Diffraction effects of telescope secondary mirror spiders on various image-quality criteria

Diffraction from secondary mirror spiders can significantly affect the image quality of optical telescopes; however, these effects vary drastically with the chosen image-quality criterion. Rigorous analytical calculations of these diffraction effects are often unwieldy, and virtually all commercially available optical design and analysis codes that have a diffraction-analysis capability are based on numerical Fourier-transform algorithms that frequently lack an adequate sampling density to model narrow spiders. The effects of spider diffraction on the Strehl ratio (or peak intensity of the diffraction image), full width at half-maximum of the point-spread function, the fractional encircled energy, and the modulation transfer function are discussed in detail. A simple empirical equation is developed that permits accurate engineering calculations of fractional encircled energy for an arbitrary obscuration ratio and spider configuration. Performance predictions are presented parametrically in an attempt to provide insight into this sometimes subtle phenomenon.