Imagine that we have an opaque mask into which are punched an ordered array of circular holes, all of the same size, located as if at the corners of the boxes of a checkerboard. Now suppose our robot puncher goes mad and makes an additional batch of holes essentially randomly all across the mask. If this screen is now made the object in Problem 13.49, what will the diffraction pattern look like? Given that the ordered holes are separated from their nearest neighbors on the object by 0.1 mm, what will be the spatial frequency of the corresponding dots in the image? Describe a filter that will remove the random holes from the final image.

Data from Prob. 13.49

Replace the cosine grating in the previous problem with a €œsquare€ bar grating, that is, a series of many fine alternating opaque and transparent bands of equal width. We now filter out all terms in the transform plane but the zeroth and the two first-order diffraction spots. These we determine to have relative irradiances of 1.00, 0.36, and 0.36: compare them with Figs. 7.40a and 7.42. Derive an expression for the general shape of the irradiance distribution on the image plane€”make a sketch of it. What will the resulting fringe system look like?

Figs. 7.40a

Figs. 7.42

Transcribed Image Text:

f(x) a = 4 Л3 1 сm -1/4 0 A/4 -1/4 0 1/4 λ 1 (cm) |Ao 14, k%3D 2т || Аз Аз mk 0 к 2k 3k 4k 5k 8k 10k 0 2т 4т бт 8т 10т 16т 20т Fourier coefficients Am 0.50 0.25 -7k -3k 3k 7k T -6k –5k -4k -2k -k k 2k 4k 5k 6k т mk