Algorithm immune to tilt phase-shifting error for phase-shifting interferometers

Abstract

As a phase shifter usually suffers from both translational and tilt-shift errors during shifting, so every pixel in the same interferogram will have a different phase-shift value. Thus nonlinear phase-measurement errors cannot be avoided, but even translational-shift error has been corrected effectively. However, based on the fact that the shifted phases of all the pixels in the same interferogram remain on the phase-shift plane, by defining this plane one can eliminate a significant number of phase errors. A new algorithm that is immune to both translational- and tilt-shift errors in a phase shifter for phase-stepping interferometers is presented. A first-order Taylor series expansion replaces the nonlinear equations for defining the phase-shift plane, and iteration of the algorithm guarantees its accuracy. Results of a computer simulation show that phase-measurement errors caused by both translation- and tilt-shift error can be compensated for completely, even when the tilt-shift error is not more than ?1%.

Phase-shifting interferometry based on induced vibrations

“…These methods assume that the phase-steps are constant for all pixels in one interferogram but typically different between interferograms. If the phase-shifter introduces non-uniform phase-shift steps along the aperture, this assumption is not longer valid and appears a tilt-shift error [5][6][7][8]. This situation usually appears when the phase-shifter -typically a PZT device-has orientation errors during the shift.…”

“…Several methods have been proposed to eliminate the tilt-shift error. In Ref [5]. an algorithm immune to both translational and tilt-shift errors is presented.…”

“…The mentioned methods [5][6][7][8] are not directly applicable in the case of a measuring system with severe mechanical vibrations. The method presented in Ref [5].…”

“…The method presented in Ref [5]. is based on a first order Taylor approximation of the tilt-shift errors so it is assumed that these tilt-shift errors are small compared with the problem phase.…”

“…If the phase-shifting error is large compared with the problem phase, the size of processing blocks must be very small and therefore the result of the iterative self-calibration algorithm can be not trustful. In presence of severe vibrations, a new problematic that appears and that cannot be solved with any of the methods exposed above [3][4][5][6][7][8] is the phase-error introduced by the movement of the camera. Note that if these vibrations introduce a camera movement the corresponding interferogram pixels will not match.…”