Statistical theory of digital interferometry: A tutorial with applications to fringe projection profilometry

Abstract

The signal-to-noise ratio (SNR) and Shannon information (SI) are crucial concepts in statistical communication theory (SCT). Understanding their relation has been crucial for the exponential increase of communication speed during the past 70 years. However, these concepts remain essentially unexplored in the context of digital interferometry (DI). This is despite DI uses common concepts with SCT such as quadrature filtering for phase demodulation. In this tutorial, we show the relevance of SNR and SI for DI, and the utility of these figures of merit when assessing phase demodulation algorithms and techniques. The statistical theory of DI presented is independent of the experiment used to obtain the fringe patterns. These fringe images may come from optical shop testing, speckle interferometry, digital holography, microscopy interferometry, isochromatic-stress, fringe projection profilometry (FPP), Talbot deflectometry, etc. Particularly, here we show that dual-sensitivity phase measurement produces a significantly higher SI entropy versus increasing only the SNR on low-sensitivity FPP. Our claims are supported by mathematical analysis, numerical simulations, and experimental results.