Quantitative analysis of the contrast modulation for multilateral shearing interferometers

Multilateral shearing interferometers (multi-LSIs) utilize the phase difference information of multiple shear directions with high accuracy and strong noise resistance. However, the interferogram fringe contrast of multi-LSIs can reverse due to the effect of contrast modulation, leading to incorrect measurement result. This issue has lacked comprehensive quantitative research to effectively guide the elimination of its effects. In this work, a quantitative analysis of the contrast modulation is proposed. This paper rigorously derives contrast modulation function, analyzing the effect of aberration and shear ratio on it. It is the first time that a quantitative theoretical model of aberration measurement range and shear ratio has been established, offering guidance in practical application for precise shear ratio adjustment to eliminate modulation effect and extend measurement range. By eliminating modulation effects, phase difference information from multiple directions can be effectively utilized, maximizing the benefits of multi-LSIs. In simulation and experiment, the distribution of fringe contrast reversal bands and the variation of aberration measurement range with shear ratio are consistent with theoretical analysis, which verifies the validity of the proposed approach. This approach aims to address the issue of interferogram fringe contrast inversion caused by modulation in multi-LSIs, providing a theoretical basis and practical guidance for precise measurement.