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two of the most serious sources of image error, namely defocus error and tracking error.

It is easily seen from Eq. (3.23) that the conversions are as follows: 5W'l = -1 n'( f) 2 5z (3.211)

These are the wavefront aberration changes resulting from a longitudinal focus shift Sz or a transverse focal (image height) shift Sri', respectively.

### 3.4 The theory of aspheric plates

The theory of aspheric plates has great elegance and simplicity. It has fundamental importance in understanding the function of wide-field telescope solutions, as we shall see in ยง 3.6. In addition, it is a powerful tool for dealing with supplementary correctors for correcting field aberrations (Chap. 4) or aberrations to correct manufacturing errors. A classic example of the latter is the analysis of possible correctors for the spherical aberration found, after launch, to afflict the Hubble Space Telescope (HST). This application will be discussed below and further in Chap. 4 and RTO II, Chap. 3.

Although the term "plate theory" or "plate diagram" was coined later by Burch [3.28], the basic theory was laid down by Schwarzschild in his classic paper of 1905 [3.1]. Burch's approach is well expounded by Linfoot [3.29]. The theory given below follows more closely the original approach of Schwarzschild which is essentially embodied in the aspheric terms of Eq. (3.20).

The theory of aspheric plates is derived directly from the concept of "stop shift". Suppose for any optical system the "stop" is at a certain location, for example at the prime mirror in a telescope system. If the effective stop is shifted by introducing a diaphragm or element sufficiently small that it takes over the role of the stop (see Chap. 2), then the aberrations of the system are modified according to the following formulae - see the works of Hopkins [3.3] or Welford [3.6] for the derivation (a more general form was given in Eq. (3.22)):

dSn dSm 8SIV SSy

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