Abstract
While several analyses of polarimeter noise-reduction have been published, little data has been presented to support the analytical results, particularly for a laser polarimeter based on measurements taken at discrete, independent rotation angles of two birefringent waveplates. This paper derives and experimentally demonstrates the reduction of both system and speckle noise in this type of laser polarimeter, achieved by optimizing the rotation angles of the waveplates by minimizing the condition numbers of the appropriate matrix equation. Results are demonstrated experimentally in signal-to-noise ratio (SNR) variations for a range of materials and spatial bandwidths. Use of optimal waveplate angles is found to improve the average SNR of the normalized Mueller matrix over speckle by a factor of up to 8 for a non-depolarizing material, but to provide little improvement for a depolarizing material. In the limit of zero spatial bandwidth, the average SNR of the normalized Mueller matrix over speckle is found to be greater than one for a non-depolarizing material and less than one for a depolarizing material.
Highlights
IntroductionA well-known method for measurement of an object’s Mueller matrix utilizes a polarized (typically laser) source, two polarizers (typically crossed linear analyzers), and two birefringent waveplates or retarders (typically quarter-wave retarders) in series with the object and an irradiance detector
A well-known method for measurement of an object’s Mueller matrix utilizes a polarized source, two polarizers, and two birefringent waveplates or retarders in series with the object and an irradiance detector
For depolarizing materials the relative polarization state between two pixels varies randomly between different PSG and PSA states For depolarizing materials, solving the matrix equation (Eq 2.7) provides no more information than is present in a single frame, and results in noise amplification since in no norm are the condition numbers small enough that the error is propagated in a 1:1 ratio
Summary
A well-known method for measurement of an object’s Mueller matrix utilizes a polarized (typically laser) source, two polarizers (typically crossed linear analyzers), and two birefringent waveplates or retarders (typically quarter-wave retarders) in series with the object and an irradiance detector. Extrapolating speckle data to the limit of zero receiver bandwidth, i.e., a single speckle on the detector, we find that the Mueller-averaged SNR over speckle can be larger or smaller than the classical result (SNR = 1) for the polarized-intensity SNR over speckle, [9] depending on whether the material is non-depolarizing or depolarizing, respectively This result is explained with reference to video of speckle patterns as seen through the modulated polarimeter
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