2.1 Gaussian optics of a prime focus reflecting telescope with a single powered mirror: sign of the paraxial parameters ... 41

2.2 Gregory and Cassegrain telescope forms: sign of paraxial ray trace quantities

(*denotes sign inversion between Gregory and Cassegrain) 44

2.3 Signs of derived quantities from the paraxial ray trace for the Gregory and Cassegrain forms 53

Chapter 3

3.1 Aberration types from the Characteristic Function 61

3.2 Paraxial values for deriving the Seidel coefficients (Table 3.3)

for some basic telescope systems 67

3.3 Seidel coefficients for some basic telescope systems.

The asterisk denotes the aspheric contribution 68

3.4 Third order aberrations for a 1-mirror telescope

(concave primary) 80

3.5 Third order aberrations and associated relations for a 2-mirror telescope in focal form 81

3.6 Third order aberrations and associated relations for a 2-mirror telescope in afocal form 82

3.7 Schwarzschild's data for the aplanatic telescope of Fig. 3.9 115

3.8 Comparison of the essential parameters in the evolution of the aplanatic telescope (from [3.13]) 116

3.9 Constructional data of the Couder anastigmatic telescope (1926) [3.25] 126

3.10 Angular spherical aberration, coma and astigmatism for three telescope cases of Table 3.3, with an f/10 image beam and a semi-field angle upr1 of 30 arcmin 140

3.11 Data for the "short" Maksutov telescope giving the results of Fig. 3.35 with D = 400 mm, f/3.0 170

3.12 Data for the "short" Maksutov system (D = 400 mm and f/3.0) optimized with an additional achromatic field flattener, giving the results of Fig. 3.37 172

3.13 Optical data of Baker Schmidt-Cassegrain Type B

3.14 Design data for the Maksutov-Cassegrain of Fig. 3.53. Aperture

3.15 d80 values (80% encircled energy diameters in ^m)

for the "short" system of Fig. 3.53 and Table 3.14 202

3.16 Design data for the Maksutov-Cassegrain of Fig. 3.55 204

3.17 Surface contributions for the aplanatic Maksutov-Cassegrain of Table 3.14 207

3.18 Data of the system of Fig. 3.72(a), adapted from Korsch [3.73] . . 226

3.19 Optical design data of the first, 2-axis solution with 4 powered mirrors and flat of Fig. 3.80 with primary f/1.5 and final image f/7.29 244

3.20 Angular tangential coma produced by transverse decentering of the secondary in the 2-mirror telescopes of Table 3.2.

\m2\ = 4; \Ra\ = 0.225. The relative aperture at the final image is N = 10. The decenter is \S/f'\ = 10 -4 267

3.21 Angular despace spherical aberration at best focus (BF)

and angular despace field coma for 2-mirror telescopes defined as in Table 3.2: \m2\ = 4, \RA \ = 0.225, \N\ = 10

and the despace is \ddx/f'\ = 10 -3, or ddx/f' = —4 ■ 10 -3, ten times the decenter S of Table 3.20. The semi-field angle for the coma is upri = 15 arcmin 284

3.22 The Zernike radial polynomials R^(p) up to degree 8

3.23 Zernike polynomials resolved in the x, y directions. This table gives all terms up to Rf and subsequent terms up to n = 10

3.24 The first five maxima of the rectangular aperture function

3.25 The first 3 subsidiary minima and maxima of the function [ JW]2 (after Born-Wolf [3.120(b)]) 300

3.26 Coefficients of various aberrations giving a Strehl Intensity Ratio of 0.8 (incoherent light, point source, circular unvignetted pupil) . 309

3.27 The effect of the obscuration factor e on the wavefront variance and the ratio (ptv/rms) with e = 0 311

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