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.

信噪比 (SNR) 和香农信息 (SI) 是统计通信理论 (SCT) 中的重要概念。了解它们的关系对于过去 70 年来通信速度的指数级增长至关重要。然而，在数字干涉测量 (DI) 的背景下，这些概念基本上仍未得到探索。尽管 DI 使用 SCT 的常见概念，例如用于相位解调的正交滤波。在本教程中，我们将展示 SNR 和 SI 与 DI 的相关性，以及在评估相位解调算法和技术时这些品质因数的效用。DI 的统计理论与用于获得条纹图案的实验无关。这些条纹图像可能来自眼镜店测试、散斑干涉测量、数字全息、显微镜干涉测量、等色应力、条纹投影轮廓仪 (FPP)、Talbot 偏转法等。特别是，在这里我们展示了双灵敏度相位测量产生显着更高的 SI 熵，而仅在低灵敏度 FPP 上增加 SNR。我们的主张得到了数学分析、数值模拟和实验结果的支持。