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

3. Gas detection Spectrum Spectrum Sensitive Optical detection system Broadband Light source Intervening Gas Cloud

4. Emission Target Detection Spectrum Spectrum Sensitive Optical detection system Broadband Light source Weak Narrow linewidth emitter

5. Typical Unfiltered Interferogram, GN(t)

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

7. 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.

8. 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.

9. The signal

10. Interferogram Segment Input Filtered Input Unwrapped Phase Instantaneous Frequency Path Difference (microns) Phase Step Detection Algorithm

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

12. 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.

13. Gaussian Modelling • The first null occurs when GN = 0 • This can be solved graphically

14. Graphical solution to GN = 0

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

16. 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

17. Experimental Arrangement

18. 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.

19. Results - Responsivity

20. 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

21. Results - Wavelength Offset

22. 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.

23. 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

24. 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.