Consider a camera with a detector array of the following cha

Consider a camera with a detector array of the following characteristics: square detectors with detector pitch (center-to-center spacing) of 25 mu m and a detector width (each individual element) of 20 mu m. There are 128 time 128 detectors in the array. Assume a light intensity given by E(x, y) is incident on the detector array. Write an expression that describes the (continuous in (x, y)) detector array. Write an expression for the discrete, sampled intensity produced by the detector array. Fourier transform the expression in part (b) to derive the spatial frequency description of the sampled intensity. Assume that E(x, y) = 1 + cos(2 pi f_xo x), where f_xo = 10 mm^-1. Plot this intensity as a function of x (label the plot). Is this intensity pattern aliased by the detector array? If so, what spatial frequency does the intensity alias to? Assume that E(x, y) = 1 + cos(2 pi f_xo x), where f_xo = 30 mm^-1. Plot this intensity as a function of x (label the plot). Is this intensity pattern aliased by the detector array? If so: what spatial frequency does the intensity alias to? Assume that E(x, y) = 1 + cos(2 pif_xo x), where f_xo = 50 mm^-1. Plot this intensity as a function of x (label the plot). Is this intensity pattern aliased by the detector array? If so: what spatial frequency does the intensity alias to?

Solution

a) E = Eo sin( wt - kx)

b) discrete = 1/25 = 400

c) fourier transform = 1/jw

d) this is aliased by detecto