Root Sum Square Approximation Of Source Aperture Convolved With Decollimation
Abstract
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 )1a^{2} + b^{2} 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.
 Publication:

Infrared Systems and Components
 Pub Date:
 September 1987
 DOI:
 10.1117/12.939861
 Bibcode:
 1987SPIE..750...79L
 Keywords:

 Apertures;
 Collimators;
 Image Processing;
 Light Sources;
 Random Errors;
 Convolution Integrals;
 Fourier Transformation;
 Optical Correction Procedure;
 Optics