseline) the reflected signals are detected with different propagation time and phase at each antenna. The phase difference between the received signals is a measure of the elevation of the reflected point on the earth surface. The radar system has to be cali-brated to eliminate systematic errors, which lead to phase offsets (URL 3).

2.4.2. Co-registration

The two images are generally referred to as master and slave. They are co-registered with sub-pixel accuracy, e.g. with an accuracy of 0.1 pixels (Hellwich, 1999). In this step, the second image is resam-pled into the geometry of the first one using a suitable interpolation method such as Shannon or bi-cubic interpolation. When both SAR images contain completely overlapping object spectra, we can then calculate the interferogram.

Some basic filtering may be applied prior to and/or following the image co-registration to enhance phase coherence. This filtering may include baseline and azimuth spectral overlap filtering to remove the effects of "baseline decorrelation".


2.4.3. Generation of an interferogram

After the two single-complex images are co-registered, the complex interferogram is computed accord-ing to:

φjeSSSSI ... 21*

21 == 2.4

Where

S1 and S2 are the corresponding SLC (single look complex) values of the co-registered images. * stands for the conjugate of a complex variable

21 ϕϕφ −= is the interferometric phase

2.4.4. Flat Earth Removal

Due to the baseline, separating the two antennas in space, the phase of the returned signal varies for each image element from near to far range. These results are clearly visible in the interferogram of a flat terrain. By estimating this effect, it can be eliminated leaving only phase difference information related to the height of the observed object on the ground. This process is termed "flat earth" removal as it involves removing the signal that would be present even if the scene were flat.

2.4.5. Phase unwrapping

One of the major problems encountered in the implementation of SAR interferometric technique is finding the real phase difference between two complex SAR images. This phase, which has been cor-rected from flat earth effect, is known to be modulo 2π since a phase is observable on a circular repeat-ing space. It is called a wrapped phase and has to be unwrapped or calculated back to its real values. Figure 2.4 clarifies the problem. In this figure we see an unambiguous phase (upper graph) and the corresponding measured phase (lower graph), which we get, as the result of the arc-tangent - function. The jumps of 2π in the meas-ured phase are clearly visible.

12

Figure 2.4: Wrapped phase and Unwrapped phase Adapted from URL3

Wrapped phase

Unwrapped phase

ϕm: Wrapped phase ϕ: The unwrappedphase


13

A number of phase unwrapping algorithms for SAR interferograms have been proposed in recent years (Ghiglia et al., 1987), (Ghiglia and Romero, 1994), (Marinelli and Laurore, 1995), (Zebker and Lu 1998). However, none of the existing phase unwrapping algorithms give satisfactory results when noisy and/or dense fringes occur. This problem is even more difficult to solve because of the side-looking configuration of SAR which causes shadow, foreshortening and layover.

Strictly, phase unwrapping is an impossible problem because an unwrapped phase array necessarily contains information that is not available in the corresponding wrapped array. That is given only an ambiguous wrapped phase array, there is no definitive way to determine which of the many possible unambiguous unwrapped solutions is correct. All the algorithms rely on at least some assumptions; the most important is that the Nyquist criterion is met through the main part of the scene (Chen, 2001). The ability to resolve the 2π ambiguities depends on the local terrain slope and phase noise level caused by signal decorrelation between the two images. This can be due to geometrical effects of SAR imagery mentioned above. When the surface is smooth the measured phase is simple to calculate, as no noise is present. The phase unwrapping applied in this study is based on the least square unwrapping algorithm. This algorithm is considered simple compared to other methods given in the literature (Hellwich, 1999) (Spagnolini, 1993), (Ghiglia et al., 1987). The method performs a mirror reflection on the wrapped phase function to yield a periodic function, and the resulting from the Poisson’s equation is solved directly using the Fourier transform. This method also uses less memory compared to other methods (Pritt and Shipman 1994), this is a very good criterion, especially if we are dealing with big images. Consider the wrapped function jkψ on a discrete grid of points.

integeris2 nnjkjk πφψ += 2.5

Where the indices j and k are the indices in row and column. We wish to determine the unwrapped phase values jkφ at the same grid locations.

Let us define the wrapping operator W that wraps all values of its arguments into the interval (-π,π) by adding or subtracting an integral number of 2π radian (rad), from its argument. Hence we have

W( jkφ )= jkψ 2.6

The wrap function satisfies the relation: jkjk ii ee φψ = . A key idea is to use a mirror reflection to extend jkψ and jkφ to periodic functions jkψ~ and jkφ~ re-

spectively (Pritt and Shipman 1994). In that case we can apply the Fourier and the cosine transfor-mations (Press et al., 2002). See Figure2.5.


14

( )( )( )( )

<<<<<<≤≤≤≤≤<≤≤≤≤

= −

NkMjNkMjNkMj

NkMj

jk

jk

kjM

jk

jk

0,00,00,20

0,0

~ ,2

ψψψψ

ψ 2.7

Figure 2.5: Mirror reflection of a function fk

jkφ can also be regarded as a periodic function jkφ~ that is defined by the mirror function.

Now two sets of phase differences are computed. Those differences in column (j index) and those dif-ferences in row ( i index ). The wrapped phase differences are then as follow:

kjkjkjy

kj

kjkjx

kj

∀∀−=∆

−=∆

+

+

,

~~

,1,,

,,1,

ψψ

ψψ 2.8

They are supposed to be in the (-π,π] interval, if not then a 2π factor has to be added or subtracted as necessary to ensure that they lie in the interval. Where x and y are the subscripts refer to differences in the i and k indices, respectively. The function we are looking for is a function jkφ that minimises the following sum (Press and al., 2002) (Zebker

and Lu, 1998):

( ) ( )∑∑∑∑−

=

−

=−+

−

=

−

=−+ ∆−−+∆−−

1

0

2

0

2,1,

2

0

1

0

2,,1

M

j

N

k

ykjkjkj

M

j

N

k

xkjkjkj φφφφ 2.9

This is the least squares solution. Derivation of equation (2.9) yields to (Pritt and Shipman, 1994):

( ) ( ) ijkjkjkjkjkjkj ρφφφφφφ =+−++− −+−+ 1,,1,,1,,1 22

0 1 2….. N-1 N ……………2N-1

fk


15

Where the periodic function ijρ is defined by y

kjyjk

xkj

xjkjk 1,,1 −− ∆−∆+∆−∆=ρ 2.10

We can now apply the two-dimensional Fourier transform

( ) ( )( )4cos2cos2 −+=Φ NnMmPmnmn ππ 2.11

Where mnΦ and mnP are the two-dimensional Fourier transforms of jkφ~ and jkρ respectively (Pritt

and Shipman, 1994). In Figure 2.6, we give a simplified flowchart for the computation of jkρ . Then

we integrate the phase derivative and get the searched unwrapped phase.

wrapped phase

k=0

j=0

calculate xjk∆

j=M+1

k=M+1

j=j+1

k=k+1

calculate jkρ

calculate yjk∆

yes

yes

no

no

Figure 2.6: simplified flowchart for the computation of jkρ

Bamler showed that such least squares approaches produce biased results, underestimating the true unwrapped phase gradient (Bamler et al., 1998), this underestimation effect is less pronounced in highly correlate regions (Franceschetti and Lanari, 1999). Thus, despite of the reasonable efficiency least squares algorithms often give disappointing results in practice (Chen, 2001). For more detail about unwrapping algorithm we can consult (Spagnolini, 1993), (Chen, 2001). After phase unwrapping has been accomplished, the DTM can be generated using geocoding.


16

2.4.6. Geocoding

The derivation of geocoded height information is carried out by solving the standard range/Doppler equations and the ellipsoid equation. (Wimmer and al., 2000), (Holecz et al., 1998). The orbit or flight path data are needed for geocoding. They describe the position and the flying directions of the sensor. The approach used here is the Range Doppler approach, where object space coordinates are computed from observed ranges, Doppler centroid frequencies and flight path data. For more detail see appendix B. The standard range/Doppler equations are given by:

( )11112 DCfrApAp λ=

−− &r&r

rr 2.12

11 rAp =−rr

2.13

( )22222 DCfrApAp λ=

−− &r&r

rr 2.14

φπλ

412 +=− rAprr

2.15

And the ellipsoid equation is:

12

2

2

22

=++

bp

app zyx 2.16

Where λ is the radar wavelength

2,1DCf is the Doppler centroid frequencies

r1 is the range distance of master image pixel.

2,1Ar

the antenna positions

2,1, Ap &r&v are the derivatives of the object position and antenna position respectively, with respect to

time. Φ is the pixel’s interferometric phase a, b are the semi-major and semi-minor ellipsoid axis.

yx pp , and zp are the coordinates of the object on the ellipsoid

Solution of the simultaneous equations 2.12-2.15 for each image pixel directly leads to its location in the selected geodetic reference. A two-step procedure consisting of phase-to-height conversion (Equa-tions 2.12, 2.13 and 2.16) and subsequent backward geocoding (Equation 2.14) can be applied if the slant range height is required (Wimmer and al., 2000).


17

The complication in repeat pass interferometry is that the radar is not flying in perfectly straight line. The platform attitude, (which has to be measured accurately using GPS) and thereby the baseline is constantly changing, which will be obviously translated into height error. The attitude change makes the motion of the two antennas different, resulting in severe phase decorre-lation. Precise motion compensation is therefore of vital importance for high resolution interferometric SAR systems. Deviations of the flight path from linear motion are so severe that it is not possible to apply a common reference line for the entire data pass (Madsen et al., 1993).

2.5. Quality of an interferogram

The performance of an interferogram chain depends on the radar sensor parameters, the accuracy of the flight track estimation and the quality of the data processing procedure. System hardware parame-ters play an essential role in the quality of the acquired data. Sufficiently high Signal to Noise Ratio (SNR), which allows accurate phase measurements is required as well as a phase stability to achieve a good resolution. Interferometric processing requires a precise reconstruction of the raw data, as it would have been ac-quired on ideal straight tracks with a constant forward velocity as well as the positioning of the differ-ent tracks within a global positioning system. Consequently accurate measurement of the absolute and relative sensor position is essential (Papathanassiou , 1999). The interferogram contains phase information useful for the computation of object space coordinates. This phase can be significant only if the scatterers on the surface of the earth have changed neither their backscattering behaviour nor their positions relative to each other. This requirement can be checked using the coherence, which helps to achieve for a successful interferometric processing. This measure of the correspondence of both SAR images is called coherence.

2.6. Coherence

The basis of InSAR is phase comparison over many pixels. This means that the phase between scenes must be statistical similar. The coherence is a measure of the phase noise of the interferogram. It is estimated by window-based computation of the magnitude γ of the complex cross correlation coeffi-

cient of the SAR images and it is given by (Hanssen, 2001):

10.

1 1

2)(2

2)(1

1

)*(2

)(1

≤≤=

∑ ∑

∑

= =

= γγN

n

N

n

nn

N

n

nn

ss

ss 2.17

N is the number of pixels in the window The interferometric coherence is defined as the absolute value of the normalised complex cross corre-lation between the two signals (Cloude and Papathanassiou, 1998). In a simplified manner, equation (2.1) becomes


18

*22

*11

*21

..

.

SSSS

SS=γ 2.18

<> stands for ensemble average The correlation will always be a number between 0 and 1. If the pixels are similar this will result in a high correlation and good results. If the pixels are not similar i.e. not correlated at a certain degree then the phase will vary greatly and the result will be noise; we talk then about de-correlation. A good coherence yields to a good DTM. Low coherence means bad phase quality and can engender many problems for the phase unwrapping. There are several parameters, which influence the coher-ence measurements, the most important are:

1. The signal to noise ratio associated with the additive system noise: this term defines the lower limit of the achievable coherence.

2. The baseline or antenna separation (baseline decorrelation): this term is crucial for the design of SAR system. Correlation decreases with baseline and data becomes completely decorrelated at long baselines (in practice more than 500m for spaceborne, (Zebker and Villasenor, 1992)).

3. The coherence decreases with increasing surface roughness 4. The coherence decreases with increasing change in the random component of the backscat-

tered fields between passes (temporal decorrelation in the repeat pass case): this can be due to the physical change of the surface roughness structure reducing the signal correlation (Cloude and Papathanassiou, 1998) as does vegetation, water, shifting sand dunes, and farm work (planting fields).

5. The loss of coherence increases as the deterministic change in surface height becomes comparable with the range resolution cell.

6. For range-tilted surfaces, the coherence increases, as the tilt angle tends to increase away from the radar; and it decreases, as the surface tends to tilt towards the radar. The total loss of co-herence occurs when the tilt angle equals the incidence angle.

7. Geometric distortions caused by steep terrain relief also decorrelate.

2.7. A comparison between airborne and spaceborne InSAR

Researchers in the field of Interferometry SAR stated that three conditions for obtaining suitable inter-ferometric data are needed:

1) a not changing terrain backscatter, 2) a stable viewing geometry and 3) a SAR processor which preserves the inherent phase information in the motion compensation

signal data. The motion compensation turned out as the most difficult effect to control in the technical part of the InSAR data acquisition in airborne InSAR. Small time difference between acquisitions in airborne sys-tems compared to spaceborne systems leads to a better temporal coherence if the mentioned conditions are met (Cloude and Papathanassiou, 1998). In the generation of digital terrain models using the repeat orbit InSAR, it is assumed that the radar signal propagates in straight path within the atmosphere. In reality the atmosphere is a refractive me-dium and the radar signal is therefore bent during an atmospheric turbulence. This refraction leads to


19

an excess delay in the radar signal (Hanssen, 2001), which can introduce significant errors in the inter-pretation of the interferometric phase data. However this problem can be less in airborne InSAR since the time between the two acquisitions is short compared to spaceborne.

2.8. Conclusion

In this chapter we reviewed the concepts and basics of InSAR. We also explained the geometrical problem related to the radar imaging as well as the methodology of generation of a DTM from a SAR pair images. The problem of unwrapping has also been explained since it is a critical step in InSAR processing. In the following chapter we will discuss about the usefulness of polarization in the InSAR application and we will give information about the data used in this work.

21

Chapter 3

3. Polarimetry InSAR

3.1. Background of radar polarimetry

Early SAR systems used one single polarization antenna for transmitting pulses and receiving their echoes. These were therefore called non-polarimetric systems. For example, if the antenna was linearly horizontally polarized, the system was a HH polarized system, that is, it used horizontal polarization for both transmission and reception. A conventional interferometric system operating with a fixed po-larization at a single frequency is not able to provide enough independent parameters necessary to de-scribe natural scattering processes when we aim to retrieve the physical parameters related to natural scattering mechanisms (Henderson and Lewis, 1998). The microwaves are part of the electromagnetic spectrum. They have a vectorial nature, and a com-plete description of the scattering problem in radar imaging requires a vectorial matrix formulation. Analyses of the SAR images always left questions unanswered like, what would the image have been if another system had been used, for example a VV or a HV or a differently polarized system? And is the polarization used optimal for the application? These questions are answered completely by the use of polarimetric systems (Boerner and Yamagushi, 2000). Radar polarimetry is a technique, which was initiated by the introduction of the concept of the `scat-tering matrix'. It remained only a theoretical concept for many years since it requires advanced hard-ware devices. It is a valuable technique for the extraction of geophysical parameters from SAR images and terrain classification (Hubert, 1999). It is also used in the fields of earth science and target identi-fication. Polarimetry SAR also called POLSAR, which issued from radar polarimetry has become an estab-lished technique in remote sensing. This is confirmed by the growing number of polarimetric airborne sensors. The generation of interferograms using fully polarimetry has been demonstrated to be a promising tool for the characterisation of different scattering processes. The approach to do this is either based on sta-tistical analysis of the polarimetric information or on scattering models, which provide an understand-ing of the physics of the scattering process (Cloude and Papathanassiou, 1998).

3.2. Polarization

3.2.1. Definition of polarization

Polarization is the term used to describe the way in which an electromagnetic (EM) wave oscillates as it travels. A vertically polarized wave oscillates up and down as it moves forward. When a wave passes through a medium of changing index of refraction, the polarization state of a single-frequency wave is transformed, and the EM wave vector is depolarized (see Figure 3.1). When a pulse leaves a transmitter, its electrical field vector can be made to vibrate in either a horizon-tal (H) or a vertical (V) direction depending on the antenna design.

Chapter 3: Polarimetry InSAR

3.2.2.

A horizontalBecause bothto have lineaInstead of tratric field vecshape that wellipse (BoerThe orientatnolds, 2000)The ellipticithe ellipticityof polarizatio

boraCirculbaElliptiba

When

00,,

===≠

22

Figure 3.1: Propagation of an electromagnetic wave in the space

Wave polarization

ly polarized wave would trace a horizontal line in the plane transverse to the propagation. vertically and horizontally polarized waves trace a line as they propagate, they are said

r polarizations. Note that the polarization described in Figure 3.1 is vertical. cing a vertical or a horizontal line perpendicular to the direction of propagation, the elec-tor of an EM wave could trace an ellipse. We would call this elliptical polarization. The ould be traced by a wave, whether linear or elliptical, is called the wave’s polarization ner and Yamagushi, 2000), (Reynolds, 2000) , and it is described in Figure 3.2. ion of the ellipse is given by the angle µ. It is known also as the tilt or dip angle (Rey-. The angle β defines the ellipticity parameter. ty and orientation angles together completely describe the polarization of any EM wave; angle describes the “fatness” of the polarization ellipse. In Figure 3.2 the different types ns are given.

onpolarizatiLinearonpolarizatiaronpolarizatical

,

Figure 3.2: Representation of an elliptical polarization

Electrical field

Magnetic field

Direction of propagation

H

V

ab

aH

aV

µ.

β


23

3.2.3. Antenna role in polarization

When a pulse leaves the transmitter, its electrical field vector can be made to vibrate in either a hori-zontal (H) or a vertical (V) direction depending on antenna design. Polarization is established by the antenna, which may be adjusted to be different on transmit and on receive. Most reflected pulses are parallel-polarized, i.e., return with the same direction of electric field vibration as the transmitted pulse. Thus, we get either a HH or VV polarization.

However, upon striking a target, the waves can undergo depolarization to some extent, so that reflec-tions with different vibration directions return. A second antenna picks up cross-polarization that is orthogonal to the transmitted direction, leading to either a VH or HV polarization mode. The first letter refers to the transmitting antenna and the second one to the receiving antenna. To polarize the wave, antennas use sometimes filters as depicted in Figure 3.3.

Figure 3.3: Polarization of a wave using filters (From URL1))

3.3. Polarization in remote sensing

In optical sensing, the polarization transformation behaviour expressed in terms of the polarization ellipse is named Ellipsometry. In Radar and SAR imaging it is denoted as Polarimetry using the an-cient Greek meaning of “measuring orientation and object shape” (Boerner and Yamagushi, 2000). For most SAR systems, only one polarization can be transmitted or received at a time. The transmit-ting antenna determines the polarization of the emitted wave, and the receiving antenna determines which polarization of the returned signal will be recorded. The radar system is designed generally to simultaneously collect imaging data of a scene in two or-thogonal polarization states on transmit and the same two polarization states on receive. From such a data set a complete scattering matrix of the reflectivity of the scene may be synthesized.

3.3.1. What is polarization useful for?

When a wave passes through a medium of changing index of refraction such us water, or when it strikes an object such as a radar target and/or a scattering surface such us a wet vegetation and it is re-flected; then characteristic reflectivity, shape and orientation of the reflecting body can be obtained (Boerner and Yamagushi, 2000).


24

Polarimetry gave birth to several new descriptive radar target detection parameters, including entropy, polarization degree, phase difference, ellipticity and orientation. The behaviour of these parameters is not identical for clutter. That is why they could lead to improvement in radar detection. Reflectivity of microwaves from an object depends on the relationship between the polarization state and the geometric structure of the object. Some ground features appear about the same in either paral-lel or cross-polarized images. But, vegetation, in particular, tends to show different degrees of image brightness in HV or VH modes, because of depolarization by multiple reflecting branches and leaves. Polarimetry has shown up till now that:

Contrasts between targets and backgrounds can be maximised by choosing the correct transmit and receive polarizations

The accuracy of crop type and land use classification results increases with the use of po-larimetry

The estimation accuracy of bio- and geo-physical parameters (such us forest biomass) in-creases (Burbidge et al., 1999)

3.3.2. Polarimetric interferometry

Polarimetric interferometric SAR, also called polarimetric interferometry (Cloude and Papathanassiou, 1998) is more sensitive to the distribution of oriented objects in a vegetated land surface than either a polarimetry or interferometry alone (Treuhaft and Cloude, 1999). POL-SAR by itself does not provide information and InSAR cannot provide textural fine structure information. It is necessary then to in-corporate fully polarimetric InSAR methods (Boerner and Yamagushi, 2000). The results can be used to enhance the contrast between different types of target and terrain, classify the terrain and ground cover in a SAR image, or extract geophysical and biophysical parameters such as surface roughness, moisture content of soil, biomass content of a forest, or thickness of thin sea ice. Compared to the conventional interferometry the application of polarimetry SAR interferometry prom-ises not only significant improvements but also new application possibilities. SAR interferometry is sensitive to the location of a surface element and its backscattering properties. The location of a surface element as mentioned in chapter 2 can be measured by the phase difference between coherent SAR images. The interferometric correlation coefficient depends on the distribution of the scattering objects within a surface element because the response of it is highly sensitive to the scattering mechanism (URL6). A radiated signal is scattered back to the radar sensor from a target as well as from neighbouring ob-jects. These undesired signals are called “clutter”. The different ground scattering contributions in the different polarizations, force the interferometry to use a combination of the different polarizations to improve the coherence. The polarimetric optimisation of the interferometric coherence is well formu-lated by Cloude and Papathanassiou.

3.3.3. Scattering matrix

For SAR system that coherently transmits and receives both horizontal and vertical polarizations, a complete 2*2 scattering matrix can be constructed for each pixel. These types of SAR systems are re-ferred to as PolSAR systems. The elements of the matrix can be used to calculate images representing backscatter at any polarization state.


25

The purpose of decomposition in radar polarimetry is to provide means of interpretation and optimum utilisation of polarimetric scattering data. The objective of any decomposition is also to combine or manipulate the scattering matrix elements in order to obtain more descriptive and discriminative target parameters, which is of decisive importance in applications of radar polarimetry (Unal and Ligthart 1998). The elements of the scattering matrix are functions of the frequency, the scattering and the il-luminating geometries. Researchers defined the scattering matrix as (Hubbert, 1994):

=

vvvh

hvhh

SSSS

S 3.1

The terms of the matrix provide the interferogram resulting from all combinations of polarization re-sponses. Note that the complex data format includes four files (HH, HV, VH, and VV) of one-look, slant range, scattering matrix data. In the next chapter this matrix will be discussed in detail.

3.4. Limitations in PolSAR

The limitations of multi-frequency polarimetric SAR include, the need for precise calibration. The large amount of data generated by such instruments (up to thirty times greater than for a conventional SAR), and the difficulties often encountered in interpreting multi-frequency polarimetric response data. The utility of the scattering matrix is how to explore the information content of polarimetric SAR data. The objective is to find a compact data set, which is more useful for DTM generation than the non-polarimetric data. Researchers have examined the fully polarization representation of the data, and found that it sometimes leads to clearer scatterer interpretation than linear polarization data (Papatha-nassiou et al., 1998). In the following section we will introduce the information about the study area as well as the radar and orbital data used in this work.

3.5. Data used

3.5.1. Study site and data

The site is situated in the tropical Tapajós National Forest with the coordinates: from about 55o west longitude, and about 03o south latitude. Tapajós National Forest is located in Sanitarém city, Pará state, Brazil, under IBAMA (Environment and Natural Renewal Resources Brazilian Institute) admini-stration. Figure 3.4 gives a general idea about the site location. The trees height varies from 10 to 25 m, with emergent trees up to 30-40. The elevation variation is between 10 m and 520 m. Since the region is suffering from rain, cloud, haze and smoke, SAR images are invaluable in provid-ing geological information due to the enhancement of the terrain caused by the side-viewing geometry, and the all-weather sensing capability.


3.5.2.

The potentiabeen shown forest type clP band (72 cand subsequeData used inGmbH (Munborne mode. It has been atember 2000.

Table 3.1: R

Image SLC1 SLC2 Flat_earth

26

Figure 3.4: map of the location of the Tapajós National Forest (From URL4)

Radar data

l role of P-band SAR for observation of tropical forest areas makes it very useful. It has that P band can contribute significantly to the accuracy of land cover type classification, assification and forest flooding observation (Hoekman and Quiñones, 1999). m) was chosen for these studies because of its potential for penetrating the forest canopy nt double bounce scattering of tree trunk and the ground. this study, has been provided by the private company Aerosensing RadarSysteme ich, Germany). The data consists of two SLCs images acquired in fully polarimetric air-

cquired during the dry season which goes from August to November at the end of Sep- More information about the data is listed in table 3.1.

adar Data Used

Polarization Wavelength Frequency Bandwidth HH, HV, VH, VV P-band 415 Mhz 70Mhz HH, HV, VH, VV P-band 415 Mhz 70Mhz

_phase NA P-band 415 Mhz NA


27

Table 3.2: Orbital data File Data Antenna1 Flight path data: Antenna position, airplane velocity, GPS time Antenna2 Flight path data: Antenna position, airplane velocity, GPS time Parameters Azimuth and range resolution, acquisition time, depression angle ect…

3.6. Airborne polarimetry hardware

3.6.1. System requirements in airborne polarimetry

System hardware parameters play an essential role in the quality of the acquired radar data. To achieve a high resolution, we need at least a sufficient SNR level (Papathanassiou et al., 1998). For interferometric applications the exact knowledge of the phase centre positions of the antennas in the order of 1/30 wavelength or better is required. To achieve a good interferogram processing, the raw radar data should be acquired on ideal straight tracks with a constant forward velocity. Positioning of the different tracks should be in a global coordinate system. The deviation of the real flight track from an ideal straight track causes errors in the range delay and in the phase of the raw data (Papathanassiou et al., 1998). Polarimetric and interferometric evaluations need high requirements on the phase preservation and accuracy of the motion compensation and data processing algorithm, especially in the case of airborne repeat pass systems. If uncompensated, these errors cause significant image quality degradation (Boni-fant, 1999).

3.6.2. Overview of the AeS-1 SAR System

The AeS-1 airborne interferometric radar owned by Aerosensing Radarsystems Company can achieve a DEM of 2.5 m grid spacing and an absolute accuracy of 5cm rms in non vegetated area (URL5). The airborne InSAR AeS-1 SAR system has been designed and manufactured at the same company. The characteristics of the AeS-1 SAR system are shown in Table 3.3. The platform is equipped with integrated real time Differential Global Positioning System (DGPS) and Inertial Measuring Unit (IMU). This allows an extremely precise positioning of the platform in the order of centimetres. Additionally, the DGPS/IMU data of the flight are processed and synchronised with the radar raw data (Holecz et al., 1998). It is also, equipped by a laptop computer for flight plan-ning, a transcription system for the recorded raw data on a disk array system to Digital Linear Tapes (DLTs). More details about the AeS-1 can be found in Appendix A.

Table 3.3: Information concerning the AeS-1 SAR System

Frequency [GHZ] 0.415 Polarization HH, HV, VH, VV PRF [Hz] 5998.8 Positioning DGPS and IMU Depression angle[degrees] 45.00


28

3.7. Conclusion

Polarimetry InSAR, how the polarization of a wave occurs between the transmission and reception, and the advantages and limitations of polarimetric interferometry in general have been discussed in this chapter. Radar data used in this work was also described. The scattering matrix, which represents the full information contained in the 4-radar polarizations, is an important component of the approach explained in chapter 4. The use of fully polarimetric data will be investigated for the generation of the coherence image. The polarimetric dependency of surface backscattering effect will be treated as a central topic in the next chapter via the optimised coherence.

29

Chapter 4

4. Mathematical formulation of the optimised coherence

In this chapter we will give a summary of the combination of SAR polarimetry and SAR interferome-try as it is described in “Polarimetric SAR Interferometry” (Cloude and Papathanassiou, 1998) and (Papathanassiou, 1999). The aim of this chapter is to show, using a mathematical formulation, the impact of radar polarimetry in the optimisation of the interferometric coherence.

4.1. Coherence optimisation using Polarimetry

A possible way to reduce the spectral decorrelation and hence to enhance the coherence is to use the entire scattering matrix. Fully polarimetric SAR data can be evaluated interferometrically in the same way as standard SAR data. We use the 2x2 complex scattering matrix given by the following equation:

=

vvvh

hvhh

SSSS

S 4.1

This matrix includes the four SLC radar images acquired in the four polarizations and will be the basic component of the following mathematical derivation, which is meant to show how the optimised co-herence is obtained in order to get a better interferogram.

4.1.1. Data representation in polarimetric interferometry

The scattering matrix provides a complete description of fully polarized radar returns from a surface. Each scattering matrix measured by a polarimetric SAR represents a single realisation from a statistical ensemble of scatterer strengths, scattering phase shifts and scattering elements positions within the radar resolution cell (Henderson and Lewis, 1998). In much of the literature on radar polarimetry, the scattering matrix, used to describe back-scattered returns from natural targets are symmetric, that is vhhv SS = , because the medium is assumed recipro-cal. The calculation of a scalar interferogram is based on two SLC images acquired in one polarization. The interferogram generation can be described as the formation of the average Hermitian product of two complex scalar signals s1 and s2 for the same resolution cell. The product is given as:

[ ] [ ]

=

= *

22*

12

*21

*11*

2*

12

1

ssss

ssssss

ss

J 4.2

From J we can obtain an expression for the phase difference )arg( *21ss=φ as

Chapter 4: Mathematival formulation of the optimised coherence

30

,...2,1,02

ReImarctan *

21

*21 ±±=+

= nWithn

ssss πφ 4.3

On the other hand the coherence is given by:

*22

*11

*21

ssss

ss=γ 4.4

In this section s1 and s2 where elements of images of a single polarized dataset. To make use of the fully polarized data, this will be represented in vector form.

4.1.2. The vectorial representation using the Pauli basis matrix

The polarimetric scattering problem can be addressed in a vectorial formulation using the concept of system vectors (Joughin et al., 1994), (Papathanassiou , 1999), (Cloude and Papathanassiou., 1998). Assuming a reciprocal scattering media the two scattering matrices S1 and S2 can be written using the following representation:

[ ]( )

( ) Tvhhvvhhvhhvvvvhh

p

SSiSSSSSS

STracek

],,,[2

121

−+−+=

Ψ=r

4.5

Where T indicates the matrix transposition and pΨ is the set of 2x2 orthogonal complex Pauli basis

matrices.

−

−

=Ψ

00

2,1001

2

1001

2,1001

2

iip

4.6

The advantage in using the Pauli basis matrix is that the elements of the resulting scattering vector are closely related to the physics of wave scattering and allow a better interpretation of the scattering mechanisms (Cloude and Papathanassiou, 1998) In linear reciprocal polarization basis and based on the reciprocity theorem, we assume that vhhv SS = and instead of four-dimensional (4-D) vector of equation 4.5, a reduced three-dimensional (3-D) scat-tering vector can be used (Cloude and Papathanassiou.,1998), (Lee et al., 1999).

[ ]Tvhhhvvvvhh

SSSSSk 2,12,12,12,12,12,1 2,,2

1−+=

r 4.7

This vector representation is also given by (Helmann and Krätzschmar, 1998), (Pottier and Lee, 1999) When the outer product is applied from the scattering vectors k1 and k2 for the master and slave im-ages, the result is a 6x6 Hermitian positive semidefinite matrix [T6] given by:


31

[ ] [ ] [ ] [ ][ ] [ ]

Ω

Ω=

=

22*

12

1211*2

*1

2

16 T

Tkk

kkT T

TT rrr

r

4.8

Where [ ] [ ] [ ]122211 ,, ΩandTT are 3*3 complex matrices composed as follow

[ ] TkkT *

1111

rr=

[ ] TkkT *

2222

rr=

[ ] Tkk *

2112

rr=Ω 4.9

[T11] and [T22] are the standard coherency matrices that contain the full polarimetric information for each separate image. [Ω12] contains not only the polarimetric information, but also the interferometric phase relations of the different polarimetric channels between the two images and this is the most important component in this methodology. Different ranges to the resolution cell as well as the possible temporal changes causes the phase differ-

ence between 21 kandkrr

. Hence, in general, 21 kkrr

≠ and, consequently,

TT

kkkk *12

*21

rrrr≠ and then [ ] [ ] T*

1212 Ω≠Ω 4.10

4.1.3. Vectorial complex representation

For the generalisation of the interferometric formulation, scientists introduced complex projection vec-tors to extend the scalar formulation into a vectorial one. Two normalised complex vectors,

21 wandw rr , which may be interpreted as generalised scattering mechanisms are defined. Two scatter-

ing coefficients are also defined 21 µµ and as the projection of the scattering vectors 21 kandkrr

onto

the vectors 21 wandw rr:

2*221

*11 ; kwkw TT

rrrr== µµ 4.11

The scalar functions 21 µµ and are linear combinations of the elements of the scattering matrices

21 SandS and form the basis of the generation of vector interferograms. The combination of equations 4.8 and 4.11, yields to a Hermitian semidefinite matrix J.


32

[ ] [ ] [ ] [ ][ ] [ ]

ΩΩ

=

=

222*21

*12

*2

212*1111

*1*

2*

12

1

wTwwwwwwTw

J TTT

TT

rrrr

rrrr

µµµµ

4.12

And we obtain an expression for vector interferogram formation as:

( )( ) [ ] 212*1

*

2*21

*1

*21 wwkwkw TTTT rrrrrr

Ω==µµ 4.13 From which we can derive the interferometric phase as

( ) [ ]( )212*12

*21

*1 argarg wwwkkw TTT

irrrrrr

Ω==φ 4.14

The generalized vector expression for the coherence in the basis ( )21 , ww rr

is then given by:

( )[ ]

[ ] [ ] 222*2111

*1

212*1

21,wTwwTw

wwww

TT

T

rrrr

rrrr Ω

=γ 4.15

The equation 4.15 is obviously more general than the coherence intγ equation given in equation 2.18

in chapter 2.

If 21 ww rr≠ , then we have, in addition to the contribution intγ , the contribution of the polarimetric cor-

relation polγ between the two scattering mechanisms corresponding to 21 wandw rr

polγγγ int= 4.16

Only in the special case of 21 ww rr= , polγ becomes 1, and γ reduces to a scalar interferometry.

To get the optimised coherence from equation 4.15, mathematically we have to maximize the Lagran-gian function of L defined as (Bedford and Dwivedi, 1970), (Papathanassiou , 1999):

[ ] [ ]( ) [ ]( )2222*221111

*11212

*1 CwTwCwTwwwL TTT

−+−+Ω=rrrrrr λλ 4.17

C1 and C2 are constants, λ1 and λ2 are the Lagrangian multipliers introduced to maximize the numerator of equation 4.15. Since L is complex, the maximization problem that should be solved is of the form:

( )21 ,

*max wwLL rr 4.18

The objective of optimizing ( )21, ww rrγ is to find those complex projection vectors 21 wandw rr

for which γ becomes a maximum (Brandfass et al., 2001).


33

The partial derivatives are then:

[ ] [ ] [ ] [ ] 111*11212

*11111212*

1

0 wTwwwwTwwL TT

T

rrrrrrr λλ −=Ω→=+Ω=

∂

∂ 4.19

[ ] [ ] [ ] [ ] 222*2

*21

*12

*2222

*21

*12*

2

*

0 wTwwwwTwwL TTTT

T

rrrrrrr λλ −=Ω→=+Ω=

∂

∂ 4.20

If we eliminate 21 wandw rr

respectively from equations 4.19 and 4.20 we will get:

[ ] [ ] [ ] [ ] [ ] 222

*21212

111

*12

122 wwAwwTT T rrrr νλλ =→−=ΩΩ −− 4.21

[ ] [ ] [ ] [ ] [ ] 111*21112

122

*12

111 wwAwwTT T rrrr νλλ =→−=ΩΩ −− 4.22

Since [ ] [ ] [ ] [ ] [ ] [ ][ ] [ ] TT TTTT *12

12212

11112

111

*12

122 ΩΩ=ΩΩ −−−− , and all the matrices involved are 3x3

complex matrices, then the system of equations 4.21 and 4.22 leads to two 3x3 complex eigenvalue

problems with common eigenvalue *21λλν = . More details can be found in (Papathanassiou, 1999).

The maximum eigenvalues found for the maximum coherence is given by maxmax νγ = . These ei-

genvalues correspond to the maximum eigenvectors max1wr and max2wr , which are the optimum scatter-

ing mechanisms denoted by optw1r

and optw2r

. The coherence derived with these optimal vectors is

called the first optimised coherence. Second and third optimised coherences are also generated. The interferogram with the highest coherence, is obtained by the projection of the scattering vectors

21 kandkrr

onto optw1r

and optw2r

, in order to derive the scalar complex images opt1µ and opt2µ .

Interferogram ( )( ) [ ] optoptoptoptopt wwkwkwT

TTT

opt 212*1

*

2*21

*1

*1 2

rrrrrrΩ=⋅⋅== µµ 4.23

A summary of the above methodology is represented on Figure 4.1.


34

R a d a r im a g e 1fu l ly p o la r iz e d

R a d a r im a g e 2fu l ly p o la r iz e d

v vv h

h vh h

SSSS

v vv h

h vh h

SSSS

[ ]Tik v hih hiv viv vih hi ,2 SS-S,SS2

1+=

[ ] [ ] [ ] [ ][ ] [ ]

Ω

Ω

=

2 2*

1 2

1 21 1*2

*1

2

16 T

TTkk

kkT

rrr

r

d e f in e

2*

221*

11 kwkwTT rrrr

== µµ

[ ] [ ] [ ] [ ][ ] [ ]

ΩΩ

=

22 2*21

*1 2

*2

21 2*111 1

*1*

2*1

2

1

TT

wwwwwwwwJ TTT

TT

rrrr

rrrrµµ

µµ

( ) ( )1a r g *21 e q u a t io ni µµφ =

( )( )21 , wwM a x rrγ

[ ] [ ]( ) [ ]( )222 2*22111 1

*1121 2

*1 TT CwwCwwwwL

TTT

nL a n g r a n g ia −+−+Ω=rrrrrr λλ

P a r t ia l d e r iv a t iv e s o f L a ne ig e n v a lu e p ro b le m

( )e ig e n v a lu em a xm a x =γ

( )r se ig e n v e c too p t im a l

P ro je c t k 1 a n d k 2 o n toth e o p t im a l e ig e n v e c to rs

c a lc u la te th e in te r fe ro g ra mm e n t io n n e d in e q u a t io n 1

w ith th e m a x im u m c o h e re n c e

i = 1 o r i = 2

Figure 4.1: Methodology of calculation of the optimised coherence


35

4.2. Conclusion

The combination of polarimetry and interferometry enables the application of both techniques to maxi-mize the phase coherence. In the literature it has been stated that this method is very promising to build digital terrain models in vegetated and forestered areas. It has been shown that the height and the underlying terrain relief of an orientated-vegetation layer can be determined with fully polarimetric interferometry by first optimising the polarimetric interferometric cross correlation to find the opti-mised coherence (Boerner and Yamagushi, 2000), (Treuhalft and Cloude, 1999). The interferometric polarimetric capability can also improve the generation of DTM’s in urban areas to retrieve the building height where the effect of corner reflectors is more pronounced and it can also be very useful for geophysical purposes such as lithology. Nevertheless, we have to mention that if the area of interest is dominated by strong, scatterers and the signals are strongly polarized then the problem is better solved with a scalar interferometry, because in this case, polarimetry does not bring any benefit for the coherence, on the contrary it will just intro-duce a lost of time in the processing part although the formulation and initial demonstrations appear to be very promising. Potential applications of polarimetric interferometry can only be verified by com-paring polarimetric interferometry signatures with ground truth data (URL6).

Chapter 5

5. Implementation, Results and Discussion

This chapter presents the results obtained during data processing. The input to our processing are the complex SLCs and the flat-earth phase. Processing is done by experimental software written in IDL programming language. For purpose of comparison and lack of time to implement the method of the coherence optimisation, the optimised coherences have been provided by Aerosensing company. The algorithms and concepts presented in the previous chapters will be tested and evaluated here.

In order to give an impression about the test area in the Tapajós National Park/Brazil, we give in Fig-ure 5.1, a representation of airborne radar SLC images acquired by the AeS1 system in the P band. The information about these images has been given already in chapter 3.

Figure 5.1: Magniand SLC1V
(a) (b) (c)
37

tude of the co-registered SLC airborne radar images: SLC1HH (a), SLC1HV (b) V (c). Image size is 16384*1024 pixels corresponding to 1.5km*10.3km

Chapter 5: Implementation, Results and Discussion

5.1. Results

5.1.1. Interferogram generation

The results of the processing will be given in the sequence of steps that is shown in the flowchart of DTM generation in chapter 1. The first output in the generation of a digital terrain model is the inter-ferogram, which contains the phase difference between the two co-registered SLC images. Several interferograms have been generated using different polarization combinations. This is to show that every combination contains different information about the phase difference. Combining all in-formation is likely to improve the final result.

(a)

Figure 5.2: Filtered interferogram(528*4112 pixels

The fringes which represent eathe study site is gently undulati

38

(b)

s related respectively to HHHH (a)). Time difference between the two

ch a 2π phase cycle appear aligng.

(c)

, VVVV (b) and HVHV (c) polarizations acquisitions is 13 minutes

ned, which indicates that the terrain of


5.1.2. Phase flat-earth removal

To simplify the phase unwrapping procedure, a first order flat earth phase removal is carried out. This is called first order because this flat earth phase has to be added back, once the interferometric phase is unwrapped. The flat-earth phase is not computed from a flat earth by considering a mean elevation height, but it is computed from a very smooth DEM already. This DEM came from the first iteration of the geocoding procedure. Since the flat-earth phase, is an unwrapped phase we have to wrap it before adding it to the interfero-gram (wrapped phase). In Figure 5.3, the flat-earth phase and the wrapped flat-earth phase are respec-tively given.

39

(a) Figure 5.3: Flat-earth phase (a) and

(b) the Wrapped flat-earth phase


40

In Figure 5.4 the images of wrapped phase before and after correction from the flat-earth phase are given. The upper left side of the image presents more fringes; this is because this part of the area is rougher compared to the gentle relief of the study area.

(a)

Figure 5.4: Interferogram before (a) and after the corr

5.1.3. Phase Unwrapping

The unwrapping phase part took us also a considerable tapplied first on the whole image interferogram corrected fgram has not a rectangular form as it is for the flat earthparts in the margins of the image to be unwrapped wherearth phase. The algorithm we are using treats the unwrapping problean error somewhere in the interferogram the error will be s

The solution to the problem mentioned is that the algorithmmargins of the complete image. Thus a part of the interferowas taken and unwrapped. What we want to mention about the algorithm that we hamake phase unwrapping, we must avoid always the use of

(b)

ection for the flat-earth phase effect (b).

ime. The program of phase unwrapping was rom the flat earth phase. Since the interfero- phase, it is obvious that there will be some e there is just the information about the flat

m not locally but globally. Hence if there is pread over the whole output result.

has to be applied just to a part far from the gram corrected from the flat earth phase

ve to consider two points. First, if we try to the full array size, especially if we have not


too many fringes, which is the case in this study. If we do a resampling of the original data, let us say to 512x512 we drastically reduce the phase noise. The second point is about the applied algorithm, it is fast and works always, but the results are not always very good, especially if we do not use a strong phase filtering before. This effect seems clear from Figure 5.5 (c), what we called here error phase map and it represents the difference between the original wrapped phase and the wrapped unwrapped phase.

(a) Figure 5.5: Unwrapped phase (a) T

41

(b) (c) he wrapping of the unwrapped phase (b) and error phase map (c)


42

5.1.4. Height estimation

The method used for geocoding the unwrapped phase calculated from spaceborne data can be de-scribed in the following steps:

1. Reading, the unwrapped phase and the orbital data about the two antennas. 2. Calculate the position of the pass point in the phase image. The pass point will be used to de-

termine the absolute phase. 3. Calculate the range for each pixel in the master image in the range direction. 4. Calculate the precise time for each line in the azimuth direction 5. Calculate the central time for orbit track one 6. Fit the central time points to the central time of the orbit. 7. Perform a least square fitting between the orbit time points and the corresponding antenna po-

sition. 8. Calculate orbit position coordinates and velocities in the azimuth direction for orbit track one

using output of step 3. 9. Apply step 8 for the pass point. 10. Step 5 and 6 for orbit track 2 (here we get the polynomial coefficients for track 2) 11. Provide an initial guess for the algorithm, the position can just be taken in the same range of

what is given in the orbital data. 12. Calculate the object point position for the pass point solving the non linear equations of

geocoding given in chapter 2. 13. Calculate orbit position track 2, related to the pass point. 14. Calculate the phase for the pass point, which is the offset phase. 15. Solve the non-linear geocoding equations and get the object position for each point. 16. Convert the height h to a geodetic system such us the WGS84.

Note that the computation of the pass point could be avoided with the help of a control point. Also, for this case we are using a polynomial function to fit the flight path points to the orbital track; this is quite sufficient since the number of points is small and the track is stable. In the case of airborne a polynomial that interpolates all the data cannot help and a cubic spline function must be used. Because of the offer mentioned reasons, the step of geocoding has been tested on an unwrapped phase related to the Etna Mountain (Sicily, Italy). This data is from the spaceborne SIR-SAR Shuttle mission and it needs just eight points for each orbit track, which is not the case for airborne flight path. In the following the unwrapped phase as well as the generated DTM are given.


(a) (b)

(c) Figure 5.6: The Etna mountain: the magnitude of the m

of the DTM (c) and the DTM given in a sha

43

as

ded

(d) ter image (a) the unwrapped phase (b), the height map view using the IDL function Shad_surf (d)


44

We would like in the following to put the light on one important step that is not always mentioned in scientific papers, perhaps because it is considered as an obvious step in the radar community. This step is the summation of the unwrapped phase with the original flat earth previously subtracted for the ease of phase unwrapping step. Without this step, the DTM given in Figure 5.6 (c), will look like the one given in Figure 5.7.

Figure 5.7: DTM generated from an unwrapped phase not added to the flat earth phase

Another point to mention is that the parameters of the relative directions of the orbits should be in-cluded in the generation of the flat earth phases. An example of wrong parameters is given in Figure 5.8.

Figure 5.8 : DTM generated with wrong orbital parameters


5.2. Generation of coherence maps

5.2.1. Coherence map from non polarimetric data

The coherence images, which give the correlation between the co-registered SLCs have been gener-ated from the complete scenes to give a general impression. The scaling from white to black corre-sponds to the coherence range from zero to one. The vectors 1wr and 2wr respectively for the HH-HH and HV-HV polarizations satisfies (see section 4.3.2):

( )Tww 0,1,15.021 −==rr

( )Tww 1,0,021 ==rr

Because of lack in field verification and a source of comparison, we will give from Figure 5.9 the fol-lowing interpretation. The Coherence maps given bellow look generally the same for almost the whole area. In the upper left part of the maps, the coherence is low; this is because of the roughness of the relief terrain. The slope terrain avoids getting a proper double bounce and the backscattering goes down.

(a) Figure 5.9: C

HH-HH

45

(b) oherence maps calculated from the (a) VV-VV (b) HV-HV(c)

(c) original images HH-VV (d)


To give and idea about the average coherence in each polarization combination, small images have been taken from the original one, and we got the results given in table 5.1. These results confirm what is already given before.

Table

MinMaAveAveIma

FigureHH

5.1: Coherence statistics f

coherence x coherence rage Coherence, Before filrage Coherence, After filtege size (pixels)

46

5.10:: Coherence maps ca-HH (a) VV-VV (b)

rom a small image

hh-hh 0.07044450 1.00000

tering 0.685795 ring 0.686649

512* 4096

lculated from small ima HV-HV(c) HH-VV (d

vv-vv hv-hv 0.0701164 0.0680359

1.00000 1.00000 0.686461 0.677791 0.687172 0.678607 512* 4096 512* 4096

ges )

hh-vv 0.0506360

1.00000 0.455054 0.456759

512* 4096


47

5.2.2. Optimised coherence

The following coherence maps generated using the optimisation theory explained in general in chapter 4 are provided by the Aerosensing company for comparison with the coherence maps generated from the non polarimetric data. We notice the coherence quality, which is the best for the first optimised coherence. (a) (b)

Figure 5.11: First optimised coherence (a), second optimised coherence ( In Figure 5.12, the first optimised coherence and the coherence geneHH-HH are shown near to each other to make a better visual compamised coherence is brighter then the non-optimised one, this is bectimised coherence is better.

(c)

b) and third optimised coherence (c)

rated from the single polarizations rison. Also it is clear that the opti-

ause the correlation in the first op-


48

(a) Figure 5.12: First optimised coherence (a), cohere

In Figure 5.13 we generated the histograms related to thfor the optimised coherence maps. The histograms of thHH-HH, VV-VV and HV-HV polarizations present apmost completely overlapping, also the peak of the histognumber of pixels, which is almost 2500. The histogram of the singular polarization coherence mmost in the beginning of the abscissa axis around the vthan 4000. This means that the correlation in this map in the comparison. The analysis of the optimised coherence histograms progenerate a higher coherence in the first order map. Theshifted to the right giving higher degree of coherence7000. For the second optimised coherence the peak is almost in the end giving very weak correlation. Hence for the improvement of the interferogram and consequen

(b) nce map of the HH-HH polarization (b)

e single polarization coherence maps as well as e singular polarization coherence maps for the proximately the same values and they are al-ram is just around the value 0.5 for the biggest

ap for the HH-VV polarization has a peak al-alue 0.2 for the biggest number of pixels, more is too low and for this reason it is not included

ve that the optimisation gave better results and peak of the first order-optimised map is really around 0.6 with an amount of pixels around almost in the middle, and for the last one, it is the first optimised coherence map can be used tly for a better DTM quality.


49

(a)

(b)

Figure 5.13:Histograms of the singular coherence maps (a) and of the optimised coherence maps (b) Values are multiplied by 1000 for better visualisation


50

5.3. Programming part

5.3.1. IDL Language

The interactive data language (IDL) is an optimised programming language for data analysis, visuali-zation and array handling. It is interpreted, and therefore not so fast as for example C language, but time can be saved a lot, while developing your own programs. For our little experience, this language seems for us very suited for image processing, because most of the functionalities mentioned in the Numerical Recipes book (Press et al., 2002) that deal with signal processing such as the FFT and the filtering using wavelet, are implemented. The problem we encountered is that the IDL community seems to be rather small and it can be very hard to find some help or useful programs in IDL in the Internet. If you are a programmer in C language, you have to be careful with IDL. As a simple example, in IDL the lines and the columns are inversed and the type of data is not specified until run time, whatever you give IDL, it will be accepted. There is a very good flexibility in IDL language but in the same time, the programmer has to be careful.

5.3.2. Handling SAR data

SAR data is stored in a complex format, since it contains the magnitude and the phase of the image pixel. Every image file contains a header, which gives the information about the size in range and in azimuth directions. Complex data cannot be visualised directly, a step before visualisation is to calculate the absolute value for every complex pixel. With IDL this is just one short command line.

5.3.3. Phase flat removal

The flat earth phase is not limited in the (-π,+π] interval as it is for the phase difference φ measured by the radar antennas. To correct the measured wrapped phase from the effect of earth phase, the flat earth phase must be in the same range as the phase φ. In IDL the following steps are necessary:

Output_1 = complex (0, flat_earth_phase)) Output_2 = exp (Output_1) Output_3 = atan (Output_2)

This three operations are given is one command line, without use of any loop

Output_image = atan(exp(complex(0, flat_earth_phase))) The example mentioned above, is just to give an idea to the reader how IDL is really suited for array processing. The most important is that the programmer knows correctly the capabilities offered by this software, and we think this point is a matter of experience and also how and in which exact position they must be used.


51

5.4. Conclusion

Results of DTM generation steps using airborne SLC images data acquired in the P-band have been presented in this chapter. For two reasons, the final step, the geocoding part could not be completed. First to understand perfectly the principle of geocoding the unwrapped phase is not an easy task, it does not matter if we are using spaceborne or airborne data. Second, dealing with airborne flight path data and the continuously changing baseline is another problem that must be handled carefully in order to get the precise height. More time allocated for these two steps would be really helpful to achieve the goal.

The interferogram of the complete image has not a rectangular shape; this means that in the image there are some values with no-data. The flat earth phase is a complete rectangular image but it has also one part in the left side that contains no-data. The interferogram has to be corrected from the flat earth phase before unwrapping. If we apply the flat phase removal to this interferogram, the parts, which are in the margin, will contain just the information about the flat earth phase, and no data about the inter-ferogram is there. The algorithm I am applying treats the unwrapping problem not locally but globally, hence if there is an error somewhere, it will be spread over the whole output result. To avoid such er-rors a section of the scene was cut out from the middle area.

Concerning the optimisation method, the first optimised coherence seems to be really helpful to gener-ate a better interferogram. Limitation of coherence optimisation is given by the temporal decorrelation. If the temporal decorrela-tion is too high, the optimisation algorithm may not provide any improvement, as the coherence will remain low independently of the choice of polarization (Papathanassiou, 1999). Our conclusions could be done better if some information about the area of study is known; such as the forest type, the den-sity of vegetation and the terrain relief.

53

Chapter 6

6. Conclusions and recommendations

The aim of this research was to investigate whether the polarimetry can be utilised to get better DTM from airborne InSAR. To this end the first task was to generate a DTM from a couple of co-registered SLC radar images ac-quired in a singular polarization. The generation of the DTM was achieved using IDL language. For each step an IDL program has been written. The second task was to study the potential of polarimetric InSAR in the improvement of the interfero-gram compared to the first part, which is the conventional InSAR. The step of phase to height conversion, which is a part of geocoding, was tested using an unwrapped phase of the Etna Mountain. The couple of SLCs used for the generation of the unwrapped phase are space borne data from the SIR-SAR Shuttle mission. Conversion from phase to height used the two orbital files related respectively to the platforms positions. Geocoding of space borne data seems to be easier than geocoding of airborne data. The orbital flight of a space borne acquisition is composed with few points whereas in the case of airborne data we need many points to geocode the DTM; this is because it is very difficult for an aircraft to follow an ideal straight line. Positions of the antennas relative to each other have to be known accurately for the accu-racy of the baseline estimation Investigation of coherence optimisation, in improving the interferogram was the second objective. The results I have obtained indicate that the coherence optimisation is good for this purpose. Comparison of the first optimised coherence with single polarization coherences illustrates the significant benefit we can get from the optimised one if we have access to fully polarimetric interferometric data. Histograms related to singles polarization coherences and optimised coherences prove that there was a significant improvement in the quality of the coherence after optimisation. The coherence is the as-sessment parameter for the quality of an interferogram. I must say that the duration of the thesis period is not sufficient if the student has to write programs for all the procedure of DTM generation from the couple of SLC radar images till the step of DTM geo-coding and from the fully polarimetric data till the optimised coherence maps. Neither the theory of InSAR and polarimetry InSAR nor the programming with a new language such as IDL is easy to han-dle due to time constraints (five months) and lack of proper documentation about the InSAR imple-mentation. Phase unwrapping conducted with other algorithms may give better results. The use of a cubic spline interpolation instead of a simple polynomial interpolation will solve the problem of geocoding air-borne data. The field of polarimetry InSAR is just in its begin stage, many questions still to be answered such as

Conclusions and Recommandations

54

- Does the investigation of the coherence optimisation method on different types of terrain such as mountainous area, bare soil, desert and wetlands and with polarimetric InSAR data acquired in multi-frequency mode bring improvement to the quality of the generated DTM - If yes which wavelength is suited for which type of terrain? My research objective is almost completed. The results I obtained in such a short time are quite satis-factory for me. This research topic was really interesting for me and I learnt many things about the InSAR. It will make a large step in my future research work, which will be concentrated on this field using Envistat data that will be provided by the European Space Agency once the Envisat satellite is launched.

55

References

Anton H., (1984), “elementary linear algebra,” Fourth edition, Library of congress cataloguing in pub-lication data, 1984.

Bamler R., Adam N. , Davidson G. W. and Just D. (1998): "Noise induced slope distortion in 2-D

phase unwrapping by linear estimators with application to SAR interferometry,", ,” IEEE Transactions on geoscience and remote sensing, vol. 36, no. 3, pp. 913-921, May 1998.

Bedford F. W. and Dwivedi T. D., (1970), “Vector calculus,” New York etc. McGraw-Hill, 528p.

1970. Boerner W. M.. and Yamagushi Y., (2000), “Extra wideband polarimetry, interferometry and po-

larimetric interferometry in Synthetic Aperture Radar,” Invited paper, Special issues on Ad-vances in Radar Systems. IEICE Transaction Community, vol. E83-B, no. 9, September(2000).

Bonifant, W. Jr., (1999), “Interferometric synthetic aperture sonar processing,” MSc thesis in electrical

engineering, Presented to the academic faculty. Georgia Institute of technology, 166p, 1999. Borner T., (1998). “Coherent Modelling of vegetation for polarimetric SAR interferometry applica-

tions. Retrieval of Bio- and Geo-Physical Parameters from SAR Data for Land Applications,” Workshop, ESTEC, 21-23 October 1998.

Brandfass M., Hofmann C., Mura J. C. and Papathanassiou K. P., (2001), “Polarimetric SAR Interfer-

ometry as Applied to Fully Polarimetric Rain Forest Data,” International Geoscience and Re-mote Sensing Symposium – IGARSS,, Sydney, Australia, 2001.

Brandfass M., Hofmann C., Papathanassiou K. P., Mura J.C., Moreira J., (2001), “Parameter Estima-tion of Rain Forest Vegetation via Polarimetric Radar Interferometric Data,” Proceeding. SPIE's Inter-national Symposium on Remote Sensing, vol. 4543, Toulouse, France 2001. Burbidge G. T. A., Simpson D. M. and Mathew C.H., (1999), “A Fully Polarimetric L-band Space-

borne SAR Instrument Targeting Land Applications,” CEOS SAR Workshop ESA-CNES, Tou-louse, 26-29 October 1999.

Chen C. W., (2001), “Statistical-cost network-flow approaches to two-dimensional phase unwrapping

for radar Interferometry,” PhD thesis, Department of electrical engineering. Stanford university, July 2001.

Cloude S. R., and Papathanassiou K. P., (1998), “Polarimetric SAR Interferometry,” IEEE Transac-

tions on geoscience and remote sensing, vol. 36, no. 5, pp. 1551-1565, September 1998. Curlander J. C., (1982), “Location of spaceborne SAR Imagery,” IEEE Transactions on geoscience

and remote sensing, vol. GE-20, no. 3, pp. 359-364, July 1982.

References

56

Franceschetti G.and Lanari R., (1999), “Synthetic Aperture RADAR PROCESSING,” Library of Con-gress cataloguing-in-Publication Data, (1999).

Gens R. and Genderen J.L., (1996), “SAR interferometry, –issues, techniques, applications,

Review Article,” Interational Journal of Remote Sensing, vol.17, no. 10, pp 1803-1835, 1996.

Ghiglia D. C., Mastin G. A. and Romero L. A., (1987), “Cellular-automata method for phase unwrap-

ping,” Journal of optical society American, vol. 4, no. 1, pp 267-280, January 1997. Ghiglia D. C. and Romero L. A., (1994), “Robust two dimensional weighted and unweighted phase

unwrapping that uses fast transforms and iterative methods,” Journal of optical society Ameri-can, vol. 11, no. 1, pp 107-117, January 1994.

Gray L. and Farris-Manning P. J., (1993), “Repeat pass interferometry with airborne synthetic aperture

radar,” Interational Journal of Remote Sensing, vol.31, no. 1, pp 180-191, January 1993. Hanssen R. F., (2001), “Radar Interferometry Data interpretation and Error Analysis,” Kluwer Aca-

demic Publishers, 2001. Hellwich O., (1999), “Basic principles and current issues of SAR interferometry,” www.ipi.uni-

hannover.de/html/publikationen/1999/isprs-workshop/cd/pdf-papers/hellwich.pdf. Helmann M. and Krätzschmar E.,(1998), "Interpretation of SAR -DATA using Polarimetric Tech-

niques" Proc. of the 2nd International Workshop on Retrieval of Bio- & Geophysical Parame-ters from SAR Data for Land Applications, Noordwijk, The Netherlands, 21.-23. October 1998.

Henderson F. M. and Lewis A. J., (1998), “Principles and applications of imaging radar,” Manual of remote sensing, 3rd edition, volume 2. Published in cooperation with the American society of photogrammetry and remote sensing, 1998.

Hoekman, D.H. and Quiñones M. J., (1999), “P-band SAR for tropical forest and land cover change

observation”, ESA Earth Observation Quarterly, no.61, pp.18-22, 1999. Holecz F., Pasquali P., Moreira J., Meier E. and Nuesch D., (1998), “Automatic Generation and Qual-

ity Assessment of digital surface models generated from AeS-1 InSAR data,” Proceedings of European Conference on Synthetic Aperture Radar, Friedrichshafen, Germany, pp 57-60, May 1998.

Hubbert J. (1994), “A comparison of Radar, optic, and Specular Null Polarization Theories,” IEEE

Transactions on geoscience and remote sensing, vol. 32, no. 3 pp. 658-671, May 1994.

Hubert R., (1999), “Pattern recognition for SAR Thematic Mapping,” Dissertation: zur Erlangung des Doktorgrades an der Naturwissenschaftlichen Fakultät der Universität Salzburg, September 1999.

Joughin I. R., Winebrenner D. P. and Percival D.B., (1994),“Probability density functions for multi-look polarimetric signatures,” IEEE Transactions on geoscience and remote sensing, vol. 32, no. 3, pp. 562-574, May 1994.

References

57

Lee J-S., Grunes M. R., Ainsworth T. L., Du L-J., Schuler D. L. and Cloude S. R., (1999), “Unsuper-vised Classification using polarimetric decomposition and the complex Wishart classifier, IEEE Transactions on geoscience and remote sensing, vol. 37, no 5, pp. 2249-2257, September 1999.

Lillesand T. M. and Kiefer R. W, (1999), Remote sensing and image interpretation:, USA publication, Fourth edition, 1999.

Lin Q., Vesecky J.F. and Zebker H. A., (1994), “Comparison of elevation derived from InSAR data

with DEM of Large Relief terrain, International Journal of Remote Sensing, vol.15, no. 9, pp. 1775-1790, 1994.

Madsen S. N., Zebker H. A. and Martin J., (1993), “Topographic mapping using radar interferometry:

Processing techniques,” Transactions on geoscience and remote sensing, vol. 31, no 1, pp. 246-256, January 1999.

Marinelli L. and Laurore L. (1995), “Une méthode simple de déroulement de phase appliquée à la res-

titution de MNT interférométrique. Bulletin S.F.P.T n0 138. 1995 Massonnet D., (1997), “Satellite Radar Interferometry,” Scientific American Article, February 1997.

Papathanassiou K.P., Reigber A., Scheiber R., Horn R., Moreira A. and Cloude S.R., “Airborne Po-

larimetric SAR Interferometry, Proceedings of IGARSS'98, Seattle, pp. 1901-1903, 1998. Papathanassiou K.P., (1999), “Polarimetric SAR interferometry,” Thesis submitted in partial fulfilment

of the requirements for the degree of Doktor der technischen wissenschaften (Doctor technicae), the faculty of natural sciences, department of physics, technical university Graz, 1999.

Pottier E. and Lee J.-S. (1999), “Application of the « h /a/alpha » polarimetric decomposition theorem

for unsupervised classification of fully polarimetric SAR data based on the wishart distribu-tion,” CEOS SAR Workshop ESA-CNES, Toulouse, 26-29 October 1999.

Press W. H., Teukolsky S. A., Vetterling W. T. and Flannery B. P., (2002), “Numerical recipes in

C++, the art of scientific computing,” second edition, Cambridge University Press, 2002. Pritt M. D. and Shipman J. S., (1994), “Least squares Two-Dimensional Phase unwrapping using

FFT’s,” IEEE Transactions on geoscience and remote sensing, vol. 32, no. 3, pp. 706-708, May 1994.

Reynolds J. M., (2000), “An Introduction to applied and environmental geophysics,” Published by John Wiley and sons, 2000

Rocca F., Prati C., Guarnieri A. M. and Ferretti A., (2000), “SAR interferometry with applications,”

\QTR(em),Surveys in Geophysics, Special Issue, November 2000. Sagués L., Lopez-Sanchez J. M., Fortuny J., Fàbregas X., Broquetas A. and Sieber A. J., (2000), “In-

door experiments on polarimetric SAR Interferometry,” IEEE Transactions on geoscience and remote sensing, vol. 38, no. 2, pp. 671-684, March 2000.

Spagnolini U., (1993), “2-D Phase unwrapping and phase aliasing,” Geophysics, vol. 58, no. 9, pp.

1324-1334, September 1993.

References

58

Treuhalft R. N. and Cloude S. C., (1999), “The structure of oriented vegetation from polarimetric in-terferometry,”IEEE Transactions on geoscience and remote sensing, vol. 37, no. 5, pp: 2620-2624, September 1999.

Unal C. M. H. and Ligthart L. P. (1998), “Decomposition theorems applied to random and stationary

radar targets,” Progress in Electromagnetics Research, PIER 18, pp. 45-66, 1998. Wimmer C., Siegmund R. Schwabisch M. and Moreira J. (2000), “Generation of high-precision DEMs

of the Wadden sea with airborne interferometric SAR,” IEEE Transactions on geoscience and remote sensing, vol. 38, no. 5, pp. 2234-2245, September 2000.

Zebker H. A. and GoldsteinR. M., (1986), “Topographic mapping from interferometric synthetic aper-

ture radar,” Journal of geophysical research, vol. 91, no. B5, pp. 4993-4999, Avril 10, 1986. Zebker H. A. and Villasenor J., (1992). “Decorrelation in interferometric radar echoes,” IEEE Trans-

actions on geoscience and remote sensing, vol. 30, No. 5, pp. 950-959. September 1992 Zebker H. A. and Lu Y., (1998), “Phase unwrapping algorithms for radar interferometry: residue-cut,

least squares, and synthesis algorithms,” Journal of optical society American, vol. 15, no. 3, pp. 586-598, March 1998

URLs URL1: http://www.Epsilon.Nought.de, accessed on January 2002. URL2: http://www.dfd.dlr.de, accessed on September 2001. URL3: http://www.nv.et-inf.uni-siegen.de/pb2/members/loffeld/phaseunwrapping.htm. accessed on

October 2001. URL4: http://www-as.harvard.edu/chemistry/brazil/lbasite.html. December 2001. URL5: http://www.aerosensing.de/ accessed on June 2001. URL6: http://airsar.jpl.nasa.gov/news/air_pacrim_kim.pdf. Kim Y., Zyl J. and Chu A. Polarimetric

Interferometry, accessed on September 2001.

The AES-1 system provided with X band Appendix A

Appendices

The AES-1 System provided with X band

From (Wimmer et al., 2000) Early in 1996, Aero-Sensing Radarsysteme GmbH began to design and build a high-resolution x-band interferometric SAR that they chose to call AeS-1. After its first test flights in August 1996, the system became operational in October of the same year. The AeS-1 is configured as a two-antenna, single-pass interferometric SAR, with a ground resolution of up to 0.5m x 0.5m, and a height accuracy of up to five centimeters. The AeS1 system basically consists of a ground and a flight segment. The block diagram in Fig-ure A.1 shows their components and interconnections. The ground segment includes a GPS ground station for Differential GPS measurements, a mobile computer for flight planning and the transcription, archiving and SAR processing subsystems. The core module of the flight segment is the radar itself (Figure A.2). It operates at a centre fre-quency of 9.55 GHz with a maximum bandwidth of 400 MHz, thus enabling the acquisition of SAR images with a best-case ground resolution of 0.5m. The transmitter/ receiver unit uses a high precision local oscillator, a digital chirp generator and an amplifier. High-speed circulators allow a fully interferometric operation up to a pulse repetition frequency of 16 MHz. Raw data are stored on-board on hard disc arrays with capacity of 432 Gbyte. With a maximum recording data rate of 32 Mbyte/s a total acquisition time of nearly 4 hours can be realised.

Three antennasCurrently onlywill be implem

A

Figure A.1: The AeS-1 flight segment

are mounted on the aircraft, forming interferometric baselines of 0.6 and 2.4 m

two of them can be operated simultaneously, but in the near future a third channel ented for further flexibility regarding to the operating modes as well as system

The AES-1 system provided with X band Appendix A

calibration. The radar is automatically controlled by a flight control system, which delivers the aircraft position in real time with an absolute accuracy below 10 m during the entire flight.

Typically, AerThanks to its Rockwell Aeroautomatic systeviation (relativplayed. No co-the use of suchcific purposes lence) is guara

Fi

Figure A.2 : Radar antenna construction as installed on a Rockwell Turbine Commander.

s1 is flown on a Rockwell Aero Commander 690 at flight of 3000…8000 m. compact design, the AeS-1 system can be installed on small aircraft such as the Commander 685 or the Rockwell Turbine Commander. The AeS-1 is a fully m. Because the flight control unit offers a display where the real track and its de-e to the nominal one) are indicated, the pilot need only follow the tracks as dis-pilot or secondary operator is required; hence operating costs can be kept low by a small aircraft. Nevertheless, high flexibility in selecting the flight height for spe-(e. g. lower altitudes resolution, high altitudes for wide swaths and less air turbu-nteed.

B

gure A.3: Block diagram shows the ground and flight segments of the AeS-1 as well as its components.

Geo-coding Appendix B

Doppler centroid Frequency: DCF

From (Hellwich, 1999) The Doppler centroid is the centre Doppler frequency or zero of the Doppler spectrum as the ra-dar beam sweeps the target. It is found by correlating power spectra with some predefined weight functions. Since the Doppler centroid generally varies over range, estimation is performed at sev-eral range positions. The Doppler centroid frequency is determined by the angle between flight direction and viewing direction of the antenna. In general it defines a hyperboloid on which the object point is located. Range and Doppler centroid frequency determine the location of an object point in two dimen-sions only. Additional information about the earth’s surface has to be provided. This is possible when the flight path is given in a coordinate system referencing to the earth surface. When the DCF is exactly 0, the object point is located on a plane perpendicular to the flight path. The phases of both SAR images are used to determine the range difference between the object point and the sensors S1 and S2. In fact range difference determines the elevation angle under which the object point is observed. After the geocoding of interferogram pixels, a DEM can be derived from the resulting object points. Figure B.1 gives a drawing plane of the Doppler centroid frequencies. Circles corresponds to “equi-range” lines and Hyperbolas to “equi-difference of range” lines, and Figure B.2 give a gen-eral overview of the ellipsoidal earth model.

Figure B

C

.1: Drawing plane is the Doppler centroid plane. Circles corresponds to “equi-range” lines and Hyperbolas to

“equi-difference of range” lines

Geo-coding Appendix B

D

Figure B.2: Geocentric coordinate system for pixel location equations illustrating the intersection of radar beam with ellipsoid Earth model.

eωr

is the earth rotational velocity vector (Curlander, 82)

SAR isodoppler contour

eωr

sensor

Center of earth

Earth model

Track

Target

Z

Y

X

IDL example Appendix C

E

Eigenvalue Problems

From (Press et al. 2002) and (Anton, 1984)

Eigenvalue problems have provided a fertile ground for the development of higher performance algo-rithms. These algorithms generally all consist of three phases: (1) reduction of the original dense ma-trix to a condensed form by orthogonal transformations, (2) solution of condensed form, and (3) op-tional back transformation of the solution of the condensed form to the solution of the original matrix. In addition to block versions of algorithms for phases 1 and 3, a number of entirely new algorithms for phase 2 have recently been discovered. In the following we will give some matrix properties, which are useful for the Eigenvector problem solution:

A matrix is symmetric if it is equal to its transpose The transpose B of a matrix A is

B=AT where aij= aji

aij are the elements of the matrix A in the row i and column j If the elements of a matrix A are real numbers, A is then a symmetric matrix. If the elements of a matrix A are real numbers, A is then a symmetric matrix. A matrix or a polynomial is called positive semidefinite if it is always non-negative, or if under

some standard operation it always gives a non-negative value. If all the matrix elements are zero except the diagonal element, the matrix is called Diagonal.

Finding the eigenvalues is equivalent to diagonalisation. An N*N matrix is said to have an eigenvector x and corresponding eigenvalue λ if:

A.x=λ.x 1 Obviously any multiple of an eigenvector x will also be an eigenvector. Equation 1 holds if

Det(A-λI) = 0 2

Where the roots are the eigenvalues of the N polynomial. Det is the determinant A matrix is called Hermitian or self-adjoint if it equals the complex conjugate of its transpose

(its Hermitian conjugate denoted by “†” or * T ) Hermitian of a matrix is equal to its Hermitian conjugate The eigenvalues of a Hermitian matrix are all real. A Hermitian matrix is called Positive Definite if all the eigenvalues are positive. The product of the matrix and its Hermitian conjugate is a unit matrix

The eigensystems is a fairly complicated business (Press et al. 2002)

IDL example Appendix D

F

IDL programming example

;***************How to cut a small window, visualise and store in a file: pro visualise stt=systime(1) openr,unit, 'Directory:/input_file', /xdr,/get_lun xysize=lonarr(2) readu ,unit, xysize print, 'x=',xysize(0) print, 'y=',xysize(1) range=xysize(0) azimuth=xysize(1) slc=complexarr(range,azimuth) readu ,unit , slc image=slc[100:799,4000:7999] ;This is just an example, you must refer to the size of the original ;array slc=0b xysize[0]=700 xysize[1]=4000 print, xysize(0) print, xysize(1) openw,unit, 'Directory:/small_slc', /xdr, /get_lun writeu,unit,xysize writeu, unit, image close, unit free_lun, unit openr,unit, 'Directory:/small_slc', /xdr, /get_lun xysize=lonarr(2) readu,unit,xysize print, 'x=',xysize(0) print, 'y=',xysize(1) range=xysize(0) azimuth=xysize(1) im= slc=complexarr(range,azimuth) readu,unit,image im=abs(im) window, 1,retain=2, xs=128, ys=512 tv, bytscl(rebin(im,128, 512), 0.,max(im)/100) free_lun, unit print,'time :',strcompress((systime(1)-stt)/60),' sec' end

Documents

Generation of Digital Terrain Models using polarimetric