A new approach using a phase-measuring algorithm in detector-width-compensated displacement-measuring interferometer

Abstract

Use of spatial phase measurement techniques in a displacement-measuring grating interferometer using detector width compensation becomes impractical due to the highly sensitive nature of the phase spectrum at the wrapped edges (−π and π) to the noise in the system. A usual unwrapping mechanism to accumulate phase fails to avoid any false jump of phase cycle near these edges and results in unwanted errors in displacement data. A new way of using such algorithms is proposed, which avoids these edges during accumulation of phase and hence reduces errors in displacement measurements. A conventional 90° phase step, four-point algorithm can be used simultaneously with a modified three-point phase algorithm, which gives a similar phase incremental value except the difference in instantaneous phase value. We have implemented this shift in origin to avoid the wrapped edges and have used a sequence of incremental phase values to generate cumulative phase and therefore displacement data by simultaneously using both algorithms in our detector-width-compensated displacement-measuring grating interferometer. Simulation results are introduced to show the usefulness and accuracy of this approach compared to a conventional phase unwrapping mechanism.