By Virendra N. Mahajan

ISBN-10: 0819405361

ISBN-13: 9780819405364

This booklet presents a transparent, concise, and constant exposition of what aberrations are, how they come up in optical imaging platforms, and the way they impact the standard of pictures shaped by means of them. The emphasis of the publication is on actual perception, challenge fixing, and numerical effects, and the textual content is meant for engineers and scientists who've a necessity and a hope for a deeper and higher figuring out of aberrations andRead more...

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As pointed out earlier, the variation of spherical aberration with q for other values of p follows the same parabola except that the location of its vertex depends on p. The vertices of the parabolas follow the lower parabolic curve in Figure 2-4, which represents a, as a function of q,, obtained by substituting Eq. (2-12b) into Eq. (2-12c). The solid dots on this curve indicate various values of p. The minimum value of spherical aberration approaches zero for p = 21 . It changes its sign for larger values of Ip .

R S Figure 4-3. Same as Figure 4-1 except that the aperture stop is located at the center of curvature C of the mirror. 5 Numerical Problems Now we consider simple numerical problems in which a spherical mirror of diamet er 4 cm and a radius of curvature 10 cm images an object 2 cm high located at a distance of 15 cm from it. We assume that the aperture stop is located at the mirror and the object lies below the optical axis. Table 4-1 gives the Gaussian as well as the aberration parameters for this problem.

O ry ¢ ^^,^ t/f p OWA ca \_ 8 Qua •^ ar u A ^. O C = N II U. Co - m O 1 o V LL V ü. mo u > M N 0 ci y u G, •3 O w ß N? fV C y 0WV Ok V V^ u a (sr c,0. = o^ Z —_ ~ y ¢ AV Q 2p CHAPTER 2. ABERRATIONS OF A THIN LENS 25 aa, =o. '3q (2-7) Thus, we obtain -1 q»^, _ - 2p nZ (2-8) n+2 Substituting Eq. (2-8) into Eq. (2-4a), we obtain the corresponding minimum spherical aberration 1 n 2 n Z n + 2 P ] ate, = - 32f 3 [ n -1 (2-9) Thus, following Eq. (2-4a), we note that, for a given value of p, a, as a function of q follows a parabola with a vertex lying at (q„d,,,a,,n;,: ).

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