Analysis of Moiré pattern for parallel binary gratings based on AND and OR operators

Abstract

A method for analyzing the Moiré pattern of a parallel binary grating based on the high-frequency component of the omitted pattern is proposed. The analysis aims to investigate the signal components that influence the dark-light band formation of the Moiré pattern. The analytical technique begins with the consideration that both grating patterns are a set of binary rectangular signals with two signal level values, “0” and “1.” Subsequently, Fourier series expansion of these two sets of signals was performed considering the frequency, initial phase, and duty cycle of the signals. The superposition of both input signals relies on algebraic equations equivalent to AND and OR operators. The final step was to eliminate the effect of the high-frequency component, which is analogous to the low-pass filter of the electronic circuit (based on averaging the signal intensity per image length). If the frequencies of the two gratings are equal, the analysis based on both operators provides an output signal depending on the initial phase (placement position) and duty cycle values. If the frequencies of the two gratings are not equal, the analysis results show that the output signal has a frequency equal to the frequency difference between the two signals. Moreover, if the two input gratings had a duty cycle of 0.5, the overlapping resulted in a triangular shape. The results from the computer program to simulate the AND and OR operators were consistently compared to the plots of the analytical equations. In addition, they are compatible with image processing results.