I'm calculating the PSF of an imaging system (with which I have generated a "bead image") and these are my instructions:
1) take Fourier Transform (FT) of bead image
2) divide by FT of bead target: consider bead target to be flat-topped disc, then FT is rotationally symmetric and equals: J1(2paf) / f J1 = first order Bessel Function of the first kind p = 3.14 . f = spatial frequency a = radius or diameter of bead
3) divide FTbeadimage by FTbeadtarget
4) FT of result in (3) is PSF of imaging system
I get stuck on the Bessel function:
FTbeadtarget = besselj(1,Z)
Z is supposed to be a disk of a particular radius - and I have all the values for it - but I can't figure out how to express, or construct it in MatLab parlour.