A new approach to characterising aspheric surfaces

In this paper, a new approach to fitting aspheric surfaces in three-dimensional space is proposed, based on the nonlinear least-squares algorithm. For the conditions tested, there are good indications that this method provides better results than conventional solutions as all the surface parameters can be estimated simultaneously based on the design equation, thus allowing the result to be directly compared to design parameters. Conventionally, aspheric surfaces can be fitted with simplified surface models, such as a second order surface or polynomial model. Using this approach the estimated parameters cannot be compared with the design values, breaking the link between the designed and measured surface. The new method is developed here and tested on computer simulated aspheric surfaces. Both ideal surfaces and surfaces with random irregularities are considered. Issues regarding the application of the fitting method to real measured surfaces are discussed.