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.