Appendices A. List of mathematical symbols 449 A. List of mathematical symbols Chapter 2 Table A.I. List of symbols for Chapter 2 Symbol Meaning Where defined A Aperture stop Fig. 2.6 aI, a2" . Coefficients for the definition of a centered surface Eq. (2.13) aE, bE, CE Positions of the Ramsden disk in a refracting Fig. 2.8 telescope b Distance from the pole of MI 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 v) 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 (DAXh Axial beam diameter of M2 in a 2-mirror telescope Eq. (2.93) (DTOTh 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 v) 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 j, l' Object-side, image-side focal length of a system Fig. 2.1, Fig. 2.2 450 Appendices Table A.2. List of symbols for Chapter 2 (continued) Symbol Meaning Where defined J{, J~ Image-side focal lengths of M I , 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 Object, image positions associated with an up­ Fig. 2.2, per ray Fig. 2.5 Object, image positions associated with a Fig. 2.8 lower ray h, I~ Primary and secondary axial image points in Fig. 2.11, a 2-mirror telescope Fig. 2.12 i, it Ray incident angles to a surface before, after Eq. (2.15), refraction or reflection (see surface number v) 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) I (suffix) The last surface of a system before the image Eq. (2.38) M Mirror (see surface number v) Fig. 2.11, Fig. 2.12 The primary and secondary mirrors of a 2- Fig. 2.11, mirror telescope Fig. 2.12 A. List of mathematical symbols 451 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, fino Eq. (2.104) n, n I Refractive index in the object, image space of Fig. 2.2 a refracting or reflecting surface (see surface Eq. (2.11), number v) Eq. (2.12) P, pi Object-side, image-side principal points of a Fig. 2.1, system Fig. 2.2 PH, P~ Object-side, image-side upper ray points defin- Fig. 2.1, ing with P, pi the principal planes of a system Fig. 2.2 PL, Pi Object-side, image-side lower ray points defin- Fig. 2.2 ing with P, pi 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 pi Fig. 2.6 pr (suffix) Denotes a principal ray, or property thereof, Fig. 2.6, which cuts the axis at E and EI 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 = lie (see sur- Eq. (2.13), face number v) Eq. (2.36) 452 Appendices Table A.4. List of symbols for Chapter 2 (continued) Symbol Meaning Where defined Tl, T2'" 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) 8, 8' 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 v) 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 f~ 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 v) 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 453 Table A.S. List of symbols for Chapter 2 (concluded) Symbol Meaning Where defined rv Parameters for the folded Cassegrain case with Fig. 2.15, M2 plane (m2 = -1) Eqs. (2.97) - (2.100) TJ, TJ' Height in the object, image plane Fig. 2.2, Fig. 2.5, Eq. (2.1), Eq. (2.23) 1/ (subscript) Counter number for system surfaces and parax- Eqs. (2.36) ial parameters, e.g. T." y." 8." d." n." i." U., - (2.38) Chapter 3 Table A.6. Additional symbols for Chapter 3 Symbol Meaning Where defined A, If Snell invariant for the paraxial aperture, princi­ Eq. (3.19), pal ray (see surface number 1/) Eq. (3.20) A Area of a circular aperture for diffraction Eq. (3.442) phenomena A' Real area of a pupil, including vignetting Eq. (3.466) A, Ao 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, Os, Supplementary aspherizing coefficients Eq. (3.77) Ds ... in the general definition of a surface 454 Appendices Table A.7. Additional symbols for Chapter 3 (continued) Symbol Meaning Where defined Terms in equations for deriving decentering Eqs. (3.355) coma - (3.357) Normalization constants for deriving Zernike § 3.9, polynomials Eq. (3.426) 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 Normalized amplitude of the object, image func­ Eq. (3.485), tion (OTF) Eq. (3.486) Afoe (suffix) Pertaining to the afocal form of a 2-mirror Eq. (3.98) telescope Aplan (suffix) Pertaining to the aplanatic form of a 2-mirror Eq. (3.106) telescope bs Schwarzschild (conic) constant Eq. (3.10) 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 455 Table A.S. Additional symbols for Chapter 3 (continued) Symbol Meaning Where defined C A constant in the diffraction integral Eq. (3.434) Primary longitudinal, lateral chromatic Eq. (3.222), aberration Eq. (3.223) 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, Coma. 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 dso 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, Le. lateral decenter Eq. (3.423) 456 Appendices Table A.9. Additional symbols for Chapter 3 (continued) Symbol Meaning Where defined E Total energy incident on a circular aperture Eq.