Optimization of a dual-rotating-retarder Mueller matrix polarimeter

Smith, Matthew H.

doi:10.1364/ao.41.002488

Cited by 178 publications

(113 citation statements)

References 12 publications

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“…In practical situations, the modulation matrix has to be measured once the optics and the modulation scheme have been defined [14,16,17,20,21]. As a consequence, one expects the elements of the modulation matrix to have some uncertainty produced by the measurement procedure.…”

Section: Error Propagationmentioning

confidence: 99%

“…This is an important issue that has been partially treated in the past, either considering how the uncertainty in the measurement of I out propagates to the demodulated Stokes vector when the modulation matrix is perfectly known [13,14] or taking into account uncertainties in the knowledge of the modulation matrix, though the full covariance matrix is not obtained [15,16]. Many papers also deal with how error is propagated in non-ideal Mueller matrix polarimeters [17,18] while others consider the optimization of such polarimeters [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Error propagation in polarimetric demodulation

Ramos

Collados

2008

Appl. Opt.

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The polarization analysis of the light is typically carried out using modulation schemes. The light of unknown polarization state is passed through a set of known modulation optics and a detector is used to measure the total intensity passing the system. The modulation optics is modified several times and, with the aid of such several measurements, the unknown polarization state of the light can be inferred. How to find the optimal demodulation process has been investigated in the past. However, since the modulation matrix has to be measured for a given instrument and the optical elements can present problems of repeatability, some uncertainty is present in the elements of the modulation matrix and/or covariances between these elements. We analyze in detail this issue, presenting analytical formulae for calculating the covariance matrix produced by the propagation of such uncertainties on the demodulation matrix, on the inferred Stokes parameters and on the efficiency of the modulation process. We demonstrate that, even if the covariance matrix of the modulation matrix is diagonal, the covariance matrix of the demodulation matrix is, in general, non-diagonal because matrix inversion is a nonlinear operation. This propagates through the demodulation process and induces correlations on the inferred Stokes parameters.

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Section: Error Propagationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Error propagation in polarimetric demodulation

Ramos

Collados

2008

Appl. Opt.

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“…Sabatke et al [136,137] derived the optimal configurations for a rotating retarder Stokes polarimeter using the condition number and related metrics in relation to the Singular Value Decomposition, and showed that there are two ways to inscribe the regular tetrahedron in the Poincaré sphere. Smith [138] optimized the dual rotating retarder…”

Section: 8: Conclusionmentioning

confidence: 99%

“…An optimal trajectory enclosing a regular tetrahedron was identified for exactly two retardances: 132° and 228°. Tyo showed that for two degrees of freedom (such as a dual variable retarder Stokes polarimeter) the trajectory forms a twodimensional surface on the Poincaré sphere, giving a continuum of optimum configurations in which the tetrahedron may be inscribed [138]. [136] that additional measurements "fill out" the trajectory, which in the presence of error does result in improved accuracy, but (at least in the case of independent identically distributed "random" measurement noise) a similar improvement would be obtained by taking additional measurements at the original four orientations and averaging.…”

Section: 6: Geometrical Interpretationmentioning

confidence: 99%

GDx-MM: An Imaging Mueller Matrix Retinal Polarimeter

Twietmeyer

2007

Frontiers in Optics 2007/Laser Science XXIII/Organic Materials and Devices for Displays and Energy Conversion

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“…These criteria are important as they emphasize the uniqueness of the system described in this dissertation. For this section, measurement strategies are discussed in terms of their components, and include systems based on rotating polarizers [64,65], rotating retarders [66][67][68][69][70][71], photoelastic modulators (PEMs) [72][73][74][75][76][77], birefringent uniaxial crystals [78][79][80][81][82], polarization gratings (PGs) [83][84][85], and variable retardance devices [2, 10, 11, 13-15, 17, 18, 51, 60-63, 86-98].…”

Section: Measurement Strategiesmentioning

confidence: 99%

Revealing Structural Organization with Liquid Crystal-based Spectral Imaging Polarimetry

Gladish¹

2000

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Structural organization refers to the particular ordering of scatterers. Probing structural organization by imaging polarized spectral scatter provides insight into the composition of a medium, and can aid in remote sensing, the identification of tissue pathologies, and material characterization and differentiation. The vector nature of polarized light enables it to interact with optical anisotropies within a medium, while the spectral aspect of polarization is sensitive to small-scale structure. However, many polarization studies have limitations, as they provide qualitative image analysis, incomplete anisotropy information, or both. The ability to image the effects of anisotropy and small-scale structure at multiple wavelengths is key for parameterizing structural organization. The Stokes/Mueller formalism is a framework that quantifies a medium's complete spectral polarization response, and allows for the parameterization of structural organization. Additionally, advances in liquid crystal (LC) technology have resulted in new polarimetric devices. These computer-controlled devices impart spectral polarization effects on the millisecond timescale with no mechanically moving hardware, providing the ability for making rapid polarimetric measurements. This dissertation describes a methodology for revealing structural organization by exploiting the Stokes/Mueller formalism and by utilizing measurements from a spectral imaging polarimeter constructed from variable retardance LC devices, such as liquid crystal variable retarders (LCVRs) and a liquid crystal tunable filter (LCTF).The methodology includes developing the system, the Stokes/Mueller model, and all i of the procedures, calibrations, and data interpretation. Developing the system also consists of component and system calibration, a system sensitivity and performance analysis, and finally test measurements for system validation. The final validation measurement is made on a mineral sample for inferring structural organization.ii DedicationIn memory of my father, Jim Gladish.iii Acknowledgments

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Optimization of a dual-rotating-retarder Mueller matrix polarimeter

Cited by 178 publications

References 12 publications

Error propagation in polarimetric demodulation

Error propagation in polarimetric demodulation

GDx-MM: An Imaging Mueller Matrix Retinal Polarimeter

Revealing Structural Organization with Liquid Crystal-based Spectral Imaging Polarimetry

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