A discontinuity in the constrained damped least squares (DLS) method of optimization

Abstract

The method of damped least squares (DLS) is probably the most widely used method in optimization of lens systems. The main obstacle in this method is the choice of weights that are applied on functions of different nature involved in the construction of a merit function. This merit function should lead to the final goal of optimizing the lens system. An alternative to DLS is the method of constrained damped least squares (CDLS). In this method functions of lens parameters are separated into two sets: (1) functions related to image quality (aberrations) that are weighted, squared, added and then minimized, and (2) all other functions, or constraints, of varied nature, that are brought to zero or negligible values and for that reason they do not require weights assigned to them. Specifically for this reason it is immaterial whether theyt are of different nature or not. Optimization in either method is carried out in successive approximations or cycles. In DLS the end point of one cycle is the beginning point of the next cycle. In CDLS there is a gap or discontinuity between these two points; its magnitude depends on the size of the residual constraint errors. If the discontinuity is too large it may adversely affect the progress of optimization. It is possible to reduce the magnitude of the discontinuity by controlling the optimization progress and then to proceed in an orderly fashion towards the final goal.