Innovation in Mathematics: Proceedings of the Second International Mathematica Symposium
Standard optical imaging systems change their focal length by mechanical movement of lenses and lens groups along the optical axes. An alternative approach is realized in nature: many biological vision systems employ stationary flexible lenses enabling different lens power dependent of the surface shape. This paper presents an entirely Mathematica-based modelling and simulation of an innovative imaging system with a liquid-filled flexible lens design. Central issue is the investigation of the exact lens surface shape as a function of the internal liquid pressure. Therefore a new Mathematica package for Zernike-Polynomials was realized. Zernike-Polynomials allow surface data fits with an accuracy below 50 nm. Spline-Interpolation is used to parametrize Zernike-Coefficients over the entire pressure range applicable in the experiment. The lens surface is implemented in the Optica package for exact modelling of the experimental setup. Ray-tracing and additional procedures for lens performance calculations have been developed. the modelling and simulation was realized on a Pentium Pro 200 MHz platform.