M s P

Fig. 1.21 Meridian sections at the Gaussian plane of the equally spaced tangential, least confusion, sagittal and Petzval focal surfaces for opposite signs of Astm 3

the wavefront function is defined by the Hamilton characteristic function as the expansion

where each function W^ involves one or several terms of the form w = aln,m fjl pn cosmd, l, n, m integers > 0, m < n. (1.48)

The first function W[0] reduces to a constant (l = n = m = 0) giving the origin coordinates of the wavefront. W[2] includes the dioptrics first-order terms curvature and tilt - i.e. the Gaussian terms - that we will refer to as

Each term of the power series W is included in an order KW of the wavefront function which can be defined by

The Gaussian terms and the third and fifth-order aberration terms involved in the Hamilton expansion of the characteristic function W are displayed by Table 1.2 where for simplicity the coefficients al,n,m, which have dimension of a length, are not shown.

For each primary aberration the shape of the wavefront can be represented either by a pure term of the type wnm = Anmpn cos md or by co-adding a first-order term (Fig. 1.22).

Table 1.2 First terms of the Hamilton wavefront function

n

m = 0

m= 1

m= 2

m = 3 Kw

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