Calculating diffraction patterns

In summary, the person is trying to figure out how to create a diffraction pattern from a square aperture. They have found an applet which can help them, but they are not sure why the pattern they are getting is one-quarter of the real image.
  • #1
Gobil
59
0
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!
 

Attachments

  • Schnars.png
    Schnars.png
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  • square_apt.png
    square_apt.png
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  • #2
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.
 
  • #3
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.
 
  • #4
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!
 
  • #5
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?
 

Attachments

  • square_apt_2.png
    square_apt_2.png
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1. What is diffraction?

Diffraction is a physical phenomenon that occurs when waves, such as light or sound waves, encounter an obstacle or aperture and bend around it, producing a pattern of bright and dark regions. This pattern is known as a diffraction pattern.

2. How do you calculate diffraction patterns?

Diffraction patterns can be calculated using the principles of wave interference and diffraction. The specific mathematical equations used will depend on the type of wave and the shape of the obstacle or aperture. Generally, a Fourier transform is used to determine the diffraction pattern.

3. What factors affect the diffraction pattern?

The diffraction pattern is affected by several factors, including the wavelength of the incident wave, the size and shape of the obstacle or aperture, and the distance between the wave source and the obstacle. The angle of incidence and the medium through which the wave travels can also influence the diffraction pattern.

4. What are the practical applications of calculating diffraction patterns?

Diffraction patterns have many practical applications in various fields such as physics, astronomy, and engineering. They can be used to study the structure and properties of crystals, analyze the properties of light and sound waves, and design optical instruments such as telescopes and microscopes.

5. Are there any limitations to calculating diffraction patterns?

While diffraction patterns can provide valuable information, there are some limitations to their accuracy. The calculations assume ideal conditions and do not take into account factors such as imperfections in the obstacle or aperture. Additionally, diffraction patterns are only accurate for certain types of waves and may not apply to other types of waves.

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