# Physics of detection of coherent light in an incoherent background using the more compact Fabry Perot interfeometer?

See the end of this post for a series of course notes on Temporal Coherence (1, 2, 3, 4, 5, 6, 7, 8, 9). These notes are from the University Of California Berkeley's course EE290F, taught by Professor J. Bokor. I am sending an email to Professor J. Bokor requesting permission to use is copyrighted class notes in this venue.

From $\operatorname{Eq.} {\left(7.11\right)}$ on page 51 of the notes

$$I_D(h) =(K_1^2+K_2^2) I_o + 2K_1 K_2 \text{Rc} \left\{ \Gamma \left(\frac{2h}{c}\right) \right\} \tag{7.11}$$

, we see that the definition of the autocorrelation of the output signal of an Michelson interferometer is identical to the self-coherence of the same Michelson interferometer.

"An autocorrelator based on a Fabry-Perot interferometer" (2013), by Professor Junghwuen An et al., introduces a new type of autocorrelator using a Fabry Perot interferometer which consists of two partially reflecting flat surfaces in parallel. The optical layout of this new type of autocorrelator is simpler and more compact than the Michelson autocorrelator used by Coutinho et al. in "Detection of Coherent Light in an incoherent background" [PDF] (1999).

Professor Jungkwuen An and his coauthors have developed a novel Fabry-Perot autocorrelator with three reflecting surfaces. Quoting from their paper:

In practice, zero delay (𝜏=0) means two optical surfaces stick together. To measure autocorrelation signal, zero delay should be done in the middle of scanning the separation between them. Once a separation between two surfaces is reduced within a wavelength distance, it is difficult to separate these surfaces again due to van der Waals adhesion. Thus, one can hardly determine the peak of an autocorrelation signal by using a Fabry-Perot (FP) interferometer, so that it leads to an inaccuracy on estimating the pulse duration. The problem of zero delay might be the major reason that a FP interferometer has not been practically used for an autocorrelator so far.

Here, we introduce FPAC with three parallel interfaces, so that zero and negative delay can be realized without any difficulty.

Based on physics concepts, my question is that can we can use Professor Junghwuen An's Fabry Perot interforometers, either with or without a 3rd reflecting surface [EDIT June 22 2016 3:25 A.M for solving the zero delay problem ], to measure the change in position of the self coherence function minimum so that we can detect the "binary" presence of a coherent laser light source in an incoherent background , rather than the change in the strength of the self-coherence function at the reference path difference.

The reason I ask this question is because we want to protect airplane pilots eyes from the harmful effects of coherent laser light pointer beams aimed at airplane cockpits wile also respecting the pilots need to see the incoherent light background clearly during approach and takeoff. Once we detect Coherent Light in an incoherent background with rapid response time, we shutter the affected quadrant of the airplane cockpit and numerically preserve the pilot's field of view consisting of incoherent light and project in onto an Planar(@Trademark) transparent display.

[EDIT June 23 2016 6:36 A.M] The development of manufacturing techniques necessary to produce a new type of optical filter is proposed. The filter is made by coating a transparent substrate with optical films in such a manner as to produce broadband interference effects. The optical thickness of each film layer of the coating exceeds the coherence length of sunlight and many artificial sources, but not the coherence length of most laser sources, resulting in a thick-film filter that discriminates between coherent and incoherent light over broad wavelength ranges. Rudimentary calculations show that by using this type of filter, a contrast ratio in excess of 1000 between coherent and incoherent light is possible using readily available materials

• I just added the reason and motivation for this question in my original question. Thank you. – Frank Jun 22 '16 at 21:07
• That is the longest question I have ever read. As I understood your question you want to know if you can make a Fabry-Perot interferometer such that you cancel out the output from interferometer destructive interference or there is some more fundamental aspect of your question. – hsinghal Jun 23 '16 at 7:36
• @hsinghal, Thank you for offering to help me. My manager and his wife were both educated in India's top university. I wish to use a Fabry-Perot intefermoter to mimic a Michelson interferometer's ability to measure the change in position of the self-coherence function first minima. The reason being the Fabry Perot(FP) interferometer is more compact than an Michelson interferometer. As a result, how might I use a 32 by 32 two dimensional array of the FP interferometers as either coherent detectors or filters to protect pilots from laser pointers which get past the Boeing 757 nose geometry? – Frank Jun 23 '16 at 9:52
• I think that laser protection can be done easily by dielectric narrow-band high reflection multi-layer coatings from the inside of cockpit glass during the fabrication process. They are cheap, largely angle insensitive and can be made for multiple selective wavelengths. These coatings will reflect only the laser light and nothing else. They can be done on polymer films which can be pasted on the cockpit glass from inside. As far as Fabry-Perots are concerned they are highly sensitive on the incident angle and wavelength hence will not be that useful. – hsinghal Jun 23 '16 at 10:10
• @hsinghal, Thank you for your nice comment. In my above original question there is an [EDIT June 23 2016 6:36AM] which describes an optical filter for discriminating coherent light from incoherent light. May I ask you to interpret it using physical optics principles here? I have 10 pages of equations and calculations I was hoping I could share with you. May I email them to you? Thank you. – Frank Jun 23 '16 at 10:46