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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

AbstractThe 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.

Topics: Mueller calculus (73%), Stokes parameters (58%), Transfer matrix (54%), Polarization (waves) (53%)

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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.

218 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.
Abstract: It is well-known that circular dichroism (CD) measurements of anisotropic media may contain artifacts that result from mixed linear anisotropies. Such artifacts are generally considered a nuisance. However, systematic artifacts, carefully measured, may contain valuable information. Herein, polycrystalline spherulites of D-sorbitol grown from the melt were analyzed with a Mueller matrix microscope, among other differential polarization images devices. As spherulites grew into one another they developed strong apparent optical rotation and CD signals at the boundaries between spherulites. These signals are shown not to have a chiroptical origin but rather result from the interactions of linear anisotropies in polycrystalline bodies. Such chiroptical artifacts should not be dismissed reflexively. Rather, they are comprehensible crystal-optical effects that serve to define mesoscale structure.

48 citations


Patent
09 Jun 2006
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: 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.

26 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.

23 citations


References
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Journal ArticleDOI
Abstract: A general symmetry argument is presented, and experiments on newly synthesized p-decyloxybenzylidene p'-amino 2-methyl butyl cinnamate are described, demonstrating that chiral smectic C and H liquid crystals are ferroelectric. Some of the properties of this new class of ferro-electrics are discussed.

1,312 citations


Journal ArticleDOI
Abstract: Part IV is divided into two sections. The first is devoted to some additions to the general theory developed in Part I, and the second section to the derivation of the matrices representing two optical elements which were not treated in Parts II and III: (1) plates possessing circular dichroism, and (2) plates cut from crystals of such low symmetry that the principal axes of absorption and refraction are not parallel. In case (2), the discussion is limited to monoclinic and triclinic crystals which do not possess optical activity.

1,290 citations


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

  • ...The Jones algebra is adequate for coherent and monochromatic light, whereas the Stokes algebra is better for natural light, which mostly is incoherent, polychromatic and unpolarized....

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  • ...We then have the choice between the Jones [1] and the Stokes [2] algebra for the description of the polarization....

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Journal ArticleDOI
Abstract: We present an algorithm that decomposes a Mueller matrix into a sequence of three matrix factors: a diattenuator, followed by a retarder, then followed by a depolarizer. Those factors are unique except for singular Mueller matrices. Based on this decomposition, the diattenuation and the retardance of a Mueller matrix can be defined and computed. Thus this algorithm is useful for performing data reduction upon experimentally determined Mueller matrices.

1,064 citations


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

  • ...The general partial polarizer P , a diattenuator, is given by the following 4 × 4 matrix (see [6]):...

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  • ...A good reference article about polarimetry and the Mueller matrix has been written by Chipman [5]....

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  • ...This factorization has been shown earlier by Lu and Chipman [6]....

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Journal ArticleDOI
TL;DR: Mise en evidence de the structure par des etudes de diffusion de rayons X haute resolution d'echantillons minces smectiques C prepares entre deux lames solides par refroidissement a partir de the phase smectique A.
Abstract: Mise en evidence de la structure par des etudes de diffusion de rayons X haute resolution d'echantillons minces smectiques C prepares entre deux lames solides par refroidissement a partir de la phase smectique A

438 citations


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

  • ...This tilt determination usually requires x-ray measurements [3]....

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Book ChapterDOI
01 Jul 2009
Abstract: W hen a stream of polarized light is decomposed into two streams which, after having been modified in a slightly different manner, are reunited, the mixture is found to have acquired properties which are quite distinct from those of the original stream, and give rise to a number of curious and apparently complicated phenomena. These phenomena have now, however, through the labours of Young and Fresnel, been completely reduced to law, and embraced in a theory, the wonderful simplicity of which is such as to bear with it the stamp of truth. But when two polarized streams from different sources mix together, the mixture possesses properties intermediate between those of the original streams, and none of the curious phenomena depending upon the interference of polarized light are manifested. The properties of such mixtures form but an uninviting subject of investigation; and accordingly, though to a certain extent they are obvious, and must have forced themselves upon the attention of all who have paid any special attention to the physical theory of light, they do not seem hitherto to have been studied in detail. Were the only object of such a study to enable us to calculate with greater facility the results obtained by means of certain complicated combinations, the subject might deservedly be deemed of small importance.

402 citations