April 2, 2020
by Abhijit Marar
Cramer-Rao Lower Bound (CRLB) calculations for self-interference digital holography (SIDH):
Since developing an instrument for performing localization-based microscopy using SIDH, we decided it would be useful to do a simple calculation of the CRLB of SIDH systems. This calculation provides the lower bound limit with which the position of the emitter can be estimated. This quantity is useful because (1) it serves as a benchmark to which the precision provided by a particular estimator can be compared, thus indicating how much room there might be for improvement, and (2) by calculating the quantity for a particular estimator under different experimental conditions, the lower bound helps in designing experiments where various parameters of the optical setup can be varied to achieve the desired level of precision. The CRLB is determined by calculating the Fisher information matrix which is a quantity that provides a measure of the amount of information the data contains about the parameter being estimated. The precision with which a parameter can be estimated is directly proportional to the amount of information the collected data contains about the parameter.
We have finished our calculations for two different SIDH configurations, and we are currently in the process of revising the manuscript.