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Journal ArticleDOI

How to measure the Mueller matrix of liquid-crystal cells

09 Oct 2001-Measurement Science and Technology (IOP Publishing)-Vol. 12, Iss: 11, pp 1938-1948
TL;DR: In this paper, a Mueller-matrix spectrometer was constructed to perform fast, dynamic measurements of the Mueller matrix of small areas of liquid-crystal cells throughout the visible range, which can be used for comparison with theoretical calculations, the determination of material parameters and modelling of the cell as an optical building block for technological use.
Abstract: The Mueller matrix is the transfer matrix in the Stokes algebra that describes the polarization of natural light. This matrix is very versatile for the task of characterizing the optical properties of liquid-crystal cells, since it can be used for comparison with theoretical calculations, the determination of material parameters and the modelling of the cell as an optical building block for technological use. We have constructed a Mueller-matrix spectrometer, with the ability to perform fast, dynamic measurements of the Mueller matrix of small areas of liquid-crystal cells throughout the visible range. To illustrate the potential of the instrument, dynamic measurements on a ferroelectric-liquid-crystal cell are presented and analysed. The optical measurements indicate that there is an asymmetry between the up and the down state, tilted smectic layers and polarization reversal initiated at the boundaries.

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Citations
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Journal ArticleDOI
J. J. Gil1
TL;DR: An objective analysis is carried out of the matricial models representing the polarimetric properties of light and material media leading to the identification and definition of their corresponding physical quantities, using the concept of the coherency matrix, which constitutes a powerful tool for analyzing and exploiting experimental and industrial polarimetry.
Abstract: An objective analysis is carried out of the matricial models representing the polarimetric properties of light and material media leading to the identification and definition of their corresponding physical quantities, using the concept of the coherency matrix. For light, cases of homogeneous and inhomogeneous wavefront are analyzed, and a model for 3D polarimetric purity is constructed. For linear passive material media, a general model is developed on the basis that any physically realizable linear transformation of Stokes vectors is equivalent to an ensemble average of passive, deterministic nondepolarizing transformations. Through this framework, the relevant physical quantities, including indices of polarimetric purity, are identified and decoupled. Some decompositions of the whole system into a set of well-defined components are considered, as well as techniques for isolating the unknown components by means of new procedures for subtracting coherency matrices. These results and methods constitute a powerful tool for analyzing and exploiting experimental and industrial polarimetry. Some particular application examples are indicated.

239 citations

Journal ArticleDOI
TL;DR: These signals are shown not to have a chiroptical origin but rather result from the interactions of linear anisotropies in polycrystalline bodies, which are comprehensible crystal-optical effects that serve to define mesoscale structure.

59 citations

Journal ArticleDOI
TL;DR: This work proposes a simple method, based on the crystal rotation technique and heterodyne interferometry, to simultaneously determine the pretilt angle and cell gap of nematic liquid crystal cells, characterized by the advantages of simplicity of installation, ease of operation, high stability, high accuracy, and high resolution.
Abstract: This work proposes a simple method, based on the crystal rotation technique and heterodyne interferometry, to simultaneously determine the pretilt angle and cell gap of nematic liquid crystal cells. When heterodyne light passes through a nematic liquid crystal cell, the phase retardation given by the characteristic parameters of the cell can be measured accurately by heterodyne interferometry. This phase retardation relates to the pretilt angle, cell gap, and angle of incidence on the cell. By using the measured phase retardations at two incident angles, the pretilt angle and cell gap of the nematic liquid crystal cell can be estimated by numerical analysis. This method is feasible, requiring only two incident angles and prior knowledge of two characteristic parameters—extraordinary and ordinary refractive indices of the liquid crystal. It is characterized by the advantages of simplicity of installation, ease of operation, high stability, high accuracy, and high resolution.

30 citations

Patent
09 Jun 2006
TL;DR: In this paper, a model of the polarization properties of an LCD cell is developed based on estimations of what the physical parameters of the LCD cell (30) are believed to be.
Abstract: Method and apparatus for testing of LCD panels is disclosed. An LCD panel under lest (30) may be mounted to a translatable table (40) between polarization state generator (10) and polarization state analyzer (16). For each location on cell (30) to be tested, a variety of known polarization states (22) are launched through the LCD cell (30) and detected by the polarization state analyzer (16). Electrical signals representative of polarization states are acquired by a computer. Within the computer, a model of polarization properties of the LCD cell (30) is developed based on estimations of what the physical parameters of the LCD cell (30) are believed to be. RMS differences between simulated polarization properties and measured polarization properties are minimized by iteratively refining the modeled physical cell properties, at which point cell thickness and other physical parameters of the LCD cell may be deduced.

30 citations

Journal ArticleDOI
TL;DR: An experimental snapshot Mueller matrix polarimeter based on wavelength polarization coding is used to get a time-resolved description of electric-field-induced fast transition within a ferroelectric liquid-crystal cell.
Abstract: An experimental snapshot Mueller matrix polarimeter based on wavelength polarization coding is used to get a time-resolved description of electric-field-induced fast transition within a ferroelectric liquid-crystal cell. The parameters extracted from experimental Mueller matrices are linked to the molecule director distribution to further determine the average trajectory and the collective behavior of these molecules while they switch over to another state.

26 citations

References
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Journal ArticleDOI
TL;DR: In this article, the Stokes vector S of a light beam that propagates through a linear depolarizing anisotropic medium obeys the first-order linear differential equation dS/dz = mS, where z is the distance traveled along the direction of propagation and m is a 4 × 4 real matrix that summarizes the optical properties of the medium which influence the stokes vector.
Abstract: We extend the scope of the Mueller calculus to parallel that established by Jones for his calculus. We find that the Stokes vector S of a light beam that propagates through a linear depolarizing anisotropic medium obeys the first-order linear differential equation dS/dz = mS, where z is the distance traveled along the direction of propagation and m is a 4 × 4 real matrix that summarizes the optical properties of the medium which influence the Stokes vector. We determine the differential matrix m for eight basic types of optical behavior, find its form for the most general anisotropic nondepolarizing medium, and determine its relationship to the complex 2 × 2 differential Jones matrix. We solve the Stokes-vector differential equation for light propagation in homogeneous nondepolarizating media with arbitrary absorptive and refractive anisotropy. In the process, we solve the differential-matrix and Mueller-matrix eigenvalue equations. To illustrate the case of inhomogeneous anisotropic media, we consider the propagation of partially polarized light along the helical axis of a cholesteric or twisted-nematic liquid crystal. As an example of depolarizing media, we consider light propagation through a medium that tends to equalize the preference of the state of polarization to the right and left circular states.

239 citations

Journal ArticleDOI
TL;DR: A complete and minimum set of necessary and sufficient conditions for a real 4 x 4 matrix to be a physical Mueller matrix is obtained and an additional condition is presented to complete the set of known conditions.
Abstract: A complete and minimum set of necessary and sufficient conditions for a real 4×4 matrix to be a physical Mueller matrix is obtained. An additional condition is presented to complete the set of known conditions, namely, the four conditions obtained from the nonnegativity of the eigenvalues of the Hermitian matrix H associated with a Mueller matrix M and the transmittance condition. Using the properties of H, a demonstration is also presented of Tr(MTM)=4m002 as being a necessary and sufficient condition for a physical Mueller matrix to be a pure Mueller matrix.

212 citations


"How to measure the Mueller matrix o..." refers background in this paper

  • ...The elements of a physically realizable Mueller matrix are subject to the following restrictions, derived by Givens and Kostinski [10] and Gil [11]....

    [...]

  • ...(18) The elements of a physically realizable Mueller matrix are subject to the following restrictions, derived by Givens and Kostinski [10] and Gil [11]....

    [...]

  • ...(iii) An optical component, which can be seen as an average over pure Mueller matrices (without depolarization), is subject to the following restriction [11]:...

    [...]

Journal ArticleDOI
TL;DR: The softmode ferroelectric liquid crystal (SMFLC) effects utilize the electroclinic response of chiral orthogonal smectic phases (A*,B*,E*) in bookshelf geometry.
Abstract: The soft‐mode ferroelectric liquid‐crystal (SMFLC) effects utilize the electroclinic response of chiral orthogonal smectic phases (A*,B*,E*) in bookshelf geometry. The SMFLC cell may be considered a retardation plate with a field controllable optic axis, with a submicrosecond response time, and a wide continuous dynamic range. A great variety of electro‐optic components and devices can be constructed based on the SMFLC effect, many of them adding novel possibilities and challenges for optical design. We discuss in the present paper different combinations of SMFLC cells with retarders and polarizers, giving optical components capable of light and color modulation. Particularly, multiple electroclinic cells in a special constellation have the potentiality to give nearly achromatic full‐modulation light valves, as well as electrically controlled high‐speed color filters, which can be used for simple and compact TV cameras. Reflective single‐cell electroclinic devices are suitable for integration with semiconductors to give high‐speed spatial light modulators and general optical processing components with high contrast and full grey‐scale capability.

87 citations


"How to measure the Mueller matrix o..." refers background in this paper

  • ...Two or three such plates can be combined in such a way that the combination is less wavelength-dependent than are the individual elements [8, 9]....

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Journal ArticleDOI
TL;DR: The Poincaré sphere representation, a geometrical method for solving problems involving the propagation of polarized light through birefringent and optically active media, is applied to several electrooptic liquid crystal problems.
Abstract: The Poincare sphere representation, a geometrical method for solving problems involving the propagation of polarized light through birefringent and optically active media, is applied to several electrooptic liquid crystal problems. The emphasis is on the twisted nematic case, for which the quiescent state solution was given by Mauguin in 1911. The Poincare construction shows that the normal modes for the undeformed twisted nematic layer are slightly ellipticity. polarized and suggests convenient experiments for measuring the ellipticity. For the field-activated state, a construction is indicated as an alternative to matrix-multiplication methods.

79 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present tools to test physical realizability of measured or computed Mueller matrices, i.e., the problem of ensuring that the output degree of polarization does not exceed unity is solved by finding an easily implementable necessary and sufficient condition.
Abstract: Development of simple tools to test physical realizability of measured or computed Mueller matrices is the subject of this paper. In particular, the overpolarization problem, i.e., the problem of ensuring that the output degree of polarization does not exceed unity is solved by finding an easily implementable necessary and sufficient condition. With G being the Lorentz metric, it states that a given matrix M is not overpolarizing if and only if the spectrum of GM T GM is real and an eigenvector associated with the largest eigenvalue is a physical Stokes vector. This result is used to characterize some M classes of special interest, and is used to test several examples from recent literature.

72 citations


Additional excerpts

  • ...The elements of a physically realizable Mueller matrix are subject to the following restrictions, derived by Givens and Kostinski [10] and Gil [11]....

    [...]

  • ...(18) The elements of a physically realizable Mueller matrix are subject to the following restrictions, derived by Givens and Kostinski [10] and Gil [11]....

    [...]