Calculating diffraction patterns

AI Thread Summary
The discussion revolves around the challenges of calculating diffraction patterns using the Fresnel-Kirchhoff formula. The user is attempting to numerically integrate terms within a double integral for a square aperture but is only obtaining a partial diffraction pattern. Suggestions include simplifying the problem to a one-dimensional top hat function to predict results analytically and checking for coding errors or scaling issues. The use of an applet for comparison is recommended to clarify the expected outcomes. The user remains uncertain about the appearance of the diffraction pattern, suspecting they may only be seeing a quarter of the expected image.
Gobil
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hi All,

I recently got interested in a general solution to diffraction from an object at verious distance and wavelengths. I came across the Fresnel Kirchoff formula (attached formula from Schnars, digital holography).

My problem is I cannot seem to replicate a diffraction that makes sense to me from this formula. My approach is to calculate numerically the terms inside the double integral, then integrate in x and y, and display the magnitude squared. If I try this with a square aperture centered in a opaque screen, I get something that looks like the image attached.

Am I doing something basic wrong?

Thanks in advance!
 

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Itg strikes me that you need to start with a very simple situation and aim at getting what you can predict analytically with your numerical method. You have probably made some simple error in your coding which you will either have to find by re-examining in detail or by breaking the problem down into individual steps. If your aperture just consists of a top hat function in one dimension then you would expect a sin(x)/x pattern, for instance.
Scaling could be a problem, too - dimensions in wavelengths etc.
 
To check your results, try to compare them against this applet for Fresnel diffraction:

http://www.falstad.com/diffraction/

One of the source options is a square aperture.
 
ok, thanks jtbell, the applet is useful, as you can see from my image, it looks like I´m just getting one corner of the actual diffraction pattern, which I don´t understand very well. I did read somewhere when doing Fourier transforms you get a one sided spectrum and have to reflect it, but I´m not entirely clear on why this is.

Any more info welcome!
 
hmm, after much fiddling around I´m pretty sure I´m putting in the right values, but for the diffraction pattern of a square aperture is the image you see below, which seems like one quarter of the real image or something like that.

any ideas?
 

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  • square_apt_2.png
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