Jjpr u upr u pp
the where dpp is the plate thickness, u = 2N the semi-aperture angle and upr principal ray angle which is the incidence angle of the beam on the plate.
The final optical design of a Gascoigne plate with field flattener for the PF will take account of all such effects as well as balancing of higher order effects. In practice, such aspheric plates will also have a balancing term in y2, as in Schmidt plates, to reduce their asphericity. Figure 4.3 gives spot-diagrams for the Gascoigne plate, field flattener corrector of the PF of the ESO 3.6 m telescope.
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