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.

Traceability of form measurements of freeform surfaces: metrological reference surfaces

“…The TWI is a special full-field interferometric measurement device for measuring the form of aspherical and freeform surfaces. [13][14][15][16][17] It combines a special noncommon path setup with ray tracing and model-based evaluation procedures to determine the form of such surfaces. The basic setup is shown in Fig.…”

“…[13][14][15][16][17] Furthermore, a beam stop in the Fourier plane of the imaging optics limits the fringe density at the detector and avoids subsampling effects. [13][14][15][16][17] With this setup, depending on the local slope of the specimen, several small subinterferograms ("patches") are generated at the detector. To avoid interference from the light of adjacent light sources, only every second light source in each row and column of the source array is switched on at the same time.…”

“…To avoid interference from the light of adjacent light sources, only every second light source in each row and column of the source array is switched on at the same time. [13][14][15][16][17] Therefore, four camera images are needed to obtain the data covering the whole SUT. The number and size of the patches generated depend on the form of the SUT and on its measurement position.…”

Measuring aspheres quickly: tilted wave interferometry

“…It has been shown by Fortmeier et al that important parts of the computation can be sped up by orders of magnitude using an analytical Jacobian approach. 35 …”

Traceability in interferometric form metrology

“…These measurement data are used to adapt the wavefront description in two reference planes of the optical system by solving yet another inverse problem [13]. The mathematical evaluation principle [11,14] is summarized below.…”