General equations for the null-screen test for aspherical surfaces with deformation coefficients

A modified approach to calculate the null screen for testing fast convex/concave aspherical surfaces with deformation coefficients is presented. Introducing the aberration polynomial into the equation of the sagitta, the null screens can be generated in a simple way, in contrast to the conventional design method. This approach is easy to implement for the calculation of the null screen since the equations presented here are easy to program computationally. The validation of this approach was done by analyzing the fast aspherical surface of a convex condenser lens (f/0.18). We obtained a percentage error smaller than 1.3% in the recovery of the coefficients that describe the shape of the surface.