Detection of weak optical signals

1
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

2
Outline

• Gas detection and Emitter detection
• Technique Description
• Derivation of Theoretical Responsivity
• Description of the Experiment
• Theoretical Vs. Experimental Results
• Conclusion

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Gas detection
Spectrum
Spectrum
Sensitive Optical detection system
Broadband Light source
Intervening Gas Cloud
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Emission Target Detection
Spectrum
Spectrum
Sensitive Optical detection system
Broadband Light source
Weak Narrow linewidth emitter
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Typical Unfiltered Interferogram, GN(t)
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Coherence Length

• The coherence length Dt of a light source is
  given by
• where t is the path difference in the
  interferometer

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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.

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Theory
Detector Reading (mV)
F.T.
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.

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The signal
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Phase Step Detection Algorithm
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Gaussian Model

• Gaussian spectrum target
• Rectangular filtered background spectrum
• Normalised self coherence function of both is
  given by

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Gaussian Model Notation

• t is the path difference
• Dk is the filtered background optical bandwidth
• d is the target optical bandwidth
• PR is the target to background power ratio after
  filtering
• erf is the error function
• k0 is the central wavenumber of the target and
  filter passbands, assumed coincident.

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Gaussian Modelling

• The first null occurs when ?GN? 0
• This can be solved graphically

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Graphical solution to ?GN? 0
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Differential Detection Responsivity

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

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Differential Detection Responsivity

• 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/Dk) 0.262

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Experimental Arrangement
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Target/Filter Combinations

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

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Results - Responsivity
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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

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Results - Wavelength Offset
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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.

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Conclusions

• The differential detection responsivity can be
  maximised by choosing the filter bandwidth to
  suit the target bandwidth
• (d/Dk) 0.262
• Design of filter transmission curve is another
  degree of freedom to be exploited to improve the
  differential detection responsivity

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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.