Spot size, depth-of-focus, and diffraction ring intensity formulas for truncated Gaussian beams

Simple polynomial formulas to calculate the FWHM and full width at 1/e2 intensity diffraction spot size and the depth of focus at a Strehl ratio of 0.8 and 0.5 as a function of a Gaussian beam truncation ratio and a system f-number are presented. Formulas are obtained by use of the numerical integration of a Huygens-Fresnel diffraction integral and can be used to calculate the number of resolvable spots, the modulation transfer function, and the defocus tolerance of optical systems that employ laser beams. I also derived analytical formulas for the diffraction ring intensity as a function of the Gaussian beam truncation ratio and the system f-number. Such formulas can be used to estimate the diffraction-limited contrast of display and imaging systems.