Computer-aided alignment for a reference transmission sphere of an interferometer

Abstract

A reference transmission sphere is an important device to measure the spherical surfaces, and it offers a high-quality spherical wave and a reference spherical surface with peak-to-valley less than l/20 (l50.6328 mm). For this value, only the manual alignment is difficult to manage it. Thus, we study the computer-aided alignment (CAA), which can provide a guide to align the individual lens. We describe the following works concerning the CAA with no iteration for the transmission spheres: (1) by analysis of the relationship between the Zernike polyno- mial coefficients and the sensitive variables, for example, the air thick- ness error, the tilt, the decenter of the transmission sphere with an analy- sis program written in Zemax program language, only several Zernike coefficients that change linearly with these sensitive variables are cho- sen; (2) the magnitude and direction of the correction are found using the Moore-Penrose generalized inverse matrix; and (3) a numerical simula- tion and successful alignment are processed for a 4-in.-diam, f/5 trans- mission sphere. © 2004 Society of Photo-Optical Instrumentation Engineers.