Wavefront sensors for adaptive optical systems

Wavefront Sensors for Adaptive Optical Systems

V. P. Lukina b,

, N. N. Botyginaa

, O. N. Emaleeva

, and P. A. Konyaeva

aInstitute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, Tomsk, Russia

bTomsk State University, Tomsk, Russia

E-mail: [email protected]

Received May 7, 2007

Abstract—Possibilities of constructing a wavefront sensor for the adaptive system in the Big Solar

Vacuum Telescope are considered. A modified correlation tracker (MCT) is proposed. The sensor is

tested by measuring the displacement of the image of the solar granulation pattern in the first and second

foci of the telescope under clear vision conditions. The change in the quality of the image being

transferred to the second focus and the measured displacement of the image of solar granulation in the

second focus with extremely good vision conditions and a certain granulation structure are analyzed. The

effect of reduction of the input aperture to 170 mm on the image quality and, hence, on MCT operation is

analyzed.

DOI: 10.3103/S8756699008040134

INTRODUCTION

Research of physical processes that occur at small space scales on the Sun requires solar telescopes with a

high spatial or angular resolution. It is known [1] that the solar atmosphere is structured and dynamic. The

structure of the solar atmosphere is determined by two important scales: altitude scale of pressure and mean

free path of a photon. In the solar photosphere, both scales are approximately equal to 70 km or 0.1 arc sec.

To work within these fundamental scales, the angular resolution of the telescope has to be better than

0.1 arc sec. Research of such phenomena as heating of the solar corona, solar activity, and variations of solar

luminosity, which affect the Earth’s climate, also requires studying the microstructure of magnetic fields of

the solar atmosphere with an angular resolution better than 0.1 arc sec.

For existing telescopes to ensure a better spatial resolution, they are equipped with adaptive optical sys-

tems (AOS), which are more complicated in the engineering aspect for solar telescopes than for stellar tele-

scopes. The main problems are caused by the fact that the day-time turbulence is more intense and the vision

quality changes with time; moreover, the wavefront sensor has to operate with visible-range radiation from

low-contrast, extended, and time-dependent objects, such as solar granulation. The turbulence near the

Earth’s surface is much more intense at daytime, because the surface is heated by directly incident light. A

typical coherence radius is r0

10� cm (at a wavelength of 500 nm) even in the best possible observation con-

ditions and for a telescope located at a typical height of 20–40 m over the Earth’s surface. In addition, the co-

herence radius characterizing the atmospheric turbulence intensity strongly fluctuates at short time scales

(seconds) and often decreases to several centimeters. For this reason, solar adaptive optical systems require a

larger number of fast-response correction elements than stellar adaptive optical systems, despite a compara-

tively small size of the input aperture of solar telescopes.

The main problem for solar AOS’s is the wavefront sensor. The sensor used for stellar AOS’s cannot be

used for solar AOS’s, because the Sun is an extended object, whereas objects that can be used as reference

stars (natural or laser guide stars) for night-time AOS’s [2] are not used for solar observations. Solar AOS’s

can use the following structures on the solar disk surface as tracking objects: solar spots, pores, and solar

granulation. Solar granulation is a problematic target for observation, because the granulation pattern has a

low contrast and changes with a time scale of the order of 1 min.

The story of solar AOS evolution at the initial stage of its development was described in detail in [1]. The

first experiments with solar AOS’s were performed in 1979 on the Vacuum Tower Telescope (VTT) on the

377

ISSN 8756-6990, Optoelectronics, Instrumentation and Data Processing, 2008, Vol. 44, No. 4, pp. 377–383. © Allerton Press Inc., 2008.

Original Russian Text © V.P. Lukin, N.N. Botygina, O.N. Emaleev, P.A. Konyaev, 2008, published in Avtometriya, 2008, Vol. 44, No. 4, pp. 119–128.

OPTICAL INFORMATION

TECHNOLOGY

Sacramento peak (California, USA). A shear interferometer was used as a wavefront sensor in that experi-

ment. The AOS was expected to work with both bright stars and solar spots. In reality, however, it improved

the quality of the star image, but failed to improve the image of the solar spot.

The first really operational solar AOS was created by the Lockheed company (USA) in the mid-1980s on

the basis of a 19-element composite mirror and a Shack-Hartmann analog wavefront sensor with 19 quad-

rant detectors for recording the displacement of images formed by 19 subapertures. As tracking objects, the

system could use images with a sufficient contrast on the global background: individual pores and solar

spots. Creation of this system was an important milestone in the solar AOS development: a real experiment

on the Dunn Solar Telescope (DST) on the Sacramento peak provided pioneering evidence of improvement

of the image quality due to inclusion of the AOS into the solar telescope system.

The next stage in the development of solar AOS’s was the creation of correlation wavefront sensors,

which could use a fragment of solar granulation as a tracking object [3]. Inclusion of an AOS with a correla-

tion tracker into the structure of operational solar telescopes located in the best places in terms of the astro-

nomical climate offers a better contrast of the solar granulation image, but the diffraction resolution can be

reached only under extremely good vision conditions (with a coherence radius of about 20 cm). Thus, the

use of the AOS within the New Swedish Solar Telescope (NSST) with an aperture of 97 cm in the La Palma

(Spain) experiment and post-processing of results provided images of granulation near a solar spot with a

resolution of 0.1 arc sec (70 km). A light filter with the central wavelength of 430 nm was used in the experi-

ment. The frame exposure time was 20 ms.

Improvement of the granulation pattern quality in solar telescopes operating under adverse vision condi-

tions still remains a difficult problem. An AOS with a correlation tracker was tested in 2001 in the Big Solar

Vacuum Telescope (BSVT) of the Baikal Astrophysical Observatory of the Institute of Solar-Terrestrial

Physics of the Siberian Branch of the Russian Academy of Sciences [4]. Fairly high-contrast solar spots

were used as tracking objects. In 2003, after the system of image recording was improved (a video camera

with an 8-bit ADC was replaced by a camera with a 12-bit ADC), the AOS provided good results for track-

ing objects being image fragments with a small pore whose contrast was better than 10%. Technological fea-

tures of the CCD matrix of the camera did not allow the same results to be obtained for a fragment of the

granulation pattern. It was already at that time that a necessity was understood to improve not only the hard-

ware of the wavefront sensor, but also the correlation algorithm. A modified correlation algorithm was de-

veloped by analyzing the data recorded during the 2004 expedition [5]; this algorithm was tested by

measuring the displacements of the solar granulation images recorded as movies.

The challenge of the present work is to demonstrate that the algorithm of the modified correlation tracker

(MCT) ensures operation of the adaptive system under conditions of real experiments with the Big Solar

Vacuum Telescope.

MODIFIED CORRELATION TRACKER AND TEST TECHNIQUE

The image of solar radiation has a low contrast by virtue of the physical nature of the tracking object

proper. Instrumental errors of solar telescopes and atmospheric turbulence substantially reduce the contrast

of the granulation pattern [6, 7]. Image transfer by additional optical elements into the second focus in actual

structures of AOS-containing solar telescopes also deteriorates the contrast of the granulation pattern. The

known method of luminosity equalization over the image field in AOS operation with a low-contrast image

requires prior exact measurements of the field intensity. A method of filtration in the range of spatial fre-

quencies of the recorded images was used in [5, 8]; in our opinion, this method is more efficient. With a cor-

rect choice of parameters of the filtering function, this method can eliminate the nonuniformity of image

luminosity caused by image-forming optics (low spatial frequencies) and image defects whose size is com-

mensurable with the size of the photodetector matrix element (high frequencies). In our case, these are the

technological features of the CCD matrix (four horizontal arrays of elements whose sensitivity is 0.4–1.2%

lower than the sensitivity of the remaining matrix elements) and random defects, which appear in the course

of measurements.

The image-displacement sensor (tracker) employs a modified algorithm of the fast Fourier transform [7]

to calculate the cross-correlation distribution function of intensity in the image plane. A principally new al-

gorithm for the displacement sensor is proposed, which differs from the traditional tracker by preliminary

filtering of the initial distribution of intensity of the measured image by means of multiplication by the fol-

lowing filtering function in the range of spatial frequencies k kx y, :

OPTOELECTRONICS, INSTRUMENTATION AND DATA PROCESSING Vol. 44 No. 4 2008

378 LUKIN et al.

H k k a k k k kB x y x x y y

( , ) exp{ [( ) ( ) ]}.� � � � �0

2

0

2

Here k k ax y0 0

, , and are the parameters of the filtering function used. It should be noted that these parameters

of the function H k kB x y

( , ) are chosen on the basis of experimental conditions to ensure a necessary

sharpness of the maximum of the cross-correlation function. As a result, our modified correlation tracker

differs from the traditional correlation tracker by the fact that the MCT calculates the cross-correlation

distribution function of image intensity for the reference and current frames preliminary filtered by the

function H k kB x y

( , ).

The correlation tracker with a modified correlation algorithm of image jitter registration was tested in the

Big Solar Vacuum Telescope in September 2005. The layout of the tracker is schematically shown in Fig. 1.

The correlation tracker provided real-time display of results in both digital and graphical form. When the

program operated in the tracking mode, the control signals through a controller with an RS-232 interface

were fed to a piezo-electric drive [9] for two-coordinate control of the angular position of the mirror. The

registration regime implied signal recording into the computer memory for further processing. A sequence

of frames 128 128� pixels (each in the 16 bit/pixel format) was first stored in the computer memory and then

on the hard disk.

In the course of real operation of the AOS, the new MCT was assumed to work with the image formed

near the second focus F2

(see Fig. 1). In the MCT tests, the image displacements were measured both in the

second and in the first focus of the telescope. This was made to verify the proper operation of the modified

algorithm with the use of the solar surface image containing objects with different levels of contrast and

noise.

The tests were performed in the following sequence. A fragment of the solar granulation image for MCT

operation was chosen by appropriate tuning of the optical system. Based on the analysis of the chosen frag-

ment, the characteristic sizes of the image structure were determined, and the parameters of the filtering

function inserted into the control program were chosen. MCT operation with the chosen image fragment was

checked. The neighboring windows on the monitor provided real-time viewing and analysis of the form of

the cross-correlation function and the displacing image fragment. If the chosen parameters of the filtering

function provided a sharp peak of the correlation function and the position of this peak moves following the

real displacement of the image, we could claim that the displacement of the chosen image fragment was ac-

tually measured. In the course of the experiments, files of the measured image displacements and images of

the reference frame and the frame averaged over the sampling time were created. For subsequent analysis of

results, a movie of the same fragments of the solar surface image was recorded. The measurements were per-

formed both in the first and in the second focus of the telescope. If the MCT worked with the image fragment

formed in the second focus, the displacements were measured in two regimes: with a closed control contour

and without control.


WAVEFRONT SENSORS FOR ADAPTIVE OPTICAL SYSTEMS 379

Fig. 1. Elements of the adaptive optics in the solar telescope: 1) BSVT lens (D � 760 mm, F � 40 m); 2) diagonal mirror; 3)

spherical mirror (F � 4m); 4) controlled mirror; 5) light filters; 6) DALSTAR video camera (128 128� pixels, 12-bit ADC,

490 frames per second); 7) Pentium VI computer, 2.4 GHz with a PC-DIG board for video signal input.

RESULTS OF MCT TESTING IN THE FIRST FOCUS OF THE TELESCOPE

The modified correlation wavefront sensor provided good results for fragments of solar granulation im-

ages with a clearly expressed structure, which had a contrast of 1.2–2.0%. The use of the MCT for measuring

the displacements of solar granulation images recorded as a movie allows us to estimate whether the parame-

ters of the filtering function were chosen correctly through measurements of the same fragment in a real ex-

periment. Displacements of the image of the same fragment of solar granulation (Fig. 2) were measured in

real time (24.09.05, 17:17) (a) and in the recorded movie (24.09.05, 17:23) (b). The measurements were per-

formed by an MCT with the following parameters of the filtering function H k kB x y

( , ): normalized parame-

ter a � 0.5 and characteristic size of the structure ( , )1 1 160 0

k kx y

� pixels. The MCT analysis window was

96 96� pixels, which corresponded to the angular size of the image of approximately 20 20� arc sec.

For the chosen parameters of the filtering function, the correlation function has a clearly expressed maxi-

mum, which is shifted together with the image. A visual estimate of image displacements on the basis of the

frames taken and a comparison with the measured values show that the MCT tracks the image displacement.

The possibility of changing the parameters of the filtering function H k kB x y

( , ) of the MCT in analyzing the

image displacement in the same movie allows us to analyze the scatter of the measured values of the image

displacement.

If the maximum of the filtering function is shifted by one harmonic, the scatter of the measured values

lies in the interval [–1, 1] pixels. Apparently, for correct measurements of displacements, it is necessary to

ensure the largest possible (for the chosen fragment) sharpness and magnitude of the moving maximum of

the cross-correlation function. The parameter ( , )1 10 0

k kx y

of the filter should be chosen equal to the size

of the most high-contrast elements of the image structure, which should be several times smaller than the

size of the analysis window and an order greater than the motionless elements of the structure induced by de-

tector defects. The half-width of the filtering function is determined by the scatter of the sizes of the most

high-contrast elements of the structure and their changes in the course of registration.

Recording and processing of long samples of image displacement allows us to use the image jitter disper-

sion to estimate the coherence radius characterizing atmospheric turbulence. For estimating the coherence

radius, we chose samples with the minimum (or no) instrumental jitter of the image associated with wind-in-

duced oscillations of the tracking (siderostatic) mirror of the solar telescope. The measurements were per-

formed with a weak wind (0.5 m/s) in the direction of the axis of siderostatic mirror attachment.

It should be noted that the BSVT is equipped with a siderostatic mechanism tracking the Sun motion over

the celestial sphere. A siderostat is an auxiliary astronomical device with a flat mirror, which moves so that

the rays of the celestial body reflected from the mirror retain one direction despite the visible daily motion of

the celestial sphere. Thus, the siderostat serves to direct the rays of the celestial body to a motionless tele-

scope.

As an example, Figs. 3a and 3b show the reference frame and the frame averaged over the sampling time

(25.09.05, 09:59). The image displacements were measured by an MCT with parameters of the filtering

function a � 0.5 and ( , )1 1 160 0

k kx y

� pixels. The root-mean-square deviation of the image displacement

was 3.47 pixels (0.730 arc sec) along the X axis and 3.52 pixels (0.740 arc sec) along the Y axis. Atmospheric

turbulence responsible for such image displacements is characterized by a coherence radius equal to 3.7 cm


380 LUKIN et al.

Fig. 2. Real-time measurements of the solar granulation image fragment displacements along the X axis (a) and along the Y

axis (b). The sampling time is 6.1 s (1000 frames with an exposure of 2.04 ms at an interval of 6.12 ms).

(a) (b)

(at a wavelength � � 0.5 �m). It is of interest that the coherence radius estimated by the formula from [6],

which relates the granulation pattern contrast in telescopes smaller than 1 m in diameter to the coherence ra-

dius, the latter being smaller than 10 cm, agrees with the value obtained from the image jitter dispersion. It

should be noted that the quality of the solar granulation image in these measurements was one of the best op-

tions observed in our expeditions in August-September 1998–2005.

RESULTS OF MCT TESTING IN THE SECOND FOCUS

The MCT operation in the second focus of the solar telescope included into the AOS was tested on

22.09.05 and 23.09.05. The structure of the solar granulation image differed from the image used for MCT

testing in the first focus of the telescope, though the total input aperture and the angular size of the vision

field of the sensor were identical. The images obtained in the second focus of the telescope are shown in

Fig. 4.

An analysis of movies recorded in the second focus showed that the image structure changed during the

2-second sampling: in addition to rather large low-contrast inhomogeneities of luminosity, the fine structure

of the image could be seen at some time instants (Figs. 4b and 4d). In a real experiment, the structure also

changes in the course of stabilization of the image fragment: either large or small elements of the structure

are more expressed at particular time instants. AOS operation is unstable. The test results showed that the

adaptive system tends to track the large-scale elements in this case. The emergence of fine scales of the dis-

tribution of luminosity of the frames leads to tracking failure.

The root-mean-square deviations of image displacements in the above-presented samples are listed in the

table; through comparisons, it is possible to estimate the effectiveness of stabilization of the image fragment

in the second focus.

MCT TESTING WITH DIFFERENT DIAMETERS OF THE INPUT APERTURE

OF THE TELESCOPE

Development of the AOS in the Big Solar Vacuum Telescope implies creating of a system correcting not

only the overall inclination of the wavefront, but also aberrations of higher orders. In such systems, the input



Fig. 3. Distribution of image intensity: reference frame (a) and frame averaged over the sampling time (b). The sample

duration is 50.12 s (8192 frames with a frame exposure time of 2.04 ms).

Fig. 4. Examples of typical measured images of solar granularity: reference frames of real measurements (a and b), the first

and 232th frames from the movie (c and d), and the image averaged over 1000 frames of the movie taken with a frequency of

490 frames per second (e).

(a) (b)

(a) (b) (c) (d) (e)

aperture of the telescope is divided by the Hartmann into subapertures, and displacements of images gener-

ated by each subaperture are registered. Therefore, the MCT was tested with the input aperture diameter be-

ing reduced by a diaphragm placed ahead of the telescope lens, either at the center or at the edge of the lens.

The quality of the solar granulation image taken in the second focus and the image displacements measured

by the MCT were analyzed.

As the input aperture diameter is reduced to 170 mm, the quality of the solar granulation image in the sec-

ond focus changes insignificantly. The samples we recorded (1000 frames with an exposure time of 2.4 ms)

mainly display a large-scale changing structure of the image; a clearly expressed fine structure of solar gran-

ularity is observed only in some individual frames. In the movie recorded with a diaphragm diameter of

220 mm, we can clearly see that the MCT operation is unstable if frames with the image structure other than

the structure of the reference frame appear, and there are some ejections (Fig. 5). In that case, the filtering

function in the MCT had the same parameters as those used with the full aperture.

In the case of image stabilization (Fig. 6), this error of the MCT can yield an extremely intense control

signal, much greater than the upper boundary of the controlled mirror range. The mirror is located in the ex-


382 LUKIN et al.

Table

Options, pixels Image displacement with an open

control contour

Image displacement during stabilization

Mean value –0.822 0.002

Root-mean-square deviation 1.64 0.61

Minimum value –5 –2

Maximum value 2 2

Fig. 5. Image displacements in the movie taken on 23.09.05 (13:12) with a diaphragm size of 220 mm.

Fig. 6. Fragments of the solar surface image: reference frames (a and c) and averaged frames (b and d).

(a) (b) (c) (d)

treme position, and the tracking error increases by a displacement caused by the extreme position of the mir-

ror. The control signal continues to grow (integral control law), and the system does not reach the

stabilization regime. Such a situation was encountered in real measurements (13:05). In the next sample

(13:06), the image structure changed insignificantly: the measurements error became smaller, and the image

stabilization was improved.

CONCLUSIONS

The use of a modified correlation tracker for measuring the image displacement in the first focus of the

telescope showed that the MCT ensures reliable measurements of the solar granulation image displacements

under good vision conditions if the parameters of the filtering function are chosen properly.

Being included into an adaptive optical system, the MCT measures the image displacement in the second

focus only if the quality of the solar granulation image is high (extremely good vision conditions and a cer-

tain granulation structure). Reduction of the input aperture of the telescope to 170 mm exerts only a slight ef-

fect on the image quality and, hence, on MCT operation. The image quality is substantially deteriorated

when the image is transferred to the second focus.

The AOS elements are currently placed outside the vacuum tube of the telescope on a holographic table

in a room with temperature drops. The length of the optical path for image transfer from the first to the sec-

ond focus of the telescope is approximately 17 m. Distortions introduced by additional optical elements of

image transfer and the medium between these elements produce a significant effect on the quality of the ini-

tially low-contrast image of solar granulation. The image structure in the second focus changes within short

samples (2 s). The MCT tries to track large-scale elements (blurred image) and yields a large error in identi-

fication of small scales by the filtering function (the fine structure of the image can be rarely seen in the mea-

surements).

In the course of evolution of the AOS within the BSVT, aimed at correcting the solar granulation image,

measures have to be taken to ensure a high quality of the optical system transferring the image to the second

focus.

ACKNOWLEDGMENTS

This work was performed within the framework of the complex integration project No. 3.2 of the Sibe-

rian branch of the Russian Academy of Sciences “Development of adaptive systems of image correction for

ground-based telescopes” and the program No. 16 of the Presidium of the Russian Academy of Sciences,

part 3, project 1 “Daytime astronomical climate and problems of adaptive telescope construction.”

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Wavefront sensors for adaptive optical systems