Model-based calibration of an interferometric setup with a diffractive zoom-lens

Abstract

The fabrication of aspheres and freeform surfaces requires a high-precision shape measurement of these elements. In terms of accuracy, interferometric systems provide the best performance for specular surfaces. To test aspherical lenses, it is necessary to adapt or partially adapt the test wavefront to the surface under test. Recently, we have proposed an interferometric setup with a diffractive zoom-lens that includes two computer generated holograms for this purpose. 1 Their surface phases are a combination of a cubic function for the adaption of aberrations and correction terms necessary to compensate substrate-induced errors. With this system based on Alvarez design a variable defocus and astigmatism controlled by a lateral shift of the second element is achieved. One of the main challenges is the calibration of the system. We use a black-box model 2 recently introduced for a non-null test interferometer, the so called tilted wave interferometer 3 (TWI). With it, the calibration data are calculated by solving an inverse problem. The system is divided in the two parts of illumination and imaging optics. By the solution of an inverse problem, we get a set of data, which describes separately the wavefronts of the illumination and imaging optics. The main difference to the TWI is the flexible diffractive element, which can be used in continuous positions. To combine the calibration data of a couple of positions with the exact placement, we designed alignment structures on the hologram. We will show the general functionality of this calibration and first simulation results.

Broadband Variable Transmission Sphere for Fizeau Interferometry

“…An Alvarez lens can transform a planar wavefront into a range of converging or diverging wavefronts and thus is variable in f-number (Figure 1). a variable-focal-length Moirè lens, capable of variation in focal length by equal and opposite rotation of two elements [13,16,17]. Bielke's system is diffractive and therefore monochromatic, requiring additional systems for other source wavelengths.…”

“…Variable-focal-length optical systems as transmission spheres have been previously proposed and tested for use in Fizeau interferometers [13][14][15][16][17][18]. Bielke designed and tested a variable-focal-length Moirè lens, capable of variation in focal length by equal and opposite rotation of two elements [13,16,17]. Bielke's system is diffractive and therefore monochromatic, requiring additional systems for other source wavelengths.…”