Estimation of Degree of Polarization in Low Light Using Truncated Poisson Distribution

The Degree of Polarization (DoP) of a light beam inside a medium contains unique information about the medium. 3D imaging techniques constitute an optimal procedure for determining the DoP under low light conditions, as the computational reconstruction process can increase the signal-to-noise ratio of the detected light. The definition of the DoP contains a division by the total number of detected photons from the sensor. However, under photon starved conditions, the number of detected photons at a single time period may be equal to zero. This may pose a division by zero problem for the computation of DoP. In this work, we consider a truncated Poisson distribution to overcome this problem and show that the mean value of the computed DoP goes to zero independently of the state of polarization of the light. The validity of our approach is verified by capturing the light fields of a test object to compute its DoP under low light conditions. The formulae derived in this work can be used to correct the deviation of the mean value of the DoP with respect to the ideal measurements.