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Hi all

I am working on digital holographic shape measurements based on speckle metrology. Mostly with single shot dual-wavelength methods to be able to measure moving objects. Recently I have started to work on the calibration part. Here you can see, one of my related papers:
www.tandfonline.com/doi/full/10.1080/155....942932#.VFySiPnF-tY

Since I want to have a simulated single shot dual wavelength holographic data to check my calibration algorithm, I am in a need to change the provided MATLAB code by Sébastien in a way to have dual-wavelength. Here the important issue for me is having two spherical reference waves with different angle of incident. Also to produce speckles in relation to Numerical aperture. (In the existed code that shared by Sébastien) the frequencies are controled by Gaussian filter while I want to control by Numerical aperture!! I emphasized on spherical reference wave, because I am going to do the system telecentric. Then I need to know that if my by calibration algorithm will be able to remove the effect of spherical reference waves or not. Telecentricity is important as we are working with some algorithms that always use wave propagation! while we are in a need for constant magnification.

PS: Let say we have an image with 10001000 pixels. Then I am interested to have small effect of spherical reference waves on all pixels.

Thank you very much
Davood

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Hi Davood,

It seems that there is a lot of information in your question, let me try to see if I got everything right;

  • You use a two-wavelength system. If I understand correctly, you want to measure the amplitude and phase at both wavelengths to lift the phase ambiguity. If so, we can treat the two wavelengths independently and simplify the problem by considering only one.

  • Then, your issue is that you have spherical references instead of off-axis plane waves, right? So if you send a plane wave as your signal, you should see concentric ring shaped fringes with the spacing between them decreasing as you go away from the center.

  • But I do not understand what you say about the numerical aperture, can you clarify?

  • I do not know much about telecentric systems, I trust you when you say that you need spherical waves.

In the code I provided, we select the information that carries the phase information by taking only the -1 (or +1 would work too) diffraction order. It is easy as it corresponds to selecting a window in the Fourier plane around the spatial frequency of the spatial beating between the two waves.
Now, in the case of a spherical wave, it is not that easy, is that the core of your problem?

There is a technique called point diffraction interferometry that consists in placing a neutral density filter with a pinhole in front of the wavefront to analyse. You observe fringes corresponding to the interference between the spherical wave created by the pinhole and the the attenuated wavefront you want to analyse. If the original wavefront is approximately collimated, you get circular fringes similarly to what you describe.

I tried quickly to look in articles about this technique to look for a method for a quantitative phase reconstruction but I did not find anything yet.

However, I am still interested in finding a solution to this problem!

I have no time right now, but next week I can try to make some simulations to see if there is a not-too-complicated solution. Maybe using a transformation to go back to a simpler system.

I would like to know more about your system but I do not have access to the article of which you gave the link. Can you send it to me by mail?

Best,

Sebastien

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Hi Sebastien

Thank you for the reply. Yes, You are right, we can divide the problem to two off-axis hologram. I think you can wait as I think I have found the solution. I will come back with a short description of my solution!!

I will send that paper that describes my work to you as well.

Best regards,
Davood

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Hi Davood,

Good to hear you found a solution!
I would be happy to hear about it.

Best,

Sebastien