Surface evaluation with Ronchi test by using Malacara formula, genetic algorithms, and cubic splines

Alberto Cordero-Dávila; Jorge González-García

doi:10.1117/12.868872

9 September 2010 Surface evaluation with Ronchi test by using Malacara formula, genetic algorithms, and cubic splines

Alberto Cordero-Dávila, Jorge González-García

Proceedings Volume 7652, International Optical Design Conference 2010; 76521F (2010) https://doi.org/10.1117/12.868872
Event: International Optical Design Conference 2010, 2010, Jackson Hole, WY, United States

Abstract

In the manufacturing process of an optical surface with rotational symmetry the ideal ronchigram is simulated and compared with the experimental ronchigram. From this comparison the technician, based on your experience, estimated the error on the surface. Quantitatively, the error on the surface can be described by a polynomial e(ρ²) and the coefficients can be estimated from data of the ronchigrams (real and ideal) to solve a system of nonlinear differential equations which are related to the Malacara formula of the transversal aberration. To avoid the problems inherent in the use of polynomials it proposed to describe the errors on the surface by means of cubic splines. The coefficients of each spline are estimated from a discrete set of errors (ρ_i,e_i) and these are evaluated by means of genetic algorithms to reproduce the experimental ronchigrama starting from the ideal.

Citation Download Citation

Alberto Cordero-Dávila and Jorge González-García "Surface evaluation with Ronchi test by using Malacara formula, genetic algorithms, and cubic splines", Proc. SPIE 7652, International Optical Design Conference 2010, 76521F (9 September 2010); https://doi.org/10.1117/12.868872

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