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(3£ SIH + E SIV )cos2 0 + (E Siii + E Siv ) sin2 0

The various powers of the ratios (yy^) and (4-) correspond simply to the terms p(m+n) and a(l+n) of the Characteristic Function of Eq. (3.16), expressing the aperture and field dependence functions for the five Seidel aberrations. The numerical factors and terms E Si ,^2>Sn, etc. correspond to the constants (¡+n)k(m+n),n in Eq. (3.16) and contain the information on the angular semi-aperture u', the focal length f of the system and the semi-field angle uprl in radians, as expressed in the formulae of Tables 3.4 and 3.5. There, the terms in (f-) represent the various powers of u', the power laws being, of course, identical to those of (yyi- in Eq. (3.181). Since all the other terms are dimensionless, while the wavefront aberrations all have the dimensions (length)1, the aberration coefficients E Si etc. also have dimensions (length)1 and are linearly proportional to the focal length of the system. Similarly, all the geometrical quantities are proportional to the focal length, which thus defines the scale of the system. This is illustrated by the relation for E Si in Table 3.5 for a 2-mirror system

in which Z and £ are dimensionless quantities. Substituting from (2.75) and (2.55) for L gives the form

expressing the linear dependence on f with otherwise only dimensionless quantities.

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