- #1

makotech222

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## Homework Statement

A very large diffraction grating has an amplitude transmission aperture function A(x) = 1/2[1+cos(kx)]e^(-x^2/a^2)

a) What is the far-field irradiance diffraction pattern when a >>1/k

B) Plot the pattern

c) Using the appropriate resolving criteria, find the grating's chromatic resolving power in terms of k and a.

## Homework Equations

## The Attempt at a Solution

Well i know the irradiance pattern is proportional to the Fourier transform of the aperture function, but trying to take the Fourier of that monster function is pretty hard. Putting it in mathematica gives off a much too complicated function to plot. I assume the function simplifies when a>>1/k, but I'm not sure how. I have no idea how to get the resolving power, so some help there would be nice. Thanks