Transcript High Sensitivity Optical Coherence Detector Optimization

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
Spectrum
Gas detection
Spectrum
Sensitive
Optical
detection
system
Broadband
Light source
Intervening
Gas Cloud
Emission Target Detection
Spectrum
Broadband
Light source
Spectrum
Sensitive
Optical
detection
system
Weak Narrow
linewidth
emitter
Typical Unfiltered Interferogram,
GN(t)
Coherence Length
• The coherence length Dt of a light source is
given by
t max
(Dt )
2

t
 t
t

t . G(t ) dt
2
2
max
max

max
G(t ) dt
2
• where t is the path difference in the
interferometer
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;
•
•
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.
Signal
Conditioning
input
optics
interference interferometer
filter
output
optics
detector
Extraction
Algorithm
Theory
PB/D+PE/
Detector
Reading
(mV)
Total
Spectral Power
Density

PB/D
F.T.
D
0
•
•
Wavenumber
Path Difference
(microns)
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.
The signal
Phase Step Detection Algorithm
Interferogram Segment
Input
Filtered
Input
Unwrapped
Phase
Instantaneous
Frequency
Path Difference (microns)
Gaussian Model
• Gaussian spectrum target
• Rectangular filtered background spectrum
• Normalised self coherence function of both
is given by
sinc(t .D )

j .2 0t


2

GN (t ) 
.e

 2t 2
D

 PR.e 4 ln 2 .erf (1.176381 )

 
Gaussian Model Notation
• t is the path difference
• D 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 GN = 0
• This can be solved graphically
Graphical solution to GN = 0
Differential Detection Responsivity
• The amount the null is displaced when the
power ratio of the target to background is
increased.
Differential Detection Responsivity
t N Dt N 0.645.


.e
PR DPR
D

2
4 ln 2
.(1.43) 2 (
 2
)
D
• tN is the path difference position of the null
•  tN is the amount that is moves when the
power ratio is increased by  PR
• Maximum detection responsivity occurs
when bandwidth ratio, (/D) = 0.262
Experimental Arrangement
light source and grating
monochromator (target)
beamsplitter
interference filter
detector
light source
(background)
system input
aperture
piezoelectric
transducer
interferometer
translation stage
audio amplifier
oscilloscope
driver
controller
Target/Filter Combinations
Set
1
2
3
Central
wavelength
632.6
651.9
674.8
Target
bandwidth
5.4
5.4
5.4
Filter
bandwidth
11
36.2
17.8
Ratio
0.491
0.149
0.303
•Maximum detection responsivity occurred in the Gaussian theory
when bandwidth ratio, (/D) = 0.262
•This lies between set 2 and 3.
Responsivity (microns/dB)
Results - Responsivity
1
0.9
0.8
0.7
theory
0.6
0.5
0.4
piezoelectric
transducer
micropositioner
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
Target to Background Bandwidth Ratio
1
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
Responsivity (microns/dB)
0.8
0.6
0.4
0.2
0
-1.5
-1
-0.5
-0.2 0
0.5
-0.4
-0.6
-0.8
-1
Central wavelength offset (%)
1
1.5
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
• (/D) = 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.