In

giving from (3.465)

Marechal and Francon [3.26(c)] give A2/180, a value derived with the approximation n ~ 3. Following Welford [3.6], we shall use the more accurate value of (3.469) which leads to the conveniently close approximation

Eqs. (3.469) and (3.470) refer to the total aberration according to (3.463) or (3.466). In practice, the modal concept of the aberration function is usually more instructive than numerical integration.

Following Marechal and Francon [3.26(c)], we shall apply Eq. (3.465) to the following aberration polynomial:

Wq = kdp2 + ksipA + ks2p6 + (kTp + kcp3) cos + kAp2 cos 2^ (3.471)

From ยง 3.2.1, the terms can be identified as defocus, third and fifth order spherical aberration, wavefront tilt and third order coma, and third order astigmatism. Since the denominator of (3.463) with zero vignetting is n, we have from (3.463) and (3.464)

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