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in which A1 and refer to a paraxial principal ray calculation for M2 as though it were a primary. Also

Mpr1 = ~(2SPr1 — r2) , in which s*r1 is the pupil shift from M2. But spr1 = 0, so that

From (3.344), this gives

Substituting from (3.343) and (3.345) in (3.341) gives (r1 - 2d1)2(r1 - 2d1 - 2r2)

r1r2

Up,r2

For the coma-free Schiefspiegler in Z-form, where upr1 and upr2 have the same sign because n1 = - 1:

Y^Sii = (S//)1 + (S//)2 = 0 , giving from (3.342) and (3.346) the condition for freedom from coma in the "axial" image

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