By Virendra N. Mahajan
This ebook 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 through 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 and their function in optical imaging and wave propagation. a few wisdom of Gaussian optics and an appreciation for aberrations will be necessary yet isn't really required. Read more...
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Extra info for Aberration theory made simple
This is indeed why a lens designer places beam splitters and windows in an imaging system in its collimated spaces wherever possible. 4 Numerical Problem As a numerical example we determine the aberrations of a plane-parallel plate placed in the path of a converging beam as shown in Figure 3-2. 5. Its thickness is 1 cm and its diameter is 4 cm. 5 cm from its axis. From Eq. 33 cm from its front surface. Substituting for n, t, and S = -8 cm in Eq. 6 x 10 -6 cm-3 . Noting that the maximum value of r is 2 cm, we obtain the peak values of the primary aberrations introduced by the plate from Eq.
Since m1 and M2 are both unity, (r, , 0,) _ (r2 , 8 2) and h 2' = hj = h, respectively. Hence, following Eq. (1-29), the aberration of the planeparallel plate at a point (r,8) in the plane of its exit pupil can be written W(r, 8, h) = WI (r, O, h) + W2(r, 0, h) . (3-12) Substituting Eqs. (3-8) and (3-10) into Eq. (3-12), we may write the primary aberration function W(r, 0; h) = a,(r ° - 4hr l cos0 + 4h2r 2 cos 2 0 + 2h 2r 2 - 4h 3r cos0) , (3-13) where (3-14) as = a51 + (Sz /L2)4as2 . Substituting Eqs.
Dt (5-4) Substituting Eq. (5-3) into Eq. (5-4), we obtain y^ = g f3 . (5-5) From Eq. p O = An dr , (5-6a) where An is the variation in the refractive index of the plate across the spectral bandwidth of the object radiation. Substituting for dtldr from Eq. (5-4) into Eq. (5-6a), we obtain y, = n nl yP . (5-6b) Thus, the angular dispersion A of a ray produced by the plate is proportional to its angular deviation p. , for r = a, where a is the radius of the plate. To reduce the chromatic aberration, we must reduce the maximum value of y,.
Aberration theory made simple by Virendra N. Mahajan