Phase microscopes are used throughout the physical, biological, and medical sciences. Applications include the study of electrical activity in neurons and changes in cell growth and dynamics such as those found in cells affected by cancer and viral diseases. Today, several imaging techniques exist to measure phase hifts. But which one is best for your application? Using statistical tools (Fisher information, the Cramer-Rao bound), we have derived a method that allows calculating the phase measurement precision of any linear optical system. The framework is therefore suitable to quantify the influence of aberrations, imaging artifacts, and even the specimen itself. We also derive the best precision achievable using classical states of light, which can serve as a benchmark for designing new and more sensitive phase microscopes. In our manuscript, several common microscopy techniques are compared against this fundamental bound, clearly showing the compromises that are inherent to many of them, especially when imaging strongly contrasted samples. Our results also show that by cleverly manipulating the wavefront of light, a standard phase microscope can be turned into an optimal system that reaches the fundamental limit in measurement precision.
