Precision analysis and low-light-level measurements using a prototype four-detector photopolarimeter (FDP)

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Abstract
A given uncertainty of the output current vector of the FDP leads to a corresponding uncertainty in the determination of the Stokes vector of incident light. Using an FDP instrument matrix measured free from imperfections in the calibration optics, and for a preset level of error for each current, the root-mean-square errors (RMSE) of the three normalized Stokes parameters (NSPs) are calculated as functions of the state of polarization of an assumed totally polarized incident beam. Experimental results are also presented that show the effect of reducing the power level of a light beam (from ∼0.2 mW to <60 nW, an attenuation range of 35 dBs) on the precision with which the NSPs are measured. The RMSE of each NSP is virtually independent of attenuation over an initial range of two decades and rises subsequently. However, it is the digitization (or quantization) error of the 12-bit analog-to-digital converter that sets the limit on precision in our FDP. The accuracy with which the NSPs are measured is also essentially independent of light level, provided that the adjusted operational-amplifier gains are correctly accounted for. The ability of our prototype FDP to resolve small changes of the state of polarization of light is tested directly by introducing known deliberate perturbations around several input states. Polarization states that are separated by 0.1° on the Poincaré sphere are found to be resolvable with an uncertainty of ∼0.03°.