Automated determination of best focus and minimization of optical path difference in Linnik white light interferometry.

It is difficult to search for interference fringes in Linnik white light interferometry with an extremely short coherence length because of the optical path mismatch of two interference arms and the defocus of the reference mirror and the test surface. We present an automated method to tackle this problem in this paper. The determination of best foci of the reference mirror and the test surface is implemented by the astigmatic method based on a modified commercial DVD pickup head embedded in the interference system. The astigmatic method is improved by setting a threshold value in the sum signal to truncate the normalized focus error signal (NFES). The truncated NFES has a monotonic relationship with the displacement of the test surface, which removes the position ambiguity of the test surface during the autofocus process. The developed autofocus system is confirmed experimentally with a dynamic range of 190 μm, average sensitivity of 70 mV/μm, average standard deviation of 0.041 μm, displayed resolution of 4.4 nm, and accuracy of 55 nm. The minimization of the optical path difference of two interference arms is carried out by finding the maximum fringe contrast of the image captured by a CCD camera with the root mean square fringe contrast (RMSFC) function. The RMSFC function, combined with a 4×4 pixel binning of the CCD camera, is recommended to improve the computational efficiency. Experimental tests show that the automated method can be effectively utilized to search for interference fringes in Linnik white light interferometry.