N2n

since the denominator of (3.463) is now n(1 — e2). In the case of defocus alone, as a typical case, (3.481) gives for the variance

In all cases, we arrive at functions of the form

which reduces to

with n = 1,2,3,... Table 3.27 gives the results for the variances in the cases given in Table 3.26 and the ratio of the peak-to-valley (ptv) aberration to the rms aberration with e = 0. Note that the ptv wavefront aberration is the same as the wavefront aberration coefficient in the case of the symmetrical aberrations defocus and spherical aberration, but twice as large in all other cases because of the ±1 limits of the cos n^> function.

In Table 3.27, the variance in the case of ripple is given as independent of e. This is true under the same condition as in the unobscured case, namely, as

Table 3.27. The effect of the obscuration factor e on the wavefront variance and the ratio (ptv/rms) with e = 0

Aberration

Wavefront function

Variance with obscuration factor e

ptv/rms (£ = 0)

Defocus (d)

kdp2

S(1 - e2)2

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