1
$\begingroup$

I am trying to write a program to compute the FFT of 1D complex aperture functions to determine diffraction patterns. Supposing I can produce the diffraction patterns successfully, I am unsure as to how to 'scale' the patterns so that the intensity on the screen is given as a function of position y. i.e. I need to convert the pixels in the Fourier Transform to positions on the screen (y).

$$\psi(y) \propto \Delta \sum_{j=0}^{N-1}A(x_j)exp(\frac{-ikx_j y}{D})$$ $$x_j = (j - (N/2))\Delta$$ where $\Delta$ is the spacing between aperture samples of the aperture function, N is the number of samples, $k=\frac{2\pi}{\lambda}$ and the other variables are apparent from the diagram below.

The FFT is of the form below, where $h_m$ represents samples of the aperture function? $$H_j = \sum_{m=0}^{N-1}h_m e^{2\pi imj/N}$$ Q: How do I go from the FFT of the aperture function so that it is scaled to be a function of screen position?

$\endgroup$
0
$\begingroup$

$k$ (better: $k_x$) is the $x$ component of the diffracted wave vector. You can construct the angle associated with the wave vector from the knowledge of the magnitude of the wave vector $|k| = \frac{2\pi}{\lambda}$ and $k_x$. Then figure out where that wave vector will hit the screen.

$\endgroup$
  • $\begingroup$ Thanks for replying. Please could you elaborate, not really sure what you mean? $\endgroup$ – user3107693 Mar 2 '17 at 20:31

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.