Towards a statistical theory of digital interferometry: a tutorial with applications to fringe projection profilometry

Abstract

The signal-to-noise ratio (SNR) and Shannon’s channel capacity are two of the main figures of merit in statistical communication theory (SCT). Understanding their relation has been crucial for the exponential increase of communication speed observed 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 and phase demodulation. Therefore, our purpose in this tutorial is to show the importance of Shannon information theory for DI. Particularly, we believe that the SNR gain is a very useful figure of merit when comparing phase-demodulation algorithms. We also show that dual-sensitivity phase unwrapping produces significantly higher Shannon’s entropy versus increasing only the SNR on low-sensitivity phase measurements. Our claims are supported by mathematical analysis, numerical simulations and experimental results.