Gaussian beam and disk overlap with shift
Calculate the overlap integral of a 2-D Gaussian beam and a uniform disk, including a shift between the centers of the beam and disk.
beamDiskOverlap(s = 0, r = 1, theta.fwhm = 1)
Shift between centers
Gaussian beam FWHM
Converts the 2-D integral to 1-D for speed. Use consistent units.
Value of the overlap integral, normalized to unity for a beam much smaller than the disk.
"Telescope illumination and beam measurements for submillimeter astrononomy," A.I. Harris, Internat. J. IR and mm Waves, 9, 231 (1988)