By Virendra N. Mahajan

ISBN-10: 0819405361

ISBN-13: 9780819405364

This publication offers a transparent, concise, and constant exposition of what aberrations are, how they come up in optical imaging structures, and the way they impact the standard of pictures shaped via them. The emphasis of the e-book 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 wish for a deeper and higher realizing of aberrations andRead more...

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**Extra resources for Aberration theory made simple**

**Example text**

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.

8 Aberrations of a Spherical Refracting Surface In this section, we discuss imaging by a spherical refracting surface. We give equations for Gaussian imaging and expressions for its primary aberrations for an arbitrary position of its aperture stop. The results given here form the cornerstone for imaging by more complicated systems. By making simple but appropriate changes in them, the results for a spherical mirror can be obtained immediately, as indicated in Chapter 4. As illustrated in Figure 1-6, consider a spherical refracting surface of radius of curvature R separating media of refractive indices n and n'.

The chief ray CR shown is for the exit pupil ErP,. Note that the aberration function referred to the new exit pupil is zero at (x o,0). , W(xz, yz; h') = WQz (xz, yz) - WQz (0 , 0 ) = WQl (LZ [(x2 - x0)9Y2]) - WQI(- L1 /LABO) . (1-12) Let the primary aberration function at ExP 1 be given by Wgi(xl,yl; h') = a51(4 + yi)z + a^ih'xi(xi + Yi) + aalh'2 + ad h' z (zi + y1) + a11h'3x1 . (1-13) Substituting Eq. (1-13) into Eq. (1-12) and noting from Figure 1-5 that the ratio of the radii of the two exit pupils is equal to the ratio of their distances from the Gaussian image plane, we can show that the old and the new peak aberration coefficients are related to each other according to 14 ABERRATION THEORY MADE SIMPLE A52 = A:i (1 -14a) Ace = At1 - 4bA sl (1 -14b) Aal = Aa , - 2bA c , + 4b2Asl (1 -14c) Adz = Aal -bA cl + 2b 2As1 (1 -14d) and AR = A1, - 2b(AQ , + Adl) + 3b2As , - 4b3A51 , ( 1 -14e) where .

### Aberration theory made simple by Virendra N. Mahajan

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