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Appendices A Appendices A. List of mathematical symbols Chapter 2 Table A.1. List of symbols for Chapter 2 Symbol Meaning Where defined A Aperture stop Fig. 2.6 a1,a2 ··· Coefficients for the definition of a centered surface Eq. (2.13) aE,bE ,cE Positions of the Ramsden disk in a refracting tele- Fig. 2.8 scope b Distance from the pole of M1 to the final image Fig. 2.11, in a 2-mirror telescope Fig. 2.12, Eq. (2.65) b Normalized value of b Eq. (2.87) C Beam compression factor Fig. 2.8, Eq. (2.39) c Curvature of a surface = 1/r Eq. (2.13) (see surface number ν) cl Velocity of light in wavefront propagation Fig. 2.3, Eq. (2.11) D Effective diameter (aperture) of a system; diame- § 2.2.6 ter of the entrance pupil (DAX )2 Axial beam diameter of M2 in a 2-mirror telescope Eq. (2.93) (DTOT)2 Full diameter of M2 in a 2-mirror telescope Eq. (2.93) d Axial distance between a given surface of a system Fig. 2.11, and the next surface (see surface number ν) Fig. 2.12, Eq. (2.37) E, E Entrance, exit pupil of a system Fig. 2.6 F, F Object, image focal point of a system Fig. 2.1, Fig. 2.2 f, f Object-side, image-side focal length of a system Fig. 2.1, Fig. 2.2 468 Appendices Table A.2. List of symbols for Chapter 2 (continued) Symbol Meaning Where defined f1,f2 Image-side focal lengths of M1, M2 in a 2- Eqs. (2.54), mirror telescope (2.55), (2.60) H The Lagrange Invariant Fig. 2.5, Eq. (2.27) H (suffix) Upper ray Fig. 2.1, Fig. 2.2 I, I Axial object, image positions of a system Fig. 2.2 IH ,IH Object, image positions associated with an up- Fig. 2.2, per ray Fig. 2.5 IL,IL Object, image positions associated with a Fig. 2.8 lower ray I1,I2 Primary and secondary axial image points in Fig. 2.11, a 2-mirror telescope Fig. 2.12 i, i Ray incident angles to a surface before, after Eq. (2.15), refraction or reflection (see surface number ν) Eq. (2.36) K Optical power of a system or element Eqs. (2.22), (2.51), (2.53) L Back focal distance in a 2-mirror telescope Fig. 2.11, (distance from the secondary to the image) Fig. 2.12 Eq. (2.61), Eq. (2.72) L (suffix) Lower ray Fig. 2.8 LTP Light Transmission Power (Throughput) Eq. (2.47) l (suffix) The last surface of a system before the image Eq. (2.38) M Mirror (see surface number ν) Fig. 2.11, Fig. 2.12 M1,M2 The primary and secondary mirrors of a 2- Fig. 2.11, mirror telescope Fig. 2.12 A. List of mathematical symbols 469 Table A.3. List of symbols for Chapter 2 (continued) Symbol Meaning Where defined m Magnification of a system Eqs. (2.1), (2.2), (2.23), Fig. 2.5 m2 Magnification of the secondary mirror of a 2- Eq. (2.55) mirror telescope N Relative aperture, f/no Eq. (2.104) n, n Refractive index in the object, image space of Fig. 2.2 a refracting or reflecting surface (see surface Eq. (2.11), number ν) Eq. (2.12) P, P Object-side, image-side principal points of a Fig. 2.1, system Fig. 2.2 PH ,PH Object-side, image-side upper ray points defin- Fig. 2.1, ing with P, P the principal planes of a system Fig. 2.2 PL,PL Object-side, image-side lower ray points defin- Fig. 2.2 ing with P, P the principal planes of a system P The distance between the primary and sec- Fig. 2.11, ondary image in a 2-mirror telescope Fig. 2.12, Eq. (2.81), Eq. (2.84) p (suffix) Denotes a field ray, or property thereof, which Fig. 2.5, cuts the axis at P or P Fig. 2.6 pr (suffix) Denotes a principal ray, or property thereof, Fig. 2.6, which cuts the axis at E and E Fig. 2.8 RA Axial obstruction ratio of a 2-mirror telescope Eq. (2.58), Eq. (2.72) r Radius of curvature of a surface = 1/c (see sur- Eq. (2.13), face number ν) Eq. (2.36) 470 Appendices Table A.4. List of symbols for Chapter 2 (continued) Symbol Meaning Where defined r1,r2 ··· Defined light rays Figs. 2.1, 2.2, 2.4, 2.6, 2.8 S Optical system Fig. 2.1, Fig. 2.6 S Scale of a telescope (arcsec/mm) Eq. (2.102) S Inverse scale of a telescope (mm/arcsec) Eq. (2.103) s, s Axial distance from an object, image to an imag- Figs. 2.2, ing surface or a principal plane (see surface num- 2.5, 2.6, ber ν) 2.11, 2.12, Eq. (2.4) T True telephoto effect of a 2-mirror telescope rel- Eq. (2.57) ative to the length L Tp Telephoto effect of a 2-mirror telescope relative Eq. (2.56) to the primary focal length f1 t Time (light propagation) Eq. (2.11) u, u Ray angles to the axis before, after refraction or Fig. 2.5, reflection (see surface number ν) Eq. (2.26) W, W Wavefront (or wavefront aberration) Fig. 2.3 before, after refraction or reflection x, y, z Cartesian coordinate system (right-hand set): z § 2.2.1, is the axial distance, y the height in the principal § 2.2.3, section Eq. (2.13) x,y,z Coordinates after refraction or reflection § 2.2.1, § 2.2.3, Eq. (2.13) A. List of mathematical symbols 471 Table A.5. List of symbols for Chapter 2 (concluded) Symbol Meaning Where defined ∼ Parameters for the folded Cassegrain case with Fig. 2.15, M2 plane (m2 = −1) Eqs. (2.97) – (2.100) η, η Height in the object, image plane Fig. 2.2, Fig. 2.5, Eq. (2.1), Eq. (2.23) ν (subscript) Counter number for system surfaces and parax- Eqs. (2.36) ial parameters, e.g. rν , yν , sν , dν , nν , iν , uν – (2.38) Chapter 3 Table A.6. Additional symbols for Chapter 3 Symbol Meaning Where defined A, A Snell invariant for the paraxial aperture, princi- Eq. (3.19), pal ray (see surface number ν) Eq. (3.20) A Area of a circular aperture for diffraction phe- Eq. (3.442) nomena A Real area of a pupil, including vignetting Eq. (3.466) A, A0 Common area, whole pupil area for a sheared Eq. (3.499) pupil A, B Constants of a linear dispersion equation Eq. (3.316) A, B Real, imaginary parts of the autocorrelation Eq. (3.503) function AS ,BS ,CS , Supplementary aspherizing coefficients Eq. (3.77) DS ... in the general definition of a surface 472 Appendices Table A.7. Additional symbols for Chapter 3 (continued) Symbol Meaning Where defined Aδ,Bδ1,Bδ2 Terms in equations for deriving decentering Eqs. (3.355) coma – (3.357) Aαβ Normalization constants for deriving Zernike § 3.9, polynomials Eq. (3.426) ∗ A1 Quantity calculated for the secondary as though Eq. (3.344) it were a primary in a Schiefspiegler A (suffix) Pertaining to third order astigmatism for the Eq. (3.471) Strehl Intensity Ratio a, b Semi-axes of an ellipse Eq. (3.4) a Aspheric plate profile constant (defining its Eq. (3.221) spherical aberration) a, b Upper and lower points of a Schmidt plate Fig. 3.27 (a), (b) Stop positions in a Maksutov telescope Fig. 3.36 a0,aI Normalized amplitude of the object, image func- Eq. (3.485), tion (OTF) Eq. (3.486) Afoc (suffix) Pertaining to the afocal form of a 2-mirror tele- Eq. (3.98) scope Aplan (suffix) Pertaining to the aplanatic form of a 2-mirror Eq. (3.106) telescope bs Schwarzschild (conic) constant Eq. (3.10) bs Laux definition of conic parameter Eq. (3.79) B (suffix) Pertaining to Bouwers’ achromatic meniscus Eq. (3.311) Bou (suffix) Pertaining to Bouwers-type meniscus Eq. (3.278) BF (suffix) Best focus Eq. (3.185) A. List of mathematical symbols 473 Table A.8. Additional symbols for Chapter 3 (continued) Symbol Meaning Where defined C A constant in the diffraction integral Eq. (3.434) C1,C2 Primary longitudinal, lateral chromatic aber- Eq. (3.222), ration Eq. (3.223) C0,CI Contrast for the object, image of a given spa- Eq. (3.483) tial frequency C (suffix) Pertaining to chromatic aberrations Eq. (3.222), Eq. (3.223) C (suffix) Pertaining to a concentric surface Fig. 3.36 C (suffix) Pertaining to third order coma for the Strehl Eq. (3.471) Intensity Ratio Comat,Comas Tangential, sagittal coma Fig. 3.18, Eq. (3.196), Eq. (3.197) CFP (also suffix) Coma-free point § 3.7.2.3 cl (suffix) Pertaining to a classical 2-mirror telescope Eq. (3.93) DK (also suffix) Dall-Kirkham form of a 2-mirror Cassegrain § 3.2.6.3(c) telescope d Thickness of an aspheric or plane-parallel § 3.6.2.3 plate or filter; or of a meniscus or lens element of a corrector d80 Diameter of the circle containing 80% of the Table 3.15 geometrical energy in the point image (PSF) d (suffix) Pertaining to defocus for the Strehl Intensity Eq. (3.471) Ratio dec (suffix) Pertaining to Gaussian effects of transverse Eq. (3.422), despace, i.e. lateral decenter Eq. (3.423) 474 Appendices Table A.9.
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