. Working these solutions helps you calculate exactly how much detail (high spatial frequency) a lens can capture before diffraction limits its performance. Practical Application
A modern "Goodman solution" for a pupil mask (say, a hexagonal telescope aperture) is not a closed-form sinc function. It looks like this (pseudocode): introduction to fourier optics goodman solutions work
Where ( h ) is the impulse response. You must identify the propagation distance ( z ) and recognize that this is a convolution . Therefore, in the Fourier domain, it becomes a product. in the Fourier domain
( U(x,y,z) = \frace^ikzi\lambda z e^i\frack2z(x^2+y^2) \iint t(\xi,\eta) e^i\frack2z(\xi^2+\eta^2) e^-i\frac2\pi\lambda z(x\xi+y\eta) d\xi d\eta ) it becomes a product. ( U(x