Systems with Annular Pupils

An important example of an imaging system with a noncircular pupil is that of a system with an annular pupil. The two-mirror astronomical telescopes represent systems with annular pupils. Examples of such telescopes, including their linear obscuration ratios given in parentheses are the 200-inch telescope at Mount Palomar (0.36), the 84-inch telescope at the Kitt-Peak observatory (0.37), the telescope at the McDonald Observatory (0.5), and the Hubble Space Telescope (0.33 when using the Wide-Field Planetary Camera). We start this chapter with a brief discussion of how the obscuration affects the aberration-free PSF and OTF of a circular pupil. We then consider its effect on the Strehl ratio of primary aberrations, their balancing, and tolerances with and without balancing. Next we obtain the polynomials that are orthonormal over an annular pupil by orthogonalizing the Zernike circle polynomials by the procedure outlined in Chapter 3. The annular polynomials are given in terms of the Zernike circle polynomials, and in both polar and Cartesian coordinates. They are also related to the balanced aberrations. The aberrated PSFs and OTFs are illustrated for the annular polynomial aberrations.