Error analysis of laser interferometric system for measuring radius of curvature

Abstract

Spherical surfaces are essential components of optical systems and imaging devices. Moreover, precision spheres are calibration standards for many accurate instruments in dimensional and mass metrology. A spherical surface's main property is its radius of curvature, which can be measured using contact or non-contact methods. Interferometry is an accurate non-contact technique, but some error sources impact it. This study investigates seventeen error sources that affect a laser interferometric system for measuring the radius of curvature of a precision sphere. The measurements are obtained using a Fizeau laser interferometer (GPI-XP, Zygo) with phase-shifting capability and a displacement measuring interferometer (ZMI-1000, Zygo). A silicon–nitride precision sphere with a nominal radius of 12.49965 mm is dealt with in this study. One of the main contributions of this study is proposing three additional error sources: focal shift, optical distortion, and y-axis vibration. Besides, deadpath, nulling, and focal shift error sources contributed 70% of the total uncertainty budget. Also, to correlate measurement accuracy with the reference surface, three transmission spheres (f/3.3, f/1.5, and f/0.65) are employed; f/0.65 reported the most accurate radius measurement of 12.49922 ± 0.00089 mm. This study also investigates the dependence of the nulling error on the coverage factor that defines the tested surface area. The analysis of the measurement uncertainty and the optimum conditions that minimize the system's potential error sources are described in this work.