The image of a circular source aperture is convolved with a Gaussian representing the random errors in the optics. The convolution is Fourier transformed. The transform of the aperture image is approximated as a Gaussian. The approximation introduces little error into the inverse Fourier transform which returns the convolution to real space. Thus, the spot diameter is given by: (Total Random and b = Image Decoll 4a )1a² + b² where a = Decoll 4σ Diam ) ' where a is the characteristic radius of the Gaussian and 4o is the diameter which encloses 86.5% of the incident light flux. The approximation introduces less than 2% error in the (4σ) total decollimation. The approximation is generalized to include diffraction effects due to the diameter of the optics.

Date Published: 20 September 1987
PDF: 13 pages
Proc. SPIE 0750, Infrared Systems and Components, (20 September 1987); doi: 10.1117/12.939861

Published in SPIE Proceedings Vol. 0750:
Infrared Systems and Components
Robert L. Caswell, Editor(s)