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With Ra = 1/3 and f = -2L from (3.101), we have b = —L/3 (3.105)

This means that the Cassegrain image is well to the left of the primary in Fig. 2.12, normally an unacceptable position.

b = +L/2 , a normally acceptable image position; but Ra = 1/2 is normally too high. We see that the image position b is a very sensitive function in the flat field condition arising out of Eq. (3.62).

Normal modern Cassegrain telescopes rarely have |m2| < 3 or Ra > 1/3. Indeed, the modern trend is to make |m2| > 4, implying that field curvature is accepted as the lesser evil. If necessary, field-flattening lenses can be used, but one must beware of transverse chromatic aberration (see § 3.5). Modern array detectors, such as CCDs, can compensate modest field curvature.

In Table 3.3, it is clear that the primary compensates some of the field curvature of the secondary, whereas in the Gregory case (Case 7) the effects are additive. However, the effective field curvatures with astigmatism are numerically quite similar. A very important advantage of the Gregory form is the fact that the sign of both Siv and the effective field curvature is the opposite of that of the Cassegrain. This means that these field curvatures in the Gregory form are convex to the incident light. This is precisely the overcorrection required to compensate the natural field curvature of almost all instruments.

b) The aplanatic telescope and its Cassegrain (Ritchey-Chre-tien) form. The Ritchey-Chretien (RC) form of the Cassegrain telescope is, in practice, by far the most important modification of the classical Cassegrain telescope. It was originally proposed by Chretien in 1922 [3.14], who was inspired by Schwarzschild's pioneer work in 1905 [3.1]. However, there is good evidence - see § 5.2 - that Chretien, at Ritchey's suggestion, had already established the aplanatic basis of his design by 1910, before he met Schwarzschild or became aware of his work. Schwarzschild established the fundamental design principles for field correction (see §3.2.6.1), but sought a faster system than that provided by the normal Cassegrain form. The Schwarzschild form also aimed for a remarkable angular field extension: it will be treated in § 3.2.7. Schwarzschild, therefore, did not discover the RC telescope, although it was implicit in his theory [3.13]. It corrects the two conditions Si and Sii to give an aplanatic telescope without any change to the desired Cassegrain geometry. Ritchey recognised the importance of this development for field extension in a very fast (for that time) Cassegrain with f/6.5. He then made the first such major RC telescope, with 1 m aperture, for the US Naval Observatory in the 1930s, a remarkable achievement with the test techniques available at that time. Without wishing to detract from the achievements of Ritchey, it might seem more logical to call this system the Schwarzschild-Chretien, a name which would reflect more justly its origins in optical design theory. However, the name Ritchey-Chretien is now firmly established.

The RC solution is defined by Eq. (3.60) for the field coma of a 2-mirror telescope, which must be set to zero for an aplanatic solution:

Aplan

For correction of SI, the second term in the square bracket is zero irrespective of the pupil position spr1. The condition for an aplanatic telescope is then f'

giving f'

Combining this with (3.41) gives a m2 - 1\2 + 2/' m2 + 1^ di(m2 + 1)3

for the general condition of an aplanatic, 2-mirror telescope.

Whether the telescope is of Cassegrain or Gregory form will again depend on the signs of m2 and f according to Tables 2.2 and 2.3 and the numerical value of d1. Table 3.2 gives the values of bs2 for the RC and aplanatic Gregory cases with m2 = —4 and +4 respectively. We see that there is a modest increase in eccentricity in both cases compared with the classical case. Eq. (3.109) can be written from (3.93)

in which the second term gives the supplement required for the aplanatic solution. Since (bs2)ci is always negative, an increase of eccentricity always takes place because of the signs of the quantities in the Cassegrain and Gregory cases, giving a negative supplement.

Equation (3.109) completely defines the solution for the 2-mirror aplanatic telescope: the condition SIi = 0 is achieved solely by the form of the secondary. The non-zero value of £ of Eq. (3.108) corrects the field coma term of a primary mirror with the same final focal length f .

Equation (3.110) confirms that the classical and aplanatic forms are identical in the afocal case of the Mersenne telescope. If we replace f by m2/1 from Eq. (2.55), we can write

in which the supplementary term is zero if m2 ^ œ.

The second condition for aplanatism, the correction Si = 0, must be established from the correct form of the primary. From Eq. (3.59), the condition is

giving from (3.108)

L 2d1

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