How to transform the diffraction image into the function of light intensity with the order of diffraction? [closed]

Question

In our pre-experiment, I got the image. It’s obvious that the order of diffraction from the top down is 3,2,1,0,-1,-2,-3, the background of optics is so easy.

Then I have to get the light intensity of the diffraction spot, denote as I(n),n in -3 to 3(in this experiment).

How to think about the problem and manipulate the processes with Mathematica? Thanks so much!

If it’s a little hard, in the future experiment, we will use CCD, with which we can get the direct image as follows:

You can also just analyze this simple case.

(Forgive me for my poor English)

Answer 1

Consider a single slit illuminated by a parallel light beam so that at time t all the points in the slit have the same phase. The light from the slit that falls on a screen parallel to the slit is considered. The near filed is complicated, but the field far away, where the angle to some point on the screen is approx. the same for all points in the slit, is much easier. We may then also neglect the effect of changing intensity due to different way length. Further, at time t al the points in the slit have the same phase. But due to different way lengths, the phase of light coming from different slits position does have different phases. This leads to interference.

Here is an simple example for relative intensities. k denotes the wave length of the light, d the distance between slit and screen, x are coordinates of the slit, y of the screen:

k = 10 ;
dist = 1000;
intensity[y_] := 
 Norm[NIntegrate[
    Exp[2 Pi I Sqrt[dist^2 + (x - y)^2] k], {x, -.5, .5}]]^2
Plot[intensity[y], {y, 0, dist/2}]