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# Estimate PSF using polychromatic PSF

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If I have a polychromatic PSF and I know the weight information per wavelength, is it possible to estimate the extracted PSFs one by one per wavelength?

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Best answer by Jeff.Wilde 8 March 2023, 07:03

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Userlevel 5
+3

Must make sure your horizontal scaling is the same at each wavelength, and don't normalize. Also, Zemax still refuses to include system transmission vs. wavelength vs. FOV as part of FFT or Huygens PSF intensity calculations.  This reduces accuracy in PSF radiometry in systems with wavelength-dependent transmission over the FOV.  I have repeatedly asked for that to be included, but so far that request has been ignored.

Userlevel 7
+3

In general, I think the answer is no because there is no unique solution (you will always have more unknowns than equations).  However, the complementary task, namely finding the best estimates for the weights given the individual monochromatic PSFs and the polychromatic PSF, is a relatively straightforward least-squares problem.

Regards,

Jeff

Userlevel 1

@Jeff.Wilde

Actually, I read below paper “Polychromatic Point Spread Function: Calculation Accuracy, Carles Font”.

I am trying to extract the monochromatic psf by wavelength band using the equation presented in the paper using the polychromatic psf and wavelength-specific weight values. What do you think of this attempt?

https://www.tandfonline.com/doi/abs/10.1080/09500349414551341

Userlevel 6
+2

@Mike.Jones When you say “Zemax still refuses to include system transmission vs. wavelength vs. FOV as part of FFT or Huygens PSF intensity calculations”, can you elaborate a little bit more?  By default for most analysis, OpticStudio doesn’t keep track of the intensity of a ray (needed for Fresnel reflection losses and Beer’s Law absorption) because this requires keeping the phase of a ray and this will be at least 2 times slower.  Both Huygens PSF and FFT PSF have a checkbox for Use Polarization which will keep track of the transmission of each ray.  You can change the Weight of field point as well to get a FOV dependent scale.

There are some things that OpticSTudio can’t do like have a variable spectral weighting across a field (i.e., blue light would have a different weight for on-axis vs off-axis fields), but I would like to hear your thoughts explained a little more on your statement above.  Thanks.

Userlevel 7
+3

@kivahan75 :

Which equation (or equations) from the paper are you trying to use?  Off hand, it doesn’t look like this paper directly addresses the problem you describe.  Can you provide more detail about the approach you would like to take?

Regards,

Jeff

Userlevel 1

@Jeff.Wilde

Below, I outline the process of estimating the monochromatic psf by wavelength given the polychromatic psf and wavelength weight values. In the process of Step4, I are considering Equation3 in the paper.

% Step 1: Define the spectral range and sampling
lambda_min = 400;   % nm
lambda_max = 700;   % nm
delta_lambda = 5;   % nm
lambda = lambda_min:delta_lambda:lambda_max;

% Step 2: Load the polychromatic PSF

% Step 3: Define the weight function

% Step 4: Calculate the chromaticity coordinates by Equation 3 at the paper

% Step 5: Extract the monochromatic PSFs by chromaticity
for ii = 1:length(lambda)

monochromaticPSFf[ii] =

end

Userlevel 7
+3

@kivahan75:

I still don’t quite understand how your approach is supposed to work.  First, this paper is not particularly well written.  I think I have a rough idea of what the authors are talking about, but they seem to use notation that comes from other papers (that they don’t reference or explain very well).  In any event, looking at the paper, the integrals in Eq. 3 seem to require knowledge of the monochromatic PSFs (or what the authors refer to as the G_lambda functions).  So, it’s inconsistent to assume you can extract unknown monochromatic PSFs from integral equations that require having these monochromatic PSFs to begin with.  Also, Eq. 3 uses the three sensitivity functions for the human eye, so the tristimulus results depend on the human vision response -- but, in general, the monochromatic PSF functions for an optical imaging system, and the resulting polychromatic PSF, have nothing to do with human vision.

Regards,

Jeff

Userlevel 1

@Jeff.Wilde

Dr. Jeff Wilde

The paper discussed in the previous response focuses on the accuracy of polychromatic point spread function (PPSF) calculations depending on the number of wavelengths and the integration
method used (Gauss or Simpson method).
yes, it does not provide a direct method to extract the monochromatic PSFs from a given polychromatic PSF and the weight information per wavelength.

To achieve my goal of extracting individual monochromatic PSFs from a given polychromatic PSF,
I think it would need additional information or assumptions about the optical system and
the monochromatic PSFs' behavior across the wavelengths.
Do you know of any papers that address this concern?