(a) Suppose that you have two thin sheets with transmission functions t = g(x, y) and t = h(x, y), and you wish to compute via Fourier optics the convolution

(b) Suppose you wish to convolve a large number of different pairs of 1-dimensional functions {g₁h₁}, {g₂h₂}, . . . simultaneously; that is, you want to compute

for j = 1, 2, . . . . Devise a way to do this via Fourier optics using appropriately constructed transmissive sheets and cylindrical lenses.

Transcribed Image Text:

gh(xo, Yo) = [ [ g(x, y)h(xo — X, Yo — y) dx dy. (8.37)