Poincaré sphere representation for spatially varying birefringence

Vella, Anthony; Alonso, Miguel A.

doi:10.1364/ol.43.000379

Cited by 16 publications

(18 citation statements)

References 35 publications

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“…The latter representation highlights the underlying symmetry between the coordinates of ì q (u) on the Poincaré hypersphere they inhabit [12].…”

Section: Solution Ignoring the Boundary Conditionsmentioning

confidence: 95%

Optimal birefringence distributions for imaging polarimetry

Vella¹,

Alonso²

2019

Opt. Express

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Star test polarimetry is an imaging polarimetry technique in which an element with spatially-varying birefringence is placed in the pupil plane to encode polarization information into the point-spread function (PSF) of an imaging system. In this work, a variational calculation is performed to find the optimal birefringence distribution that effectively encodes polarization information while producing the smallest possible PSF, thus maximizing the resolution for imaging polarimetry. This optimal solution is found to be nearly equivalent to the birefringence distribution that results from a glass window being subjected to three uniformly spaced stress points at its edges, which has been used in previous star test polarimetry setups. IntroductionPolarimetry is the measurement of the polarization state of light and/or the polarization properties of materials. Such measurements are usually characterized in terms of the Stokes parameters and the Mueller matrix, respectively, which are directly accessible from measurements of the intensity. Imaging polarimetry, in which the polarization is measured as a function of position, is particularly important in applications ranging from microscopy to remote sensing.Conventional techniques for Stokes polarimetry require multiple intensity measurements, either through time-sequencing or by splitting different polarization components into several separate detection channels [1,2]. For example, one common method uses a rotating quarter-wave plate (QWP) followed by a fixed linear polarizer, in which the Stokes parameters are deduced from successive intensity measurements with the QWP oriented at different angles [3]. While these techniques can produce highly accurate measurements, they can be relatively complicated and/or time-consuming, generally involving moving parts or multiple beam paths.When a short acquisition time is desirable, rapid polarization measurements may be taken using single-shot polarimetry, in which the Stokes parameters are estimated from a single intensity measurement. A variety of methods exist for single-shot polarimetry, involving gradient index lenses [4], patterned nanoscale gratings [4], or a split aperture composed of multiple polarizers [5]. One particularly simple method, referred to as star test polarimetry, uses a spatially-varying birefringent mask (BM) followed by a uniform polarization analyzer in the pupil plane of an exit-telecentric imaging system. With an appropriately chosen birefringence distribution, the inserted elements can encode full polarization information into the shape of the PSF in the rear focal plane of the lens. This method has been demonstrated experimentally using a stress-engineered optic (SEO), which is a BK7 glass window subjected to stress with trigonal symmetry at its periphery, followed by a circular analyzer [6,7]. Natural applications for this approach are those in which the object is a sparse set of discrete points, such as in astronomy and confocal microscopy. A recent specific application was the real-time monitorin...

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“…The latter representation highlights the underlying symmetry between the coordinates of ì q (u) on the Poincaré hypersphere they inhabit [12].…”

Section: Solution Ignoring the Boundary Conditionsmentioning

confidence: 95%

Optimal birefringence distributions for imaging polarimetry

Vella¹,

Alonso²

2019

Opt. Express

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“…It does, however, have the simple geometric interpretation over the Poincaré sphere, as shown in Fig. 2: it equals the angle between the projections of q a and q b onto a plane normal to either of the eigenpolarizations [6]. Note that this interpretation is different but fully equivalent to that given by Courtial [9], [10].…”

Section: Geometric Phasementioning

confidence: 98%

“…This representation is useful for understanding the effects of spatially-varying birefringence on the performance of an optical system. For example, simple geometric interpretations in terms of the Poincaré hypersphere were given to both the widening of the PSF and the reduction of the Strehl ratio of imaging systems, due to spatially-varying birefringence of its elements [6]. This formalism has also been used for the design of birefringence distributions that are optimal for different goals, such as the generation of bottle beams [11] and of polarimetric systems [12].…”

Section: Applicationsmentioning

confidence: 99%

“…However, some applications benefit from using elements with tailored spatially-varying birefringence, and several technologies have been proposed for implementing these elements, including metasurfaces [1], liquid crystal devices such as q-plates [2], d-plates [3] and light valves [4], as well as stress-engineered birefringence [5]. In this work, we discuss a geometric description of spatially-varying birefringence distributions [6] based on a generalization of the Poincaré sphere geometric construction, which is usually employed to describe beam polarization and not birefringent elements.…”

Section: Introductionmentioning

confidence: 99%

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Birefringent distributions tailored for imaging and other applications

Alonso

Vella²

2018

2018 17th Workshop on Information Optics (WIO)

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“…The Poincare sphere can represent any possible polarization state or Stokes vector. Poincare sphere has been successfully utilized in polarization metrology , representation of phase by twisted nematic liquid crystal spatial light modulators , analysis of fiber polarization mode dispersion , DOP surfaces and maps for analysis of depolarization , evolution of linear and circular polarization in scattering environments , hybrid elliptically polarized vector fields and hybrid polarized vector beams , representation for spatially varying birefringence , and representation of the fixed polarizer rotating retarder optical system. Additionally, detection and diagnosis of chronic disease has also been performed successfully by projecting different polarization states of light on Poincare sphere .…”

Section: Introductionmentioning

confidence: 99%

Mapping of retardance, diattenuation and polarizance vector on Poincare sphere for diagnosis and classification of cervical precancer

Zaffar

Pradhan

2020

Journal of Biophotonics

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The mapping of diattenuation, polarizance and retardance vector (normalized Stokes vector) on Poincare sphere, evaluated from Mueller matrix of optically anisotropic stromal region of cervical tissues, is presented for cervical precancer detection and its staging. This reveals that the changes in the polarization states shown by these normalized Stokes vectors corresponds to the degradation of linearly arranged collagen fibers, breakage of the collagen cross links in the stromal region and change in the density of scattering sites when cervical cancer evolves. The distinct nature of real and imaginary parts of the refractive index for linear, linear-45 and circular polarization from the optically anisotropic stromal region underscore the various polarization structures of the connective tissue region which get modified during the pathological changes. It has been found that versatility of these vectors for normal and precancerous cervical tissue of various grades may be utilized as a key distinction for qualitative staging of cervical precancer tissue. Quantitative classification of precancerous stages of cervical precancer has been determined with 95%-100% sensitivity and 93%-100% specificity through the evaluation of linear and circular diattenuation, linear polarizance and linear birefringence from the components of the respective vectors. K E Y W O R D S cervical cancer, diattenuation vector, Mueller matrix, Poincare sphere, polarizance vector, retardance vector, stromal region

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Poincaré sphere representation for spatially varying birefringence

Cited by 16 publications

References 35 publications

Optimal birefringence distributions for imaging polarimetry

Optimal birefringence distributions for imaging polarimetry

Birefringent distributions tailored for imaging and other applications

Mapping of retardance, diattenuation and polarizance vector on Poincare sphere for diagnosis and classification of cervical precancer

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