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Chapter 12:
Observation of Aberrations
12.1 Introduction In this chapter, we describe briefly how the primary aberrations of an optical system can be observed. The emphasis of our discussion is on how to recognize a primary aberration and not on how to measure it precisely. Since the optical frequencies are very high (10 14 –10 15 Hz ), optical wavefronts, aberrated or not, cannot be observed directly; optical detectors simply do not respond at these frequencies. We have seen in Chapter 8 that the image of a monochromatic point object formed by an aberrated system is characteristically different for a different aberration. Another and more powerful way to recognize an aberration is to form an interferogram by combining two parts of a light beam, one of which has been transmitted through the system. An aberration in the system yields an interference pattern that is characteristically different for a different aberration. Here, we briefly discuss the interference patterns for primary aberrations. 12.2 Primary Aberrations Considering an optical system with a circular exit pupil of radius a and letting (r,θ) be the polar coordinates of a point in the plane of its exit pupil, the functional form of the primary phase aberrations may be written Φ(ρ,θ)=⎧ ⎩ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ A s ρ 4 +A d ρ 2 A c ρ 3 cosθ+A t ρcosθ A a ρ 2 cos 2 θ+A d ρ 2 A d ρ 2 A t ρcosθ Spherical combined with defocus Coma combined with tilt Astigmatism combined with defocus Defocus or field curvature Tilt or distortion, (12-1) (12-2) (12-3) (12-4) (12-5) where, as in Section 1.6, A i is a peak aberration coefficient representing the maximum value of the corresponding aberration across the pupil and ρ=r∕a is a normalized radial variable. When Φ(ρ,θ)=0 , the wavefront passing through the center of the exit pupil, for a point object, is spherical centered at the Gaussian image point. Let its radius of curvature be R. For an aberrated system, Φ(ρ,θ) represents the optical deviation of the wavefront from being spherical at a point (ρ,θ). In Eq. (12-1), when A d =0 the aberration is spherical. Nonzero A d implies that the aberration is combined with defocus; i.e., the aberration is not with respect to a reference sphere centered at the Gaussian image point but with respect to another sphere centered at a distance z from the plane of the exit pupil according to Eq. (8-6).
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