Interpretation of visible moiré between repetitive periodic-like gratings in the image domain

An image domain approach to the interpretation of visible moiré phenomena in repetitive grating multiplicative superposition has been proposed. The local frequency method provides the instantaneous period and orientation of generated moiré. These parameters of the moiré have been sorted into real and pseudo patterns by the Fourier expansions analysis. With the combination of these two steps, the concept "equivalent period contribution threshold" has been introduced. It is found that different thresholds bring different integral domains and results for the calculation of average intensities of generated moiré waveforms. This proves that different thresholds would introduce different average intensity distribution (macrostructure effects) in different moiré patterns. With the local intensity variation (microstructure effects), the human eye would confuse different macrostructure effects but only consider them the same. The interpretation is that the macrostructure versus microstructure effects garble discernment of the human eye and result in different visible moiré phenomena. This is significant for visible moiré effects in various repetitive grating (both of cosinusoidal and binary patterns) superpositions in the image domain. It also presents and summarizes the coexistence of real and pseudo moirés in repetitive, periodic-like layer superposition.