Far-field modeling of Moiré interferometry using scalar diffraction theory

A far-field model of Moiré Interferometer (MI) using the mode decomposition method is proposed using the analytical formulation of the scalar diffraction theory. The wave propagation within the defined MI far-field domain is solved analytically for a single frequency surface relieved grating structure, following the Rayleigh-Sommerfeld formulation under the paraxial approximation. It is shown that the electrical field solution of the single frequency grating structure follows the linear relationship in the spatial frequency domain. Furthermore, we show that the far-field electrical field and the intensity interferogram can be calculated using the mode deposition method. A series of MI interferograms is obtained from the Finite Element Analysis (FEA) deformation field using chirp-z transform and inverse chirp-z transform. By performing strain extraction using Continuous Wavelet Transform (CWT), the simulated interferograms are validated and matched against the FEA deformation field. It is concluded that the proposed far-field modeling of MI is accurate and computationally efficient. The proposed method can help design high resolution and high sensitivity MI and interpret complex MI interferogram patterns.