- #1

richardbruce

- 7

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I am having trouble with my Fourier optics. I am trying to simulate Fresnel diffraction using the following form of the equations:

Li(xi, yi) = K * magnitude (FT{ P(xp, yp)E(xp, yp) } p= xi/ld ;q= yi/ld) ^2

K = 1/(ld)^2

E(xp, yp) = e^(i*(PI/ld)*(xp^2+yp^2))

P is the aperture function (0 for transparent, 1 for opaque)

l is the wavelength of light, in my case 575e-9 (middle of the visible spectrum)

d is the distance between the aperture and image planes (17mm in my case)

FT is the Fourier Transform

This equation is slightly simplified because I am only interested in the radiance.

My aperture function P and image function Li are on the scale of 1um per pixel. This means that for every pixel increment in xi the increment in xp is 1e-6/(17e-3 * 575e-9) = 102m. This must be wrong. The image should be expanded onto the image plane not shrunk. Can anyone see my mistake?