= 0.1633 (for field ± 1.5°)


= +0.55556


= -14.20358


= -0.55417

solution is striking, but the curved field must be borne in mind in making this comparison. Also, at this relative aperture, the obstruction supplement due to the field is so large that the image potential is not exploitable in practice without serious vignetting.

Finally, the question may legitimately be posed, since the equations for an aplanatic telescope are perfectly general for both Cassegrain and Gregory forms, whether a Couder anastigmatic form exists as a Gregory telescope with a real intermediate image. The answer is given by Eq. (3.174) defining the condition for freedom from astigmatism in an aplanatic telescope. Since / must be negative for the Gregory form, it follows from (3.174) that d1 must be positive. But this means that M2 must lie behind the concave primary and can only form a virtual image of the real primary image. Indeed, the secondary mirror is itself virtual, since the light from the primary cannot reach it! The virtual secondary M2 is then larger than the primary. This geometry is confirmed from Eqs. (3.177) and (3.178) giving negative values for L and /2.

It follows that a Gregory equivalent to the Couder anastigmatic telescope, giving a real final image, does not exist. This is the analogous situation to the virtual image Gregory form of Schwarzschild's impractical telescope form of Fig. 3.8.

3.2.8 Scaling laws from normalized systems to real apertures and focal lengths

The above formulation of third order aberration theory is quite general, but we have seen that it is useful for the comparison of different systems to normalize as in Tables 3.2 and 3.3 with

for the focal case. The general form of the wavefront aberration function in the third order approximation was given by Eq. (3.21) as

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