The complex amplitudes of a monochromatic wave of wavelength "Lambda" in the z=0 and z=d planes are f(x,y) and g(x,y), respectively.Assuming that d = 10^4(Lambda), use harmonic analysis to determine g(x,y) in the following cases:

(a) \(f(x,y) = 1;\)

(b) \(f(x,y) = exp[(-j\pi/\lambda)(x+y)];\)

(c) \(f(x,y) = cos(\pi*x/2\lambda);\)

(d) \(f(x,y) = cos^2(\pi*y/2\lambda);\)

(e) \(f(x,y) = \sum_{m}^{}rect[(x/10\lambda)-2m], m = 0, \pm1, \pm2,...,\) where rect(x) = 1 if |x| <= 1/2, and 0 otherwise