A multiplicative analogical moiré phase-shifting Twyman-Green technique for Nd:YAG rod wavefront distortion measurement

Abstract

Nd:YAG rod wavefront distortion has been quantified in a Twyman-Green interferometer which employs the multiplicative analogical moiré phase-shifting method for demodulation. The measuring procedure is based on the superimposition of a transmission grating located outside the interferometric module with a phase modulated high-frequency Twyman-Green spatial carrier. Later, a set of fringe patterns, provided by low-pass filtering of the phase-shifted multiplicative moiré patterns obtained, is combined in a generic phase-shifting algorithm (GPSA). The interesting test information is achieved once the previous procedure has been carried out with and without the transparent object located in the measuring area. The wavefront distortion (WFD) is calculated by the subtraction of these results provided by the GPSA, or directly if a differential phase-shifting algorithm (DPSA) is employed. The WFD obtained is in accordance with characteristics of the test object. The comparison of the results obtained with both families of algorithms provides information about the sensitivities to error sources of the DPSA employed. A first approximation to the analysis of significant error sources of DPSAs is presented.

Error behaviour in differential phase-shifting algorithms

“…Several papers 12,18,19 have been devoted to the accuracy and sensitivity of PSAs whereas DPSAs are also hardly without studying. 5,20 The accuracy of difference phase evaluation is determined by two error classes mixed in practice: systematic errors and random errors. Systematic errors should be estimated by theoretical and numerical studies while random errors can be directly calculated by experimental analysis.…”