On the Fundamental Sensitivity Limit of Incoherent Optical Methods for Full-Field Displacement Measurements

The sensitivity (i.e., the minimum measurable displacement) of incoherent optical methods for full-field displacement measurements [e.g., optical flow (OF) and digital image correlation (DIC)] is essentially limited by the bit depth of the digital camera due to the quantization with round-off errors. The sensitivity limit has been recently exceeded by a multipixel averaging method, achieving super-sensitivity. However, a critical question has not been answered: Is there a limit to the achieved super-sensitivity? In this work, we investigate the fundamental sensitivity limit regardless of the involved signal-processing algorithms. Specifically, we derive the Cramér-Rao lower bound (CRLB) on the variance of displacement estimators, that is, the minimum value of the variance that may be attained by any unbiased estimator. Since the minimum standard deviation (SD) of the displacement estimation corresponds to the minimum measurable displacement, the CRLB is suitable to represent the fundamental sensitivity limit. Furthermore, the derived fundamental sensitivity limit is illustrated and validated by theoretical simulations and laboratory experiments, respectively.