I would like to find the system transfer function corresponding to a two dimensional matrix of optical transfer function where:
Each of the 3 times 5 = 15 interferometers produce 15 sets of interference patterns that overlap each other with each interference pattern having a different spatial frequency. It may be possible to use Fourier transforms to minimize the overlap between adjacent interference patterns.
Each of the 15 multiple interferometers has different combinations of sensing parameters so that each interferometer reacts specifically and singularly
I read this elegant paper in Optical Society of America, December 1967 with URL https://www.osapublishing.org/josa/abstract.cfm?uri=josa-57-12-1486 which states that:
"We can multiply the transfer functions of the individual elements to obtain the system transfer function under only two circumstances: (1) If the system is coherent and we wish to work in complex amplitudes. (2) If, regardless of the coherence, we are willing to analyze the system in terms of the mutual intensity."
Earlier today, I thought the following use of the n-dimensional Dirac Delta function was appropriate. Because each of of the 3x5 interferometers has different combinations of sensing parameters so that each interferometer reacts specifically and singularly, would it be accurate to multiply the individual transmittance, finesse and the contrast factor functions by the Dirac delta function in an 2-dimensional space?
But after I read the above paper Transfer Function for Cascaded Optical Systems by John B. DeVelis and George B. Parent , I am somewhat confused.
I googled endlessly yesterday and today and found no useful hits about this topic except the article authored by John B. DeVelis and George B. Parent in December 1967.
The reason I ask this question is I wish to solve the applied mathematics problem of calculating the transmittance, finesse and contrast ratios of a 2 dimensional system of optical elements. I show here the transmittance, finesse and contrast ratio for a single Fabry Perot interferometer which I derived today.
In the excellent Optics Express January 2013 paper," An autocorrelator based on a Fabry Perot interferometer. by An et al." there is an Appendix which describes the optical transfer function for a Fabry Perot interferometer with 2 or 3 interfaces. Using the product of this function and its complex conjugate you can calculate gain as a function of transmitivitty, reflectivity , wavelength and the optical path delay(tau) which I will show later today as t^2/( 1- r^2 * 2 * cos 2 pi/lambda * tau + r^4).
[EDIT August 2 2016 11:46 PM Frank ] This is what I was trying to say on July 12 2016 . Please read https://www.osapublishing.org/optica/abstract.cfm?URI=optica-3-8-836 titled "Interdimensional optical isospectrality inspired by graph networks by Sunkyu Yu, Xianji Piao, Jiho Hong, and Namkyoo Park of the Photonic Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, South Korea.
Please straighten out this puzzle for us.
