Proceedings Volume 2265

Polarization Analysis and Measurement II

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Proceedings Volume 2265

Polarization Analysis and Measurement II

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Volume Details

Date Published: 14 September 1994
Contents: 7 Sessions, 50 Papers, 0 Presentations
Conference: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation 1994
Volume Number: 2265

Table of Contents

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Table of Contents

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  • Advances in Polarimetry
  • Polarization of Optical Elements and Materials I
  • Polarization Analysis
  • Poster Session
  • Polarization Analysis
  • Polarization of Optical Elements and Materials II
  • Poster Session
  • Astronomy and Remote Sensing
  • Mathematics of Polarization and Scattering
  • Poster Session
  • Astronomy and Remote Sensing
Advances in Polarimetry
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Standard polarization components: progress toward an optical retardance standard
Kent B. Rochford, Paul A. Williams, Allen H. Rose, et al.
NIST is developing a quarterwave linear retarder designed to have a retardance stable within 0.1 degree(s) over a variety of operational and environmental conditions. In this paper we review several design strategies and early results of this effort. These have led to a promising prototype design consisting of a double rhomb TIR retarder constructed from a low stress- optic glass. We also review several measurement methods that are used in our evaluations.
Principal angles and principal azimuths of an in-line symmetric three-reflection bare-mirror system: application to circular polarization of VUV radiation
Ayman Mohammed Kan'an, Rasheed M. A. Azzam
Contours of constant principal angle (Phi) and constant principal azimuth (Psi) for an in-line, symmetric, three-reflection mirror system are presented. The three mirrors are assumed to use uncoated substrates of the same homogeneous isotropic material with complex relative dielectric function (epsilon) . By assigning values to (Phi) from 45 degree(s) to 85 degree(s), the constraint on complex (epsilon) is determined numerically and represented graphically. The special case of (Phi) - 45 degree(s), which applies to a right-angle parallel-mirror beam displacer, permits an analytical solution. These results have important applications for the production of circular polarization over the entire spectrum, and especially in the VUV where transmission-type devices are not possible. The performance of the three-mirror system as a VUV quarter-wave retarder/circular polarizer using different methods is also considered.
Polarization alignment of polarization maintaining fiber using coherent detection
A new method of polarization alignment into PM fiber based on electronic coherent detection is presented. The electric field resulting from interference between the polarization eigenmodes of a PM fiber at a linear polarizer when the light coupled into the fiber is amplitude modulated is solved for. The results of polarization alignment experiments using a current modulated laser diode are compared with the theory. Even though current modulation of a laser diode produces a complicated electric field, it is shown that the measurements made in the experiments agree well with the simple model. The new method is used to align the input to a PM fiber coupler with a polarization extinction ratio (PER) of 25 dB (limited by coupler crosstalk) and to align into a 1 km long PM fiber with a PER of 20 dB (limited by fiber crosstalk).
Fast imaging polarimetry with precision universal compensator
Guang Mei, Rudolf Oldenbourg
A new type of imaging polarimeter for fast and orientation independent measurement of birefringent fine structures is proposed. The new imaging polarimeter was implemented as a polarized light microscope incorporating a precision universal compensator made of two electro-optic modulators. A video camera and computer-assisted image analysis system provide fast measurements of optical anisotropy (retardance magnitude and azimuth) in the specimen at ALL POINTS of the image constituting the field of view. The images document fine structural and molecular organization within a thin optical section of the specimen. The sensitivity of the current instrument is 0.1 nm of specimen retardance, measured in 0.43 seconds at all 640 X 480 image points. Examples of measurements of birefringent fine structures are presented.
Spatiotemporal strain distribution mapping using novel optical heterodyne polarimeter
Kazuhiko Oka, Tomoko Yamaguchi, Yoshihiro Ohtsuka
A novel method for mapping spatiotemporal strain distributions in a photoelastic sample is described. In an optical heterodyne polarimeter developed, a circularly polarized beam of light is transmitted by a photoelastic sample which is being loaded with time, and then photomixed with a local oscillator beam with linearly polarized two-frequency components. The photocurrent generated in a MOS TV camera possesses the two orthogonal filed components of the signal beam transmitted by the sample, from which the spatiotemporal orthogonal principal strains induced in the sample can be determined. No use of mechanically movable components for polarization alignment allows us to follow a rapid change in the strain distribution. The major advantage of this method is that the orthogonal in-plane principal strains and the out-of-plane strain can be determined independently. The spatial and temporal resolutions in the maps are 0.18 mm and 2.9 ms, respectively.
Fiber optic in-line polarimeter: system design and computer-aided analysis
Bernhard Scholl, Jens C. Rasmussen, Hans Juergen Schmitt
This paper describes a polarization analyzer for the determination of the polarization state inside a single-mode fiber. Four different detection points formed by grinding off the cladding on one side of the fiber are used for measurement. A small part of the light is coupled out at these points and is measured by a standard photodetector placed just on top of the polished areas. At each of the detection points, a polarization dependent signal can be obtained. Hence, a relationship between these signals and the polarization at the end of the fiber can be found by calibrating this measurement instrument with a classical off-line polarization analyzer. Concluding we realized a measurement instrument which not only determines the polarization but also can adjust any wanted polarization state at the fiber output of the instrument.
Polariscope using the phase-shifting technique
Two-dimensional birefringence measurement method using phase shifting technique has been already proposed. However, it has some problem that 16 images data are required for one birefringence distribution analysis and that its accuracy is not highly enough. To overcome this problem, the birefringent distribution measurement method using two special phase shifting techniques to reduce the collected images and to get the high sensitivity relative retardation are established. One is a local-sampling phase shifting technique using the Babinet-Soleil compensator as a phase shifter in order to get high sensitivity. The other is using the one-step phase shifting technique for quick birefringence distribution measurement using a birefringence wedge plate. In this method, only 2 images are enough to analyze the two- dimensional birefringence distribution. These experimental procedures and the results that are compared with the Babinet-Soleil compensator and of the optical components are discussed.
Development and calibration of an optical fiber polarimeter
Charles S. Brown, Marcus W. Shute Sr., Diedre D. Williams, et al.
Mueller matrix polarimetry is a powerful technique for the experimental determination of the polarization properties of optical media. However, the technique has only rarely been applied to optical fiber applications. In this paper we describe the development and calibration of an optical fiber polarimeter for the measurement of Mueller matrices of short (approximately 1 meter) samples of single-mode optical fibers (SMF). Since the SMF samples were short, the polarimeter was designed to measure the Mueller matrix elements associated with birefringence only. The Mueller matrices were measured for a straight (no external twist) and externally twisted SMF sample. The technique is shown to offer a straight forward way to identify and characterize the birefringence of SMF with internal and external birefringences.
Polarization of Optical Elements and Materials I
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New method for the determination of the G factor for a spectrophotofluorometer
Edward Collett, Enrique Homar
In modem spectrophotofluorometers diffraction gratings are used to select the excitation and emission wavelengths of fluorescent solutions, respectively. Diffraction gratings, however, are polarization sensitive. In a spectrophotofluorometer the polarization contribution ofthe emission diffraction grating (known as the grating or G factor) must be known. In this paper an analysis of the measurement of the G factor is made using the formalism of the Stokes polarization parameters and the Mueller matrix calculus. The analysis shows that the current method for determining the spectral polarization behavior of the emission diffraction grating (the G factor) assumes the optical source in the cuvette chamber, e.g., a tungsten lamp or a fluorescent solution is unpolarized. In practice, these sources are usually partially polarized. Consequently, for this and other reasons we have developed a new method for obtaining G using a right angle prism placed in the cuvette chamber of the spectrophotofluorometer. The right angle prism has the unique property that it behaves as a perfect retarder and when incident polarized light is reflected from the diagonal surface of the prism the Stokes parameter s is zero. By setting the incident polarizer to +45and then setting the analyzer to the horizontal and vertical directions, respectively, the correct G factor can be determined. In the final part of the paper we describe the
Birefringent characteristics of two new crystalline materials: CeF3 and LaF3
Michael J. Derks, Greg A. Kopp
We present data on two recently available uniaxial crystalline materials, cerium fluoride (CeF3) and lanthanum fluoride (LaF3). The characteristics presented include birefringence, transmission, temperature sensitivity, and field of view for wavelengths from the ultraviolet into the near infrared. Possible applications in polarization dependent devices are discussed. The optical properties of CeF3 and LaF3 are compared with commonly used crystalline materials.
Periodic and quasiperiodic nonquarterwave multilayer coating for 90-deg reflection phase retardance at 45-deg angle of incidence
Mostofa M. K. Howlader, Rasheed M. A. Azzam
All possible solutions for a periodic stack of 10 ZnS-ThF4 bilayers on a Ag substrate that produce 90 degree(s) differential reflection phase shift at 45 degree(s) angle of incidence and 3.39- micrometers wavelength are determined. The angular and wavelength sensitivity of several of these designs is considered. To increase the reflectance, reduce the diattenuation, and improve the sensitivity of the 20-layer reflection quarter-wave retarder (QWR), we also consider quasiperiodic stacks. These designs are obtained by iteration starting from an initial high- reflectance 10-bilayer, non-QWR, periodic structure and adjusting the thicknesses of the two films of the topmost bilayer to realize the desired 90 degree(s) retardance. Again multiple solutions are obtained for each initial design and their angular and wavelength sensitivity are analyzed. It is found that the best sensitivity corresponds to the lowest and nearly equal optical thicknesses of the two films of the topmost bilayer. Performance comparable to that reported in the literature, obtained for more complicated stacks in which the thicknesses of all 20 films are different, are reported.
Fabrication of two-dimensional rough surfaces for light scattering and polarization measurements
The fabrication of characterized rough surfaces on photoresist is described. The technique used here can be separated into tow parts: first, a photoresist coating, generally 5 to 15 microns thick, is deposited on a flat glass substrate and baked in an oven; second, the plate is exposed, one line at a time, by a laser beam in a raster scanning method. Plate displacement is controlled by a PC computer in order to create the desired structure on the photoresist. Several deterministic and randomly rough gratings have been fabricated and characterized with a stylus profilometer.
Polarimetry and scatterometry using a Wollaston polarimeter
A high precision polarimeter based on a dual-beam analyzer prism is capable of polarimetric accuracy's near +0.2% over the visible to near-IR range. Accuracy's were determined using computed Fresnel polarizances from fused silica at several incidence angles. A comparison of polarization measurements made at several different laboratories is presented.
Polarizer uniformity measurements taken with an imaging polarimeter
J. Larry Pezzaniti, Russell A. Chipman, Stephen C. McClain
The objective of this paper is to evaluate four types of polarizers in terms of three criteria: (1) their contrast ration, (2) the uniformity of their contrast ratios across 20 mm apertures, and (3) the uniformity of their transmission axis orientations across 20 mm apertures. The types of polarizers evaluated are calcite Glan-Thompson polarizers, polarizing beam splitters, silver glass polarizers, and stretched polymer polarizers. The measurements are performed with a rotating polarizer imaging polarimeter.
Polarization Analysis
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Fresnel's interface reflection coefficients for the parallel and perpendicular polarizations: global properties and facts not found in your textbook
This paper reviews recently obtained results related to Fresnel's reflection coefficients which play a central role in the optics of light reflection by surfaces and thin films. Topics include conjugate and reciprocal interfaces between transparent media, reflectance matching between normal and oblique incidence, and reflectance switching. For light reflection at interfaces between transparent and absorbing media, contours of constant pseudo-Brewster angle and of constant principal angle are presented in the complex plane, along with a discussion of a condition of maximum minimum parallel reflectance at oblique incidence. Conformal mappings that describe the transformation of the Fresnel coefficients between normal and oblique incidence, and between the s and p polarizations at the same angle, are included. Reflectance for incident light of arbitrary polarization is also considered. Finally, trajectories that describe the evolution of the Fresnel coefficients with angle of incidence are presented.
Progress in polarization ray tracing
Polarization ray tracing is a collection of methods that extend geometrical ray tracing allowing the calculation of the evolution of polarization states along ray paths and the determination of the intrinsic polarization properties, such as diattenuation and retardance, associated with ray paths. This paper compares the suitability of the Jones, Mueller, and 3D polarization ray tracing calculi, examining the issues of local vs. global coordinates, amplitude vs. phase representations, inclusion of the wavefront aberration function, partially polarized light, measurements of images by polarimeters, and diffraction image formation by low and high numerical aperture beams.
Complex-amplitude noise characteristics of analog liquid crystal spatial light modulators
A simple complex-amplitude model is developed and used to establish the behavior of amplitude an polarization state noise. A simple experiment based upon this model shows that the dominate source of noise in a twisted nematic liquid crystal cell results from polarization state fluctuations. A Stokes polarimeter is described and then used to measure the polarization state dynamics of a commercially available liquid crystal modulator.
Ellipsometric measurements applied to liquid crystal display technology
Leonard G. Hale, Donald B. Taber, Eric Schonning, et al.
Variable angle transmission ellipsometry has been used to characterize the various elements of the liquid crystal display (LCD) architecture. Ellipsometric data, which are in the form of polarization ellipses as a function of incident angle, are analyzed using the 2 X 2 extended Jones matrix formalism. Information which can be deduced from the ellipsometric data includes the birefringence, cell gap, twist angle, and pretilt angle of the liquid crystal cell, polarization efficiency of the polarizers, as well as the retardation values of birefringent compensators. The ellipsometric method is capable of complete characterization of the polarization state of the transmitted light.
Poster Session
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Mueller matrix formalism in imagery: an experimental arrangement for noise reduction
Bernard Le Jeune, Jean-Pierre Marie, Pierre-Yves Gerligand, et al.
In polarization imagery, absolute and random errors must be considered, but in most polarimetric setups, absolute errors are due to nonideal retardation plates for the most part. The contributions to random errors come principally from the physical noises of the camera (Shot noise, quantization), and from the laser intensities fluctuations: these can be greatly reduced, and the retardation plates used here must be submitted to a calibration procedure. Sixty four images are digitized and a generalized linear least square fit is calculated. Experimental noise estimations have been made for the polarization system, and so errors estimations of the Mueller parameters have been analytically and experimentally deduced. Experimental results demonstrate the possibility to estimate the level of the noise, and then to obtain a good estimation of the Mueller matrix elements. The matrix can then be used for decompositions which can provide useful information about the studied targets or media.
Polarization Analysis
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Ellipsometric measurements on SiO2 by intensity ratio technique
Yu-Faye Chao, C. S. Wei, Wei-Te Lee, et al.
A PSA photometric ellipsometric technique is used to measure the ellipsometric parameters, (psi) and (Delta) . Taking intensity ratios of A equals I((pi) /4+dp,dA)/I((pi) 4+dp/,(pi) 2+dA) and B equals I(-(pi) /4+dp,dA)/I(-(pi) /4+dp,(pi) /2+dA) to their first order approximation under small azimuth deviations of polarizer (dp) and analyzer (dA), we find that at fixed dA these two ratios have opposite gradient with respect to dp and intersect to each other at a special dp where Aequals B EQ tan2(psi) , and the position of this dp is linearly related to cos (Delta) . For comparison, (psi) and (Delta) of a SiO2/Si thin film are measured by conventional null ellipsometry and intensity ratio technique. An higher percentage error on (Delta) is expected for this PSA system. The source of errors will be discussed.
Polarization of Optical Elements and Materials II
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Modulated interference effects: use of photoelastic modulators with lasers
When photoelastic modulators (PEMs) are used with lasers as light sources, modulated interference effects may occur. Interference which occurs due to the reflection of light at the surfaces of the PEM optical element is modulated because the surfaces of the optical element are in relative motion synchronized with the oscillations of the modulator. Since the modulated interference frequencies are exactly the same as the polarization modulation frequencies being studied, they can be very troublesome. This paper will describe these effects quantitatively, give a simple test for their existence in an optical system and describe some techniques for their suppression or elimination.
Tunable birefringent filters using liquid crystal variable retarders
The design of tunable birefringent filters utilizing liquid crystal retarders is discussed. Liquid crystals, which can be manufactured as electrically-variable, true zero-order retarders, can be used in most fixed birefringent filter designs to allow spectral tunability. The wavelength range for liquid crystal retarders includes the entire visible spectrum and most of the near infrared. Typical response times for current devices are approximately 10 ms. Two common filter designs that lend themselves well to liquid crystal variable retarder technology are Lyot and Solc filters. Each of these filters can be tuned to any wavelength within the transmission range of the optical components by incorporating with each fixed birefringent element a liquid crystal retarder capable of varying retardance through one full wavelength. The characteristics of an assembled liquid crystal tunable filter are presented, and design considerations for tunable birefringent filters are discussed.
Compensation of extraordinary ray pencil astigmatism generated by a birefringent crystal in convergent beam
Jean-Jacques P. Arnoux
SPOT is the French Earth sensing satellite, with 3 models in orbit and the fourth model to be launched in 97. Each satellite is equipped with two multispectral cameras with a 10 meter spatial resolution. The separation of the registered spectral channels is performed by dichroic filters, with an average incidence of 30 degree(s). Since SPOT 1, in the early 80's, a thick quartz plane parallel plate is placed before the dichroic filters, to make the camera not sensitive to polarization of the observed scenes. For the new generation of SPOT 5 cameras, the resolution has been improved to 5 m, and the astigmatism introduced by the quartz crystal on the extraordinary ray pencil is no more compatible with the image quality high demanding requirements. We first determine the impact of the Quartz thick plate on the extraordinary rays for a perfectly converging beam, and then for the true beam exiting the SPOT 5 telescope. We propose to compensate the geometrical aberrations due to the birefringence by adding a negative crystal with the optic axis set parallel to that of the positive crystal. The compensating crystal is placed after the dichroic filters. We propose to use Sapphire as compensating crystal. Finally we verify the camera image quality to be in accordance with the requirements.
Poster Session
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Evaluation of the spatial inhomogeneities of ferrofluid thin plates polarimetric characteristics for active imagery
Pierre-Yves Gerligand, Bernard Le Jeune, Jack Cariou, et al.
When a static magnetic field, perpendicular to the propagation direction of a laser beam is applied to a magnetic liquid, birefringence and dichroism can be present in this material. These properties have been used to realize an adjustable wave plate for polarimetric modulation applications in active imagery. The first measurements of the linear birefringence have been made by using a continuous laser source and the results have shown the possibility for such a material to realize polarimetric modulation. So we have to obtain a good spatial homogeneity of the polarimetric properties of the retardation plate. This measurement method has been developed in the case of an imagery application using a pulsed laser beam: in this case the temperature effects which could appear in the first set up are removed. Results show the possibility to develop adjustable wave plates based on ferrofluids for which it is possible to make polarimetric modulation at high speed.
Astronomy and Remote Sensing
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Liquid Crystal Polarimeter for solid state imaging of solar vector magnetic fields
Laurence J. November, Lawrence M. Wilkins
The Liquid Crystal Polarimeter (LCP) is a low-voltage complete Stokes polarimeter and spectral analyzer designed for measuring solar vector magnetic fields. The polarimeter consists of polarization and spectral analyzer sections each containing multiple commercially available nematic and ferroelectric liquid crystals which are modulated in phase at up to 31.5 kHz frequency. Used in conjunction with a Lyot birefringent filter and 2 ccds, the system provides a complete polarization/spectral measurement for solid-state direct imaging of the vector magnetic flux, Doppler velocity, intensity, and equivalent width in a spectral line. Simultaneous 2 ccd imaging gives reduced atmospheric seeing systematics, and automatic ccd gain and dark-current correction. The liquid-crystal design provides a considerable simplification to previous designs with greatly improved speed, sensitivity, reliability, and accuracy. Some of our tests of liquid crystals and of the LCP are described.
Zurich Imaging Stokes Polarimeters I and II
We present the design of the Zurich Imaging Stokes Polarimeters (ZIMPOL) I and II along with the first measurements and scientific observations. ZIMPOL I which was developed for precision solar vector polarimetry, uses two piezoelastic modulators and CCD arrays that have every other row covered with an opaque mask. During exposure the charges are shifted back and forth between covered and light-sensitive rows in synchrony with the modulation. In this way Stokes I and one of Q, U, or V can be recorded. Since the charge shifting is performed at frequencies well above the seeing frequencies and both polarization states are measured with the same pixel, highly sensitive and accurate polarization and information can be recorded. ZIMPOL II will record simultaneous images of all four Stokes parameters with a single CCD detector chip. A micro-lens array collects all of the photons and directs them to the unmasked pixel rows. This provides three storage rows for each set of four rows. The efficiency for simultaneous recording of all four Stokes parameters is six times that of ZIMPOL I.
Use of Mueller and non-Mueller matrices to describe polarization properties of telescope-based polarimeters
P. H. Seagraves, David F. Elmore
Systems using optical elements such as linear polarizers, retarders, and mirrors can be represented by Mueller matrices. Some polarimeters include elements with time-varying polarization properties, multiple light beams, light detectors, and signal processing equipment. Standard Mueller matrix forms describing time-varying retarders, and beam splitters are presented, as well as non-Mueller matrices which describe detection and signal processing. These matrices provide a compact and intuitive mathematical description of polarimeter response which can aid in the refining of instrument designs.
Polarization sensitivity modeling of reflective imaging systems
Polarization modeling of imaging systems has assumed more importance in recent earth remote sensing systems. Santa Barbara Research Center (SBRC) has developed computer programs that model the polarization characteristics of optical systems. This single ray simplified approach can be used when coating design information is not available or for modeling of an as built instrument using measured component data. For systems without exotic coating designs, the polarization ray trace capability of the optical design program CodeV is used to perform polarization modeling. Two polarization modeling case studies are reported. Measured component data is used for single ray modeling of the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor currently being built at SBRC. CodeV was used to model the full bundle of a five mirror off axis unobstructed ground based calibrator.
Polarization effects in radiometry
David S. Flynn, Cliff Alexander
The field of radiometry describes the fundamental radiative processes that are commonly involved in the operation of a passive imaging sensor. Scattering from surfaces is described in radiometry by the bidirectional reflectance distribution function (BRDF) defined by Nicodemus. As it is commonly defined, radiometry does not describe polarization effects in the radiative transfer processes. Vector scattering theories have attempted to describe polarized surface scattering with a 2 X 2 BRDF matrix. Polarimetry suggests that a 4 X 4 Mueller-like matrix is required to describe polarized surface scattering. In this paper, radiometric terms are redefined as polarized, vector quantities in a manner consistent with polarimetry. A full 4 X 4 BRDF matrix is derived from the scattering matrix. (Actually a 3 X 3 BRDF matrix with one row and column of complex values is adopted to simplify the equations and to facilitate relating the BRDF matrix to both the scattering cross section and the 2 X 2 BRDF matrix adopted in vector scattering theories.) A directional reflectance matrix and directional emittance vector are defined and their relationship is given. It is observed that the polarization character of surface reflectances and emittances are commonly not measured completely, and it is recommended that measurement programs be initiated to measure the full polarization character of common materials.
Luminescent x-ray polarimeter
Igor P. Tindo, Israel L. Beigman
A new type of sensitive X-ray polarimeter is proposed, based on the measurement of the azimuthal anysotropy of the angular distribution of the photoelectrons produced by photoabsorption of the infalling X-ray photons in the luminescent X-ray converter. The latter is a 3(2)-dimensional structure consisting of the luminescent (scintillating) two-component elements - thin fibers or films, the diameters (thickness) of which is smaller as the penetration depth of the photoelectrons. The device can be used at the hot plasma diagnostics in space-based astrophysical experiments and in laboratory.
Mathematics of Polarization and Scattering
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Special unitary groups in polarimetry theory
In this paper we consider application of the general theory of unitary matrices to the problem of wave propagation and scattering involving polarized waves. Having outlined useful parameterizations of these low dimensional matrix groups, we then develop a general processing strategy which we suggest is useful for the extraction of physical information from a range of scattering and propagation matrices in optics and radar. Examples are presented of application of the unitary matrix structure to the problems of absolute phase definition and random wave scattering.
Effects of near-specular scattering on polarimetry
Near-specular scattering (NSS) accompanying a specular beam causes errors in polarimetric measurements, especially for rough surfaces or in the short wavelength region. The Muller matrix for reflection or transmission including the NSS effect will be formulated and analyzed. NSS can cause a polarizer to have slight retardation and nonvanishing extinction ratio. NSS also can cause a retarder to be slightly diattenuated. Null ellipsometry is immune to incoherent and unpolarized NSS, but still cannot avoid partially coherent and polarized NSS. Polarimetric measurements of reflectance or transmittance pick up all types of scattering. NSS can be minimized by keeping the irradiated area and the receiving solid angle as small as possible.
Optimum angles for a Mueller matrix polarimeter
Amrit Ambirajan, Dwight C. Look Jr.
The four optimum rotation angles for a Mueller matrix polarimeter consisting of a quarter wave plate in conjunction with a linear polarizer, are found. This is done by using the determinant and condition numbers of the system measurement matrix as objective functions in a minimization procedure. The four angles so found result in the polarimeter's estimate of the incident Stokes vector to have a minimum sensitivity with respect to fluctuations in the detected flux and errors in the angular position of the optical components constituting the polarimeter. Four optimal angles are presented. These four angles also retain a simplicity of form for the measurement matrix.
Unified formalism for polarization optics: further developments
Charles S. Brown, F.U. Muhammad
We report further developments of the unified formalism for polarization optics. The unified formalism for polarization optics was designed to use the Stokes-Mueller matrix equation and the Lorentz group to provide a conceptual framework and a systematic method to model and to understand complicated polarization phenomena in optical media (like optical fibers systems, devices, and networks). To address polarization issues for complicated systems, we introduce several new Mueller matrixes. First, both the deterministic and the stochastic Mueller matrix for arbitrary but uniform dichroism and birefringence are given. Next, the Mueller matrixes for optical media with successive (series) and/or simultaneous (parallel) dichroism and birefringence along the optical path are given. Also, we report a comparison of measured Mueller matrix data with a theoretical model of a short (approximately 1 meter) optical fiber (with low internal linear birefringence) under the influence of a constant external twist. The agreement between measurement and theory are excellent. Finally, we argue that more complicated optical fiber systems and configurations with more than one source of dichroism and birefringence can be modelled or approximated by using combinations of the appropriate arbitrary (deterministic and/or stochastic), series, and/or parallel Mueller matrixes given above.
Lorentz group underpinnings for the Jones and Mueller calculi
F.U. Muhammad, Charles S. Brown
When preparing or examining a complicated optical system involving polarized light, one usually relies on one of a number of bookkeeping matrix formalisms that keep track of the various polarization components. The best-known are the 2 X 2 complex matrix calculus developed by Jones and the 4 X 4 real matrix calculus developed by Mueller. In this paper we show that both the Jones and Mueller calculi have their mathematical foundation in the Lorentz group. In the Jones approach one is working with one of the spinor representations of the Lorentz group. The Mueller approach involves the use of the vector representation of the Lorentz group. From the deterministic point of view the Jones and Mueller calculi are equivalent when considering completely-polarized monochromatic light. However, stochastically speaking, the two approaches do not yield the same physical predictions.
Polarization analysis of depolarizing optical systems
Sergey S. Girgel, Victor A. Emelyanov, Nikolay N. Fedosenko
On the basis of Oloude's orma1ism limitations for Mueller's matrices for arbitrary depolarizing optical systems are obtained explicitly and reduced to three inequalities. Parameterization of matrices is made.
Poster Session
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Phase-shift control in electro-optical analyzers
Victor M. Grigoryev, Nikolai I. Kobanov
Adjustment and stabilization of an optimal value of control voltage is a common problem in spectrum polarimetry when using electrooptical polarization analyzers. In this paper we give a description of a method to determine the quarter-wave phase shift when handling control signals of square form (of the type of a `meander'). The method is based on the symmetry property of the light characteristic of the optical shutter for modulators featuring a linear electrooptical effect. The version under consideration uses a standard quarter-wave plate. The plate of choice for this application is an achromatic quarter-wave plate. A high sensitivity of measurements is attained because the steepest parts of the light characteristic (near quarter- and 3/4-wave) participate in the signal shaping. The method may be used successfully to certify new specimens of quarter- and half-wave plates. Optical crystals that have longitudinal electrooptical effect, are often used in polarized light analyzers. The serve to create a controlled phase shift between the ordinary and the extraordinary rays. Voltages that give rise to a phase shift between the rays in (lambda) /2 and (lambda) /4, respectively, are called the half-wave and quarter-wave voltages (U(lambda /2),U(lambda /4)). It is these quantities that are most often featured in electrooptics.
One kind of error in modulational polarimetry
Nikolai I. Kobanov
In laboratory and astronomical polarimetry it is often still customary to employ sinusoidal voltages to control electro-optical modulators. In this case, signals on the main and double frequencies are usually recorded. Control voltages are reasonably high, up to 2 divided by 5 thousand volts, when using crystals like ADP, KDP, KD*P, and of some other types. Obviously, with so high values, nonlinear distortions of control voltages of up to 5 divided by 7% are almost unavoidable. In this paper, in a rather concise form, it is shown that nonlinear distortions of control voltage provide the source for spurious signals. A simple analytical expression is obtained, which relates the spurious signal amplitude to the amount of nonlinear distortions of modulating voltage. By examining a numerical example, it follows in particular that in some cases this factor is able to restrict the sensitivity of circular polarization measurements to 10-3 divided by 10-4. The aforesaid applies also for many objective polarimeters designed for measuring the rotation of the linear polarization plane.
Light depolarization in optical waveguides with irregular boundaries of dielectric layers
Andry V. Kovalenko, Vitalij N. Kurashov, Natalia I. Deriougina
In the paper it is considered the problem of eigenmode conversion in optical waveguides with inhomogeneous boundaries of dielectric layers. Random boundary profile is treated as fluctuations of refraction index in boundary layer. The intensity of depolarized scattered light is expressed through dispersion and correlation radius of dielectric layer boundaries. Both longitudinal and transversal correlations of boundary profile are taken into account, therefore obtained results are true for a case of arbitrary variations of electromagnetic field in space of fluctuation size.
Polarization-based devices in solar observations at the Sayan Observatory
Victor M. Grigoryev, Nikolai I. Kobanov, Valery I. Skomorovsky
Several polarization devices for solar observations designed at Sayan observatory are discussed, namely: (1) An electrooptical deflector is used to analyze circular polarization in a spectral line for longitudinal magnetic field measurements. This deflector located after the spectrograph slit incorporates a KD*P crystal and a Savart-plate. In contrast to usual deflectors, it transmits both Zeeman spectral-line components. But it also produces spatial modulation of separation of the Zeeman-split components. (2) An electrooptical deflector of the same type is located in the focal plane of the spectrograph before the photometer slit, to obtain subsequent measurement of the spectral line wings and the line Doppler shift. (3) An electrooptical analyzer is used to measure the magnetic field vector. It incorporates two KD*P crystals and a polarizing prism. The KD*P crystals are controlled by rectangular voltage pulses (+U(lambda /4), 0, -U(lambda /4) at frequency f0 for the first crystal and +/- U(lambda /4) at 3f0 for the second one). Such an analyzer permits measurement of the Q, U and V Stokes parameters. The properties of the modulator and the control device are discussed. (4) The differential velocity measuring device incorporates an electrooptical deflector and a polarizing beam-splitter located before the spectrograph entrance slit. The device is used to investigate local 5-minute oscillations. The corresponding method of the radial velocity measurements is based on measuring the relative spectral line positions at two different points of the solar image. This method is completely free from spectrograph seeing effects. A modification of this method permits differential solar rotation measurements. The signal calibration methods are also discussed together with their applicability to the determination of the line profile slopness and its variation over the solar image.
Parametric resonance in optical resonator systems with anisotropic modulators
Alexander M. Kul'minskii, Valerii N. Severikov, Alexander P. Voitovich
The mode behavior in a resonator with distributed anisotropic element is analyzed. It is noticed that taking into consideration of influence of the wave polarization parameters (azimuth and ellipticity) on the amplitude-frequency ones and vice versa is very important in anisotropic laser (or resonator systems, especially at internal modulation of their anisotropy. It is shown that the modulation of the anisotropy directions in the optical resonator without gain medium can lead to considerable change of the mode behavior giving as a result the phenomenon of parametric resonance. The parametric resonance condition means sudden change of the resonator mode characteristics because of decrease of Q-factor and possible `quenching' of the part of eigenmode spectral components.
One method of imaging polarimetry for remote sensing purposes: the technique accuracy investigations
Oleh Lychak
This paper is dedicated to investigation of accuracy characteristics of Earth surface mapping, using polarimetric technique. The author had proposed and realized a special technique for application of natural polarized scattered Sun light; linear and circular polarization components of reflected light are used. The images were obtained by four-channel photograph surveying system which included camera MSK-4 with isopanchromatic type film, four glass spectral filters and four polarizing elements, placed before objectives. Such images were obtained for anisotropy properties study of underlying surface which is modeled as little anisotropy absorption medium. The accuracy analysis of proposed technique is done by means of computer modeling on the base of real images. Statistical characteristics of output data deviation as function of survey parameters deviation are given. The regression equation of obtained data is built.
Anisotropically saturating nonlinearity of the polymer films with bacteriorhodopsin
Elena Y. Korchemskaya, Marat S. Soskin, Dmitriy A. Stepanchikov
In this work the anisotropically saturating nonlinearity of the polymer films based on bacteriorhodopsin (BR) have been studied both theoretically and experimentally. It is shown that the control of the relation between nonlinear susceptibility tensor-components in the polymer films with BR is possible by means of the variation of the light recording intensity and the relation between the recording beams intensity too.
Advance of the design and technology of birefringent filters
Valery I. Skomorovsky
Practical aspects of constructing very wide-field of view elements of Lyot Birefringence Filters (LBF) using the new Te02 and PbMoO4 crystals are discussed. The field of view exceeds that of the Halle and Zeiss LBF designs that use wide field elements based on half-wave plates. The combination of the new crystals between themselves and with calcite provides a possibility of constructing wide angle Solc filters covering a rather large spectral range. Because of the required tight tolerances on the parameters of the wave plates new methods and an optical system have been developed to orientate a crystallographic axis in the elements and control the thickness and parallelism of the element surfaces during finishing. The optical system set up on a polishing machine and the mirror installed under the polishing tool allow direct interferometric measurement of retardation and parallelism of the crystal plate during the polishing process. Details of these methods and the optical conoscope are discussed. Examples of the performance of the new wide-field elements are presented.
Chromatic dispersion characteristics of highly birefringent optical fibers
Velko Peyov Tzolov, Marie Fontaine
A new numerical approach based on the solution of the full vectorial Maxwell equations is applied to investigate the waveguiding dispersion parameters of birefringent optical fibers. A mathematical procedure particularly suitable for solving the nonlinear eigenvalue problem is used to determine precisely the constant of propagation for the HEx11 and HEy11 polarized modes. For elliptical core fiber, the normalized group-delay and the normalized chromatic dispersion for these two polarized modes are computed for a large range of the normalized frequency. The dispersion coefficients obtained from these characteristics curves have a crucial importance in the mathematical description of various phenomena in linear and nonlinear Kerr-like elliptical core fibers. The proposed approach is based on a finite-element scheme and could be applied for arbitrary refractive-index profile of any multimode fiber.
Investigation of stress-induced birefringence in large semiconductor wafers by imaging polarimetry
Andrzej L. Bajor
A computer-controlled polarimeter has been constructed. A wafer up to 6' in dia. is placed in a parallel beam of light between two sheet linear polarizers, whose transmission axes are set at 45 degree(s) and are simultaneously rotated by a stepper motor versus the immobile wafer. Four images of the wafer grabbed in the video frame grabber's memory at four incremented angles of the polarizer' transmission axes are then analyzed by a suitable procedure to yield tree maps: birefringence, the principal azimuth and transmission. The retardation error is usually smaller than 4 X 10-3 radians, whereas that of the principal azimuth and transmission of a degree and of a percent, respectively. The four images are grabbed within 3 - 4 seconds (10 such averaging cycles--if necessary--consumes less than 50 seconds), and the maps are calculated within 6 - 7 seconds including corrections for background birefringence and transmission. The polarimeter is suitable for quick investigation of large-area wafers, since the data are acquired from a dense (256 X 256) network of points giving a reasonable spatial resolution. In this work some results of investigations of birefringence induced by residual stresses in GaAs, GaP and Si are presented.
Instrumental polarization effects of the German Vacuum Tower Telescope (VTT) at Tenerife
Polarimetry is an important method to investigate the physics of the solar atmosphere. If the magnetic field strength is not strong enough to produce completely split Zeeman profiles the degree of polarization is a measure for the field strength. Measuring both the circular and linear polarization allows in principle the construction of the magnetic field vector including magnitude and direction. Unfortunately these highly desired measurements are in many cases affected by the instrument's optic itself. Especially telescopes which don't have a rotation symmetry with respect to their optical axis suffer from these problems. This is also the case with our German Vacuum Tower Telescope at Tenerife and this paper shall show the instrumental effects which are to be expected. One of the effects is crosstalk between linear and circular polarization. We show a method where this crosstalk can be considered as a tool and may be used--under certain assumptions--to derive the true size of magnetic elements which may cover only a fraction of the resolution element.
Ultraviolet/visible polarimetric signatures for discrimination
Stephen L. Hammonds, Dimitris Lianos
The feasibility of polarization technology to solve some of the stressing problems faced by BMDO has been demonstrated theoretically and experimentally. Aim point selection and the ability to discriminate targets from decoys, debris, etc. have been identified as the most stressing requirements for current BMDO interceptors. Simulations predict and field tests confirm that polarization technology has the potential to satisfy these requirements. Studies indicate that polarization signatures are more sensitive to target shape and dynamics than radiometric data. Polarized self emission signatures were found to provide the precise orientation of an object in precessional motion. The additional information gained from polarization may enhance an interceptor's capability to distinguish a target from decoys. Methods for the detection of linearly polarized UV radiation from missiles is briefly summarized. A novel optical system which simultaneously measures linear polarization Stokes vector elements on a single focal place is introduced. Preliminary measurements of polarized light from UV lamp reflections and from model rocket motor tests have been made with this system.
Astronomy and Remote Sensing
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Polarization errors associated with birefringent waveplates
Although zero-order quartz waveplates are widely used in instrumentation that needs good temperature and field-of-view characteristics, the residual errors associated with these devices can be very important in high resolution polarimetry measurements. This paper will discuss how the field-of-view characteristics are affected by retardation errors and the misalignment of optic axes in a double crystal waveplate. The paper will then describe the retardation measurements that were made on zero-order quartz and single-order `achromatic' waveplates and how the misalignment errors affect those measurements.
Polarization characteristics of the NASA Marshall Space Flight Ctr. (MSFC) Experimental Vector Magnetograph
A new vector magnetograph is being developed at NASA's Marshall Space Flight Center (MSFC) to measure polarization from active regions on the Sun. This paper will describe the polarization characteristics of the elements that make up the MSFC EXperimental Vector Magnetograph (EXVM) polarimeter. Based on those characteristics, the systematic errors associated with this polarimeter will be modeled and the polarization resolution that could be achieved in a space-based (or balloon-based) instrument will be discussed.