Absolute surface metrology by rotational averaging in oblique incidence interferometry

Abstract

A modified method for measuring the absolute figure of a large optical flat surface in synchrotron radiation by a small aperture interferometer is presented. The method consists of two procedures: the first step is oblique incidence measurement; the second is multiple rotating measurements. This simple method is described in terms of functions that are symmetric or antisymmetric with respect to reflections at the vertical axis. Absolute deviations of a large flat surface could be obtained when mirror antisymmetric errors are removed by N-position rotational averaging. Formulas are derived for measuring the absolute surface errors of a rectangle flat, and experiments on high-accuracy rectangle flats are performed to verify the method. Finally, uncertainty analysis is carried out in detail.

Surface measurements in oblique incidence for multiple elements piezoelectric x-ray bimorph mirror

“…6, it can be seen that although the deformation caused by the piezoelectric ceramic is theoretically linear concerning voltage, the response function at 150 V is closer to the simulated value for the actual mirror measurement. Since the threshold of voltage was set in the calculation of the optimal loading voltage, the voltage obtained using the least squares method has limitations, and subsequent work is intended to continue optimizing the algorithm with iterative processes to further optimize the mirror surface and develop the oblique incidence absolute measurement method 10,14 .…”

“…To accurately measure the height profiler of the highprecision reflector mirror, Vannoni et al 9 derived the conversion equations of oblique incidence and normal incidence and performed sets of error analyses about the oblique incidence. Ma et al 10 carried out the error analysis in the interpolation process for recovering to a full-aperture mirror surface. Lin et al 11 proposed an absolute measurement method for oblique incidence measurement.…”

Multiposition Rotation Interference Absolute Measurement Method for High-Precision Optical Component Surfaces

“…e approach was demonstrated to obtain a closedform solution if one of the measurements conducted included the azimuthal rotation of one of the flats by some angle. is approach was formalized by Evans and Kestner [8], who proposed the basic N-position rotation theory, which was further developed by Küchel [9] and Lin et al [10]. In this theory, the measured wavefront is decomposed into a rotationally symmetrical component and a rotationally nonsymmetrical component, and the nonrotational symmetrical component is eliminated by azimuthal rotation through N positions to obtain the absolute optical surface information.…”

Absolute surface form measurement of flat optics based on oblique incidence method

“…proposed an absolute surface metrology by rotational averaging in oblique incidence for the X-ray mirrors [15] , but they only analyzed the number of rotations on the measurement accuracy, and more rotations of the reflective reference flat are required. Han et al proposed a Zernike polynomial decomposition based on the skip flat test [16] , and the defect of the method is that only lowfrequency components of the sample can be retrieved.…”