Axial alignment for high-precision interferometric measurements of steeply-curved spheres

Abstract

Incorrect positioning of a steeply-curved sphere along the optical axis of a laser Fizeau interferometer introduces a measurement error that is proportional to the cosine of the inclination angle of the ray trace within the cavity, and directly proportional to the misalignment. The standard metrology solution is to subtract a fitted parabola from the 3D image, which corrects for most of the error, but neglects higher terms. As a consequence, measurements of steeply curved parts may have residual errors resembling spherical aberration. Here we calculate the magnitude of the error and present it in a graphical format that allows for straightforward quantification of the residual error as a function of the measured quadratic or power term in the measured 3D surface form. While our recommendation is to employ automated alignment for best results, we also consider options for higher-order software corrections for geometric misalignments.

Traceability of form measurements of freeform surfaces: metrological reference surfaces

“…When performing these measurements, care was taken to measure close to the position where the Zernike-coefficient defocus is zero and to correct the measurements to this exact condition by subtracting the defocus and appropriate spherical aberration terms. 11 The longitudinal (height) measurement uncertainty of this setup amounts to 11 nm (k ¼ 2).…”