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Mathematical Modelling and Data Analysis

Department 8.4

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Title: Analytical Jacobian and its application to tilted-wave interferometry
Author(s): I. Fortmeier, M. Stavridis, A. Wiegmann, M. Schulz, W. Osten and C. Elster
Journal: Optics express
Year: 2014
Volume: 22
Issue: 18
Pages: 21313--25
Optical Society of America
DOI: 10.1364/OE.22.021313
ISSN: 1094-4087
Web URL: http://www.osapublishing.org/viewmedia.cfm?uri=oe-22-18-21313&seq=0&html=true
Keywords: Aspherics,Interferometry,Mathematical methods (general),Metrology,Surface measurements,TWI,figure,tilted-wave
Tags: 8.42,EMRP_Form,Form,SimOpt
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.

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