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Chapter 3:
Optical Systems with Annular Pupils
In this chapter, we discuss the imaging properties of a system with an annular pupil in a manner similar to those for a system with a circular pupil. The two-mirror astronomical telescopes discussed in Chapter 6 of Part I are a typical example of an imaging system with an annular pupil. The linear obscuration ratios of some of the well-known telescopes are 0.36 for the 200-inch telescope at Mount Palomar, 0.37 for the 84-inch telescope at the Kitt-Peak observatory, 0.5 for the telescope at the McDonald Observatory, and 0.33 for the Hubble Space Telescope. Expressions for the PSF, OTF, and encircled, ensquared, and excluded powers are given. The Strehl ratio of an aberrated system is considered and tolerances for primary aberrations are discussed. Symmetry properties of aberrated PSFs are discussed, and pictures of the PSFs for primary aberrations are given as examples. The line of sight of an aberrated system is discussed in terms of the centroid of its PSF. Numerical results are given and compared with the corresponding results for systems with circular pupils wherever possible and appropriate. We start this chapter with a discussion of the PSF, encircled, ensquared, and excluded powers, and the OTF of an aberration-free system. Equations are developed in a way that the results for a circular pupil can be obtained as a limiting case of the annular pupil. It is shown that the obscuration in an annular pupil not only blocks the light incident on it, but it also reduces the size of the central disc and increases the value of the secondary maxima of the PSF. It also increases the OTF value at high spatial frequencies while reducing it at the low frequencies.
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