Correction of Errors in Polarization Based Dynamic Phase Shifting Interferometers

Polarization based interferometers for single snap-shot measurements allow single frame, quantitative phase acquisition for vibration insensitive measurements of optical surfaces and have been successfully used on a variety of interferometer types. This technique generally involves the simultaneous acquisition of three or more images on the same camera or multiple cameras, which are phase shifted by polarization. Examples of these types of systems would include the multiple camera system of Smythe and Moore [1], and more recently, systems utilizing a micro-polarizer phase mask [2] on a single camera. Application of these polarization based phase sensors requires the test and reference beams of the interferometer to be orthogonally polarized. As with all polarization based interferometers, these systems can suffer from phase dependent errors resulting from systematic polarization aberrations; this is especially true in high numerical aperture systems. This type of measurement error presents a particular challenge because it varies in magnitude both spatially and temporally between each measurement. It typically manifests as “fringe print-through” where a small component of the intensity fringe pattern appears in the measured surface. In this paper, a general discussion of phase calculation error presented. We then present an algorithm that is capable of mitigating phase-dependent measurement error on-the-fly. The algorithm implementation is non-iterative providing sensor frame rate limited phase calculations. Finally, results are presented for both a high numerical aperture system, where the residual error is reduced to the shot noise limit, and a system with significant birefringence in the test arm.