Wolfram Computation Meets Knowledge

Wolfram Summer School


Russell Chipman

Science and Technology

Class of 2019


Project: Representation of Wavefronts for Families of Lenses


Develop algorithms to describe the image qualities of families of lenses, the Cooke triplets. Aberrations were mapped as the lens elements are “bent” using a grid of 9^3=729 lenses. Ray tracing performed with the Mathematica-based polarization ray tracing program Polaris-M from www.airyoptics.com.

Summary of Results

The image aberrations have been mapped through the lens space, showing how different aberrations have optima in different areas. Data is shown for spherical aberration, coma, astigmatism, and field curvature Zernike polynomials. As a final result, obtained a representation of all the aberrations as a function of lens constructional parameters.

Future Work

Extending this method for wavefront aberrations to the polarization aberrations of lenses induced by anti-reflection coatings and other polarization effects in the optical system. A practical limitation in lens design is the curse of dimensionality. Lenses often have 100, 200 or more parameters. As the number of dimensions increases, eventually it is impractical to extend functions over large regions of these high dimensional spaces.

Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022