- #1

struggling_student

- 9

- 1

Let ##u## be the position on the aperture relative to some chosen axis which also goes through the screen. Let the position on the screen relative to that axis be ##x##. The opacity function is a function of ##u##, i.e. ##f=f(u)##.

The wave that goes through point ##u## on reaching the screen has amplitude

$$A f(u) \cos\left(\frac{2\pi}{\lambda}\sqrt{(x-u)^2+L^2 }\right) du,$$

and the resulting diffraction will be

$$A \int_{\mathbb{R}} f(u) \cos\left(\frac{2\pi}{\lambda}\sqrt{(x-u)^2+L^2 }\right) du.$$

It's a function of ##x## and we would square it to get intensity. I'm not sure how to proceed or what I did wrong. This approach is the only approach I am interested in. I'm trying to obtaining something similar to Fourier transform. What's missing here?