Incomplete active polarimetry: Measurement of the block-diagonal scattering matrix

Fully tunable active polarization imager for contrast enhancement and partial polarimetry

“…It is thus necessary to determine which couples of polarization states allow extraction of the desired coefficients of the Mueller matrix with optimal precision. This issue has been addressed theoretically in such works as [19,30]. We will, in the following, investigate how a polarimetric imager with full degrees of freedom can further improve acquisition of partial polarimetric information.…”

“…Several authors have tried to optimize the condition number of the matrix Q T;S to minimize error propagation during this inversion [19,30]. Indeed, the condition number of a matrix measures the sensitivity of the solution of a system of linear equations to errors in the data.…”

“…[19] presented a way to optimally extract the nonzero components of a block-diagonal Mueller matrix of the form 13 using only eight acquisitions. This interesting result has been obtained by optimizing the PSG configurations and using the Stokes imaging system in analysis.…”

“…We consider that this Stokes imaging system uses the four optimal states that allow minimization of errors due to propagation of the noise when inverting the measures [9]. According to [19], the two optimal PSG states are (79.8°,14.7°) and (−42.5°,37.6°) (azimuth and ellipticity). The condition number of the matrix Q Ω T;S associated with these states is 6.9.…”

“…However, these images have to be acquired with illumination and analysis states that depend on the scene and may lie anywhere on the Poincaré sphere. In other cases, it may be sufficient to extract only partial information, such as particular coefficients or set of coefficients of the Mueller matrix [18,19]. In such applications, the fixed states adapted to acquisition of the whole Mueller matrix may not be optimal for acquiring the required information with a minimum number of measurements.…”