General Analysis of Aplanatic Cassegrain, Gregorian, and Schwarzschild Telescopes

W. B. Wetherell; M. P. Rimmer

doi:10.1364/AO.11.002817

Applied Optics
Vol. 11,
Issue 12,
pp. 2817-2832
(1972)
•https://doi.org/10.1364/AO.11.002817

General Analysis of Aplanatic Cassegrain, Gregorian, and Schwarzschild Telescopes

W. B. Wetherell and M. P. Rimmer

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W. B. Wetherell and M. P. Rimmer, "General Analysis of Aplanatic Cassegrain, Gregorian, and Schwarzschild Telescopes," Appl. Opt. 11, 2817-2832 (1972)

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Abstract

The properties of two-conic reflecting aplanats are analyzed and discussed on the basis of third order aberration theory. Techniques for designing infinite conjugate two mirror aplanats and computing their image properties are developed. The secondary mirror alignment characteristics of Ritchey-Chrétien and aplanatic Gregorian telescopes are examined and neutral point locations defined. Design configurations corrected for a third Seidel aberration (astigmatism, image curvature, or distortion) are identified and their properties discussed. The properties of Ritchey-Chrétien and aplanatic Gregorian telescopes are compared.

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Corrections

William B. Wetherell, "General Analysis of Aplanatic Cassegrain, Gregorian, and Schwarzschild Telescopes: Erratum," Appl. Opt. 13, 242_1-242 (1974)
https://opg.optica.org/ao/abstract.cfm?uri=ao-13-2-242_1

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Parameter	RC	CG	EG
D_p (m)	3.0	3.0	3.0
B (m)	2.1	2.1	2.1
F_p	2.2	2.2	1.454
F	12	−12	−12
S (m)	5.252	8.553	5.252
c_p (m⁻¹)	−0.075758	−0.075758	−0.11464
κ_p	−0.01725	−0.01935	0.004978
Aspheric sag at 1.5 m^a	445	431	1521
c_s (m⁻¹)	−0.30294	−0.30294	0.62936
κ_s	−1.25463	0.49240	0.36823
Aspheric sag at 0.3435 m^b	172	39^b	164
D_s^c (m)	0.687	1.008	0.687
l_ep (m)	−8.608	−8.608	−6.369
l_ω₀ (m)	0.056	−0.051	−0.011
m	5.455	−5.455	−8.254
β	0.318	0.318	0.481

Parameter	RC	CG	EG
Central obstruction diameter ratio
∊_s_a = \|D_s_a/D_p\|	0.20	0.30	0.20
∊_s = \|D_s/D_p\|	0.23	0.34	0.23
∊^a (baffled)	0.34	0.34	0.29
Image characteristics
R_I (m)	−1.415	1.827	0.836
α_I^b (min of arc)	3.49	3.83	3.27
Distortion^c (μm)	0.16	0.12	0.24
Alignment tolerances
\|Δy_ω₀\|^d (μm)	18.0	18.3	3.6
\|Δy_cc\|^e (μm)	0.42	0.29	0.20
\|ΔS\|^f (μm)	4.8	4.8	2.0

Parameter	RC	CG	EG
D_p (m)	3.0	3.0	3.0
B (m)	2.1	2.1	2.1
F_p	2.2	2.2	1.454
F	12	−12	−12
S (m)	5.252	8.553	5.252
c_p (m⁻¹)	−0.075758	−0.075758	−0.11464
κ_p	−0.01725	−0.01935	0.004978
Aspheric sag at 1.5 m^a	445	431	1521
c_s (m⁻¹)	−0.30294	−0.30294	0.62936
κ_s	−1.25463	0.49240	0.36823
Aspheric sag at 0.3435 m^b	172	39^b	164
D_s^c (m)	0.687	1.008	0.687
l_ep (m)	−8.608	−8.608	−6.369
l_ω₀ (m)	0.056	−0.051	−0.011
m	5.455	−5.455	−8.254
β	0.318	0.318	0.481

Parameter	RC	CG	EG
Central obstruction diameter ratio
∊_s_a = \|D_s_a/D_p\|	0.20	0.30	0.20
∊_s = \|D_s/D_p\|	0.23	0.34	0.23
∊^a (baffled)	0.34	0.34	0.29
Image characteristics
R_I (m)	−1.415	1.827	0.836
α_I^b (min of arc)	3.49	3.83	3.27
Distortion^c (μm)	0.16	0.12	0.24
Alignment tolerances
\|Δy_ω₀\|^d (μm)	18.0	18.3	3.6
\|Δy_cc\|^e (μm)	0.42	0.29	0.20
\|ΔS\|^f (μm)	4.8	4.8	2.0

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Applied Optics