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dPi = (^t^) (" ff) [p4i - kpiPp^ +(dpi )o (3.240)

Eq. (3.240) can then be expressed in the convenient form dpi = 5k{ NDf [ppi - kpippi ]+(dpi)o (3.242)

The thickness constant (dpi)0 for the axial thickness has no optical effect since a plane-parallel plate in the parallel incident beam produces no angular aberration on axis or in the field. The profile of the function (ppi - kpippii) is shown in Fig. 3.28. The abscissa is ppi, the ordinate the function for various values of the parameter kpl.

Fig. 3.28. Profile function (pp; — fcpiPp) for Schmidt corrector plates with various values of the form profile parameter kpi. The glass plate is formed by considering the area under the curves to be filled with glass down to an abscissa tangential to the curve in question. To the resulting axial thickness, the constant thickness (dpl)0 is added to give the necessary minimum plate thickness. (After Bahner [3.5])

Fig. 3.28. Profile function (pp; — fcpiPp) for Schmidt corrector plates with various values of the form profile parameter kpi. The glass plate is formed by considering the area under the curves to be filled with glass down to an abscissa tangential to the curve in question. To the resulting axial thickness, the constant thickness (dpl)0 is added to give the necessary minimum plate thickness. (After Bahner [3.5])

The choice of the optimum form is determined by the best balance for the spherochromatism. The assumption is made in Eq. (3.242) that the ray heights at the mirror are identical with those at the plate. In practice, all such small discrepancies are taken care of by the standard ray tracing and optimization procedures of optical design programs.

From (3.236) the plate profile (3.242) gives the required wavefront aberration

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