Analytic-domain lens design with proximate ray tracing

Abstract

We have developed an alternative approach to optical design which operates in the analytical domain so that an optical designer works directly with rays as analytical functions of system parameters rather than as discretely sampled polylines. This is made possible by a generalization of the proximate ray tracing technique which obtains the analytical dependence of the rays at the image surface (and ray path lengths at the exit pupil) on each system parameter. The resulting method provides an alternative direction from which to approach system optimization and supplies information which is not typically available to the system designer. In addition, we have further expanded the procedure to allow asymmetric systems and arbitrary order of approximation, and have illustrated the performance of the method through three lens design examples.

Calibration and performance assessment of microgrid polarization cameras

“…for each of the noise terms in Eq. (12), producing E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 4 ; 3 2 6 ; 3 8 1…”

“…While the result is a nonlinear equation, we can obtain a second-order power series representation by taking the Maclaurin series expansion in the noise variables n θ and extract the second-order terms. 11,12 This produces a lengthy polynomial expression in the four noise variables, but if we assume that the noise terms are independent of one another, then the ensemble average of all mixed-noise terms (i.e., terms having n 0 n 45 as factors) becomes zero. This greatly simplifies the expression.…”

Efficient characterization of phase space mapping in axially symmetric optical systems

“…A natural strategy to avoid tracing too many rays is to characterize the phase mapping equations with some type of functional relations. For axially symmetric optical systems, the classical approach has been to approximate ray coordinates at image space through Taylor series expansions with respect to three independent object-pupil coordinates (a recent example can be found in Zheng et al [2]). Nowadays, the computer graphics community appears to be especially interested in such an approach [1,3,4], coining the keyword polynomial optics, and applying it even in the absence of axial symmetry.…”