By Rudolf Kingslake
If one is after the unique mathmatics of optical layout, this can be a solid booklet.
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Extra info for Lens Design Fundamentals
2 Temperature Coefficient of Refractive Index If the ambient temperature in which the lens is to be used is liable to vary greatly, we must consider the resulting change in the refractive indices of the materials used. 50 However, for crystals it is likely to be much greater, and for plastics it is very large: . 00001 per C . 0056, quite enough to alter the focus significantly. In a reflex camera this would be overcome during the focusing operation before making the exposure, but in a fixed-focus or rangefinder camera, or one depending on the use of a focus scale, something must be done to avoid this temperature effect.
293900. The difference is caused by spherical aberration. 2 The (y – nu) Method Because of the linear nature of paraxial relationships, we can readily submit the paraxial ray-tracing equations to algebraic manipulation to eliminate some or all of the paraxial angles, which are actually only auxiliary quantities. For example, to eliminate the angles of incidence i and i 0 , we multiply the first part of Eq. (3-1) by n and the corresponding expression for the refracted ray by n 0 , giving ni ¼ nu þ nyc; n 0 i 0 ¼ n 0 u 0 þ n 0 yc Now the law of refraction for paraxial rays is merely ni ¼ n 0 i 0 ; hence equating these two expressions gives n 0 u 0 ¼ nu þ yðn À n 0 Þc (3-2) This formula can be used to trace paraxial rays, in conjunction with the transfer y2 ¼ y1 þ ðd=nÞðn10 u10 Þ (3-3) It will be noticed that, written in this way, Eqs.
7 RAY TRACING AT AN ASPHERIC SURFACE An aspheric surface can be defined in several ways, the simplest being to express the sag of the surface from a plane as follows: Z ¼ a2 Y 2 þ a4 Y 4 þ a6 Y 6 þ . . Only even powers of Y appear because of the axial symmetry. The first term is all that is required for a parabolic surface. 16 Result of tilting a lens surface. use the power series given in Eq. (2-2), but a great many terms will be required if the sphere is at all deep, that is, has significant sag.