Open AccessAnalytical Jacobian and its application to tilted-wave interferometry
Author(s) -
Ines Fortmeier,
Manuel Stavridis,
Axel Wiegmann,
Michael Schulz,
Wolfgang Osten,
Clemens Elster
Publication year - 2014
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.22.021313
Subject(s) - jacobian matrix and determinant , wavefront , interferometry , optics , perturbation (astronomy) , computer science , algorithm , physics , mathematics , quantum mechanics
Tilted-wave interferometry (TWI) is a novel optical measurement principle for the measurement of aspherical surfaces. For the reconstruction of the wavefront and the surface under test, respectively, perturbation methods are applied, which require the calculation of the Jacobian matrix. For the practical use of the instrument, a fast and exact calculation of the Jacobian matrices is crucial, since this strongly influences the calculation times of the TWI. By applying appropriate approaches in optical perturbation methods we are able to calculate the required Jacobian matrices analytically when the nominal optical path through the system is given. As a result, calculation times for the TWI can be considerably reduced. We finally illustrate the improved TWI procedure and apply methods of optimal design to determine optimal positions of the surface under test. For such applications the fast calculation of the Jacobian matrices is essential.