Sun, W., McBride, J.W. and Hill, M.
A new approach to characterising aspheric surfaces.
Precision Engineering, 34, (1), . (doi:10.1016/j.precisioneng.2009.05.005).
In this paper, a new approach to fitting aspheric surfaces in three-dimensional space is proposed, based on the
nonlinear least-squares algorithm. The method is superior to 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.
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