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.