Detection of weak optical signals

D.R. Selviah, R.C. Coutinho, H.A. French and H.D. Griffiths

Department of Electronic and Electrical Engineering,

University College London,

United Kingdom

Outline

• Gas detection and Emitter detection

• Technique Description

• Derivation of Theoretical Responsivity

• Description of the Experiment

• Theoretical Vs. Experimental Results

• Conclusion

Gas detection

BroadbandLight source

InterveningGas Cloud

Sensitive Optical detection system

Spectrum Spectrum

Emission Target Detection

BroadbandLight source Weak Narrow

linewidthemitter

Sensitive Optical detection system

Spectrum Spectrum

Typical Unfiltered Interferogram, N()

Coherence Length

• The coherence length of a light source is given by

• where is the path difference in the interferometer

max

max

max

max

2

22

2

)(

)(.)(

d

d

Basics• Technique combining optical and

digital signal processing to detect coherent or partially coherent sources in an incoherent environment;

• Employs an optical narrowband filter to generate a specific feature in the self coherence function measured with an interferometer;

Signal Conditioning

Extraction Algorithm

detector output optics

interferometer interference filter

input optics

• Unlike Fourier transform spectroscopy (FTS), the path difference is scanned in a tiny region surrounding the first minimum of the self coherence function (interferogram), thus achieving faster frame rates;

• The recorded interferogram is processed using a computer algorithm to extract a phase step in the fringe signal; its position is used to declare detection.

Theory

• If a spectrally narrow emission source enters the field of view, the net degree of coherence of the scene changes, shifting the position of the first minimum in the self coherence function (see next slide). This shift is measured and used for detection;

• The approach senses the change in the spectrum through measurements of the change in a region of the interferogram, which makes it a lot faster than other spectral approaches.

0

Wavenumber

TotalSpectral PowerDensity

PB/

PB/+PE/

F.T.

Path Difference (microns)

Detector Reading (mV)

The signal

Phase Step Detection Algorithm

Input

FilteredInput

UnwrappedPhase

Instantaneous Frequency

Path Difference (microns)

Interferogram Segment

Gaussian Model

• Gaussian spectrum target

• Rectangular filtered background spectrum

• Normalised self coherence function of both is given by

0

222 2.

2ln4N .

)176381.1(erf..

).(sinc

)( jeePR

Gaussian Model Notation• is the path difference• is the filtered background optical bandwidth• is the target optical bandwidth• PR is the target to background power ratio after

filtering• erf is the error function

• 0 is the central wavenumber of the target and filter passbands, assumed coincident.

Gaussian Modelling

• The first null occurs when N = 0

• This can be solved graphically

Graphical solution to N = 0

Differential Detection Responsivity

• The amount the null is displaced when the power ratio of the target to background is increased.

Differential Detection Responsivity

• N is the path difference position of the null

• N is the amount that is moves when the power ratio is increased by PR

• Maximum detection responsivity occurs when bandwidth ratio, () = 0.262

222

)()43.1.(2ln4.

.645.0

ePRPR

NN

Experimental Arrangement

driver

controller

audio amplifier

oscilloscope

light source and grat ing monochromator (target)

detector

beamsplitter

interference filter interferometer

t ranslat ion stage

light source (background)

piezoelectric t ransducer

system input aperture

Target/Filter Combinations

Set Centralwavelength

Targetbandwidth

Filterbandwidth

Ratio

1 632.6 5.4 11 0.4912 651.9 5.4 36.2 0.1493 674.8 5.4 17.8 0.303

•Maximum detection responsivity occurred in the Gaussian theory when bandwidth ratio, () = 0.262•This lies between set 2 and 3.

Results - Responsivity

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Target to Background Bandwidth Ratio

Re

spo

nsi

vit

y (m

icro

ns/

dB

)

theory

piezoelectrictransducer

micropositioner

Results - Responsivity

• Theory and experiment have similar form with the experiment confirming the bandwidth ratio for the highest responsivity.

• Discrepancy in the magnitude of theory and experiment.

• Theory used a larger range of power ratios from 0 - 1.11, experiment used 0.005 - 0.31

Results - Wavelength Offset

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-1.5 -1 -0.5 0 0.5 1 1.5

Central wavelength offset (%)

Re

spo

nsi

vity

(m

icro

ns/

dB

)

Discussion

• In our model we assumed a Gaussian target spectrum.

• Other line shapes for emission and absorption should be included in the theory.

• We assumed a rectangular filter response.

• More realistic filter responses should be included.

Conclusions

• The differential detection responsivity can be maximised by choosing the filter bandwidth to suit the target bandwidth

• () = 0.262

• Design of filter transmission curve is another degree of freedom to be exploited to improve the differential detection responsivity

Conclusions

• Experimentally a coherent narrow linewidth source, a laser could be detected at about -44 dB below the broadband white light background.

• Experimentally an LED about 40 nm linewidth source could be detected at about -33 dB below the broadband white light background.