Differential computation method used to calibrate the angle-centroid relationship in coaxial reverse Hartmann test

Abstract

A differential computation method is presented to improve the precision of calibration for coaxial reverse Hartmann test (RHT). In the calibration, the accuracy of the distance measurement greatly influences the surface shape test, as demonstrated in the mathematical analyses. However, high-precision absolute distance measurement is difficult in the calibration. Thus, a differential computation method that only requires the relative distance was developed. In the proposed method, a liquid crystal display screen successively displayed two regular dot matrix patterns with different dot spacing. In a special case, images on the detector exhibited similar centroid distributions during the reflector translation. Thus, the critical value of the relative displacement distance and the centroid distributions of the dots on the detector were utilized to establish the relationship between the rays at certain angles and the detector coordinates. Experiments revealed the approximately linear behavior of the centroid variation with the relative displacement distance. With the differential computation method, we increased the precision of traditional calibration 10 rad root mean square. The precision of the RHT was increased by approximately 100 nm.

Precise positioning of the test surface and screen in a coaxial software configurable optical test system

“…The software configurable optical test system (SCOTS), one of the successful approaches, is widely used because of the advantages of full-field acquisition, fast and automatic data processing, a large dynamic range, no requirement for a reference wavefront and high accuracy [4][5][6][7]. However, in the SCOTS, the positioning accuracy of the test surface and screen has a significant impact on the shape measurement results [8][9][10].…”

“…(b). The differential computation method[8] (figure2(c)) is used to measure the sum of L 1-flat and L 2-flat (L 1 and L 2 in the flat crystal system, respectively). A 3D CMM is used to measure at least three points on the flat surface.…”