Optical design through optimization using freeform orthogonal polynomials for rectangular apertures

With the increasing interest in using freeform surfaces in optical systems due to the novel application opportunities and manufacturing techniques, new challenges are constantly emerging. Optical systems have traditionally been using circular apertures, but new types of freeform systems call for different aperture shapes. First non-circular aperture shape that one can be interested in due to tessellation or various folds systems is the rectangular one. This paper covers the comparative analysis of a simple local optimization of one design example using different orthogonalized representations of our freeform surface for the rectangular aperture. A very simple single surface off-axis mirror is chosen as a starting system. The surface is fitted to the desired polynomial representation, and the whole system is then optimized with the only constraint being the effective focal length. The process is repeated for different surface representations, amongst which there are some defined inside a circle, like Forbes freeform polynomials, and others that can be defined inside a rectangle like a new calculated Legendre type polynomials orthogonal in the gradient. It can be observed that with this new calculated polynomial type there is a faster convergence to a deeper minimum compared to “defined inside a circle” polynomials. The average MTF values across 17 field points also show clear benefits in using the polynomials that adapted more accurately to the aperture used in the system.