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Calculating diffraction patterns

by Gobil
Tags: diffraction, patterns
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Jan10-13, 08:37 AM
P: 59
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!
Attached Thumbnails
Schnars.png   square_apt.png  
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Jan10-13, 10:39 AM
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sophiecentaur's Avatar
P: 12,261
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.
Jan10-13, 10:46 AM
jtbell's Avatar
P: 11,869
To check your results, try to compare them against this applet for Fresnel diffraction:

One of the source options is a square aperture.

Jan10-13, 10:52 AM
P: 59
Calculating diffraction patterns

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

Any more info welcome!
Jan10-13, 01:55 PM
P: 59
hmm, after much fiddling around Im pretty sure Im 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?
Attached Thumbnails

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