Measurement of the Radius of Curvature of a Mini Spherical Surface with Virtual Grating Phase Shift Technique

Spherically optical components of small diameters have found wide applications in many fields. Radius of curvature (ROC) is an important parameter as it determines their optical characteristics. For measuring the ROC of a mini spherical surface, a static microscopic carrier interferogram is taken, and virtual grating phase shift technique (VGPT) is adopted in this paper. By using the computer, four virtual gratings are generated, their reference frequency being the same as the carrier frequency of the test interferogram, and their modulation phases being 0, π/2, π and 3π/2, respectively. By multiplying the test interferogram separately with the four virtual gratings in intensity, four moire fringe images are obtained. By applying Furrier transform and low pass filtering, a set of four carrier-free phase shift fringe images are obtained. And finally by applying four step phase shifting algorithm and least square fitting (LSF), the ROC of the test spherical surface is obtained. Furthermore, the result agrees well with its nominal value and measurement result by Zygo interferometer. This indicates that adopting VGPT for measuring ROCs of mini spherical surfaces is practicable and has relatively a high accuracy.