# Software to calculate diffraction figure at focal point of concave mirror?

1. Jul 16, 2011

### halfelven

Classic paraboloidal mirror. Incoming flat wavefront of known wavelength (500 nm, green light), propagating parallel to the major axis of the mirror. The wave hits the mirror and is being sent back towards focus. At the focal plane, there's a flat CCD or some other light detector. Upon hitting the detector, the wave creates the well-known diffraction figure, http://en.wikipedia.org/wiki/Airy_disk" [Broken] and the surrounding diffraction rings.

[PLAIN]http://k.min.us/ibX9Pu.png [Broken]

Is there a software I could use to actually calculate the diffraction figure? Something that would come back with an accurate Airy disk and circles if I give it a parabolic mirror to compute? It's okay if the program works in 2D instead of 3D (so the wavefront is a line instead of a plane), it might be faster that way.

More importantly, I need to change the shape of the mirror, so that there's a small defect at the center, a channel or a scratch the shape of a ramp or sawtooth, of known shape: the mirror is 200 mm in diameter, focal length is 1200 mm, the scratch is 200 mm long (the whole diameter), 10 mm wide and 0.125 microns deep - yes, microns, it's a subtle defect, around lambda/4 for visible light. The program needs to be capable of computing the new shape of the diffraction pattern at the focal plane.

Or, in a 2D section instead of 3D, the scratched mirror would look like this (the sketch below is NOT to scale):

[PLAIN]http://i.min.us/ieo5yu.png [Broken]

Anything available at all? Thanks!

This is not homework. I'm having a dispute with some folks, they are arguing that the Airy pattern will not change at all as long as the scratch is less than lambda/4 deep. No argument seems to convince them, but they declared that a wavefront analysis on a computer will settle the case.

I'm pretty knowledgeable, I've a Bachelor's in Physics, but I work in the computer industry, so feel free to suggest even obscure or less user-friendly programs.

Last edited by a moderator: May 5, 2017