Substitution in (3.121) gives
as the form required on the primary to correct the spherical aberration. For the normalized Cassegrain DK of Case 5 in Table 3.2 with L=+0.225, /' = +1 and m2 = -4, Eq. (3.125) gives (6s1)_dk = -0.73633, an ellipse. The primary for the DK form is thus somewhat less aspheric than the parabola of the classical telescope. In the Gregory case, the primary would be a hyperbola but nearer the parabola, because m2 = +4 and / = -1.
The form of Eq. (3.125) becomes singular in the afocal case. If we substitute from (2.55) and (2.75) the relations
/ = m2/1 and L = / — m2d1 , then we have the generally determinate form
In the afocal limit case with m2 ^ ro, the square bracket term becomes unity, giving
from Eq. (2.72). From Table 2.3 we see that Ra is positive in the Cassegrain (normal DK) case, again giving the elliptical form for the primary; while Ra is negative for the Gregory case, giving a hyperbola.
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