Distortion Controlled Optical Design Using Orthogonal Surface Polynomials

The design of high quality very wide-angle optical systems (FFOV > 100 degrees) relies on distortion to obtain a sufficient resolution at, usually, the center of the field of view. Using distortion shape as a parameter during optimization to reach a magnification target is a common technique to achieve optical foveation during the lens design process. This method allows resolution enhancement at selected parts of the field of view since less care is given to parts of the image that are deemed less important. However, accurate control of distortion can be a challenge during optical design since the standard aspherics polynomials don't correlate directly to image magnification. This may in fact slow down optimization since the merit function is much less optimized to approach a solution.In this paper, we address this problem by presenting a method to simplify distortion control during the optical design phase. To achieve this, the use of orthogonal polynomials is used for defining the optical surface shape and will then be used to compare the height of the image plane at a given field of view. We show that in the case of simple and paraxial system, this process is orthogonal and achieve a solution in a single optimization step. We will finally discuss the limits of this method and how it applies to modern lens design problems.