Introduction To Fourier Optics Third Edition Problem Solutions Info

F(u) = ∫∞ -∞ f(x) exp(-i2πux) dx = ∫∞ -∞ exp(-x^2) exp(-i2πux) dx = exp(-π^2 u^2)

Find the transfer function of the system.

A coherent imaging system has a pupil function given by: F(u) = ∫∞ -∞ f(x) exp(-i2πux) dx =

P(u) = circ(u)

The point spread function of the system is given by: F(u) = ∫∞ -∞ f(x) exp(-i2πux) dx =

H(u) = ∫∞ -∞ h(x) exp(-i2πux) dx = ∫∞ -∞ sinc(x) exp(-i2πux) dx = rect(u)

h(x) = sinc(x)

PSF(x) = |h(x)|^2 = |∫∞ -∞ P(u) exp(i2πux) du|^2 = |∫∞ -∞ circ(u) exp(i2πux) du|^2 = (2J1(2πx))/(2πx))^2