title: Analytical Jacobian and its application to tilted-wave interferometry.
abstract: 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.
authors.forename: Ines
authors.initials: I
authors.lastname: Fortmeier
authors.forename: Manuel
authors.initials: M
authors.lastname: Stavridis
authors.forename: Axel
authors.initials: A
authors.lastname: Wiegmann
authors.forename: Michael
authors.initials: M
authors.lastname: Schulz
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Osten
authors.forename: Clemens
authors.initials: C
authors.lastname: Elster