## L

1.5, this gives

for the same value f'/g = 35 postulated before. This is an important result. It shows that a change of the mirror aspherics to correct about 60% of the coma of the classical Cassegrain completely liberates the condition for correcting E S/// = E S/v = 0 of (4.72) by adding the term in ^S// appearing in (4.76) and (4.77). This is very sensitive because E « f'/g is a huge multiplier of its effect - an illustration of the see-saw diagram interpretation of Eqs. (4.75) due to Burch [4.10]. If ^S// is a free parameter, the position g becomes completely uncritical.

Let us consider now the other most important case, the strict RC telescope. Here (E S/)Tei = (E S//)Tei = 0, while (E S///)Tei is given by Eq. (3.119). Eqs. (4.64) can then be written for the correction of all four aberrations

ES/ |
= (S/ )cor |
= 0' |

E S// |
= (S//)cor |
= 0 |

= f ( l ) + (S///)cor |
= 0 | |

ES/V |
\ / = (S/V )TeI + (S/V ) cor |
= 0, |

Proceeding as before, the condition E S/// = E S/v = 0 is then simply f ' + f f 'L

—n n for the case of a "thin" corrector of one or more elements of the same glass. It is important to note that the stop-related quantity E is absent in (4.78) and

(4.79) because both (Si)c used above, lead to n' = +0.430

and (Su)cor are zero. The values of Table 3.2, as as the requirement for fulfilling this condition for the optical geometry of Table 3.2. This value of n' is physically impossible. It is the opposite situation from what we had with Eq. (4.72) for the classical Cassegrain with f '/g = 35. Now, the compensation of the astigmatism of the telescope alone, without a stop-induced supplement from a coma term, requires a corrector whose power is too weak to compensate the field curvature. A real solution can only exist for lower magnifications m2 than the value —4 assumed: but this is not the modern trend. In the classical Cassegrain case of Eq. (4.72), a solution exists if g is increased; but in the RC case Eq. (4.79) is independent of g.

We now consider in detail the advantage of a 2-glass solution for a thin doublet corrector of a strict RC telescope. The astigmatism condition can be written kli + kl2 = -

from (4.73) and (4.78), while the field curvature condition is the same as for the Cassegrain, given in (4.74) as

Subtracting (4.80) from (4.81) gives

Using again the values of Table 3.2 and setting n'2 = 1.65 , ni = 1.50

The difference of about 4% in the powers gives the required astigmatism while the absolute values combined with the refractive indices give the required Petzval sum from (4.81). (By contrast, with a single glass, the powers Kl1 and Kl2 could be freely chosen to correct (Sj)cor = (Sjj)cor = 0, only the sum being important for (Sjjj)cor or (Sjv)cor, correction of both being

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