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kd = 0.25A

Third order Spherical Aberration alone

45 kS1

ks1 = 0.24A

Third order Spherical Aberration with optimum focus

kdp2 + ksip4

1 k2kS1 + 6

ks1 = 0.95A kd = -0.95A

Third order Coma alone

kcp3 cos ^

kC 8

kc = 0.20A

Third order Coma with optimum Tilt

(kT p + kc p3) cos $

k2 k2 kT 1 kC 4 + 8 , kT kc + 3

kc = 0.60A kT = -0.40A

Third order Astigmatism

kAp2 cos

k2 k A 6

kA = 0.17A

Ripple (concentric sinusoidal zones)

kZ cos( /J

kl 2

kz = 0.10A

Fig. 3.106. Idealized sinusoidal ripple showing 3 complete wavelengths of ripple in the pupil radius

since (Wq)2 = 0. This result is independent of nz or Xz. Relative to the square of its coefficient kZ, it has easily the highest variance of the aberrations listed, giving the single error tolerance for Iq/I0 = 0.80 of 0.10X. This is a measure of the high significance of ripple and justifies the complex measures taken to avoid zones and keep their amplitude low.

3.10.6 The diffraction PSF in the presence of small aberrations and an annular aperture

Table 3.26 supposes the full circular pupil is operative. In practice, the normal case in reflecting telescopes is the annular aperture, whose diffraction PSF was considered in ยง 3.10.4. Following Schroeder [3.22(g)], we must now consider the effect of an obscuration factor e in a pupil normalized to pm = 1. Eq. (3.472) can be taken over directly with the changed limits of integration,

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