Laser beam-quality/aperture-shape scaling relation.

Many high-energy lasers (HELs) have noncircular output apertures. Some are rectangular in shape with or without a central or noncentral (up to 30%) obscuration. However, most high-energy laser propagation codes (especially those developed for systems analysis) model the aperture as either an unobscured circle or as a circle with fixed (e.g., 10%) obscuration. We present a beam-quality/aperture-shape scaling relation which can be useful when applying these codes to realistic designs for HELs. Our analysis also yields a generalized formula for angular size of the Airy disk and definitions of a characteristic aperture length and aperture quality.