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Traditional "crossed-grating" moire as well as the newer "sam- pled-grating" (scanning) moire have proved to be effective methods of shape measurement. There is speculation that the moire patterns of a sampled grating, which are due to aliasing, can be modeled with crossed gratings. We compare the two by writing notationally consistent models of each and show that while crossed gratings can correctly predict the frequencies of a sampled grating, they cannot correctly predict the am- plitudes. Our sampled-grating model is a new formulation that accounts for multiple stages of sampling and transmission. We show how neglect- ing multiple stages can lead to mistakes in moire analysis. We demonstrate our models with an experiment using a digital imaging system. Subject terms: moire patterns; aliasing; scanning moire; digital imaging; crossed gratings; sampled gratings; CCD image sensors; Nyquist sampling theorem; image processing.

Sampled-grating and crossed-grating models of moire patterns from digital imaging