(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 g 1 h 1 , g 2 h 2 , 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 gh(xo, Yo) g(x, y)h(xo X, Yo y) dx dy (8 37)

Question: (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

(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

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

(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

(8.37)

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

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

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a To compute the convolution ghxo yo we can use the Fourier transform properties of thin lenses Let Fkx ky be the Fourier transform of gx y and Gkx ky ... View full answer

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