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Extra resources for Reflecting Telescope Optics I: Basic Design Theory and its Historical Development (Astronomy and Astrophysics Library) (Pt. 1)
24) as a functionality of the amounts showing at the correct facets of Eqs. (3. 33). this manner may be tremendously simpliﬁed by way of introducing from Eq. (2. seventy two) f1 − d1 = L m2 (3. 34) and from Eq. (2. ninety) f2 = L m2 + 1 (3. 35) The parameter L, the again focal distance from the secondary, is a truly handy parameter for the ﬁnal expressions, including the process focal size f and the secondary magniﬁcation m2 . The relief offers (SI )2 = (SI )02 + (SI )∗2 (3. 36) with y1 f four (SI )02 = (SI )∗2 = y1 f four m2 − 1 m2 + 1 L (m2 + 1)3 four L (m2 + 1)3 bs2 four Combining those supplies 2 (3. 37) (3. 38) 74 three Aberration concept of telescopes y1 f (SI )2 = four L m2 − 1 m2 + 1 (m2 + 1)3 four 2 + bs2 (3. 39) via analogy with the deﬁnition of ζ above for the first reflect in Eq. (3. 30), we now deﬁne ξ = ξ0 + ξ∗ = m2 − 1 m2 + 1 (m2 + 1)3 four 2 + (m2 + 1)3 bs2 , four (3. forty) giving ξ= m2 − 1 m2 + 1 (m2 + 1)3 four 2 + bs2 (3. forty-one) and y1 f (SI )02 = four Lξ zero , (SI )∗2 = y1 f four Lξ ∗ (3. forty two) we've, ﬁnally y1 f (SI )2 = four Lξ (3. forty three) with a purpose to confirm (SII )2 and (SIII )2 from Eq. (3. 24), we nonetheless require the parameters A and (HE)2 from the paraxial vital ray. Eqs. (2. 36) A 2 to (2. 38) provide ypr2 = spr1 (d1 − f1 ) − d1 f1 upr1 f1 (3. forty four) and A2 = spr1 (f1 − d1 ) + d1 f1 − 2f2 (spr1 − f1 ) upr1 2f1 f2 (3. forty five) Now substituting (3. 34) and (3. 35) within the expression for A2 in (3. 33), this reduces to A2 = y1 f m2 − 1 2 if additionally f1 is changed by way of to A2 = , f m2 (3. forty six) from (2. 55). comparable substitutions in (3. forty five) lead −spr1 L(m2 − 1) + 2f 2Lf 2 − d1 f (m2 − 1) Then from (3. forty six) and (3. 47), we now have ﬁnally upr1 (3. forty seven) 3. 2 attribute functionality and Seidel (3rd order) aberrations A A f y1 = 2 − d1 2f spr1 + − upr1 L L(m2 − 1) f seventy five (3. forty eight) From the deﬁnitions above Eq. (3. 19), we've got (HE)2 = ypr2 y2 (3. forty nine) ypr2 and y2 are given in Eqs. (3. forty four) and (3. 33) respectively. Substituting back from (3. 34) and (2. fifty five) for f1 , those equations decrease simply to f y1 (HE)2 = − d1 spr1 − upr1 L f (3. 50) For the ﬁeld curvature (SIV )2 , we require (Pc )2 . From the deﬁnitions above Eq. (3. 19), this can be easily (Pc )2 = + 1 m2 + 1 m2 + 1 = = f2 L f − m2 d1 (3. fifty one) from (2. 55), (3. 34) and (3. 35). the second one equation of (3. 24) can now be utilized to the calculation of the coma contribution (SII )2 utilizing Eqs. (3. forty two) for (SI )02 and (SI )∗2 and (3. forty eight) and (3. 50) for A and (HE)2 . The relief is made very simple by means of the A 2 indisputable fact that the shape of the equation (3. forty eight) is equal to (3. 50) with the exception of an extra time period, and that ξ zero and ξ ∗ have a typical issue. the result's (SII )2 = y1 f three −d1 ξ + f L (m22 − 1) − spr1 ξ upr1 , 2 f (3. fifty two) within which the elements (SII )02 and (SII )∗2 are given via (SII )02 = y1 f three y1 f three ξ zero −d1 − L 2f spr1 + upr1 f (m2 − 1) (3. fifty three) ξ ∗ −d1 − L spr1 upr1 f (3. fifty four) and (SII )∗2 = those are utilized within the 3rd equation of (3. 24), mixed with (3. forty eight) and (3. 50) to figure out (SIII )2 . This ends up in y1 f 2 (SIII )02 = (SIII )∗2 = y1 f 2 ξ0L ξ∗L −d1 spr1 − L f −d1 spr1 − L f + 2f L(m2 − 1) 2 u2pr1 (3.