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We have previously reported a new design for drift-free liquid-crystal polarization modulators (LCMs) based on liquid-crystal variable retarders (LCVRs). Here, we study their performance on Stokes and Mueller polarimeters. LCMs have polarimetric responses similar to LCVRs and can be used as temperature-stable alternatives to many LCVR-based polarimeters. We have built an LCM-based polarization state analyzer (PSA) and compared its performance to an equivalent LCVR-based PSA. Our system parameters remained stable over a wide range of temperature, precisely from 25°C to 50°C. Accurate Stokes and Mueller measurements have been conducted, paving the way to calibration-free polarimeters for demanding applications.

We report a new design for temperature-stable polarization modulators. Each modulator is composed of two liquid crystal variable retarders (LCVRs) positioned in such a way that their temperature drifts mutually compensate. We propose a model for the temperature-dependent polarization response of LCVRs, which permits us to establish expressions for the operating point of the system and for its accessible retardance range. We have validated such a model experimentally by thorough analyses of LCVR temperature responses, and we have built a polarization modulator that is stable over a wide range of temperature with commercially available LCVRs.

It is possible to introduce tolerancing with the realizability test of Givens and Kostinski [J. Mod. Opt.40, 471 (1993)] with a minor modification: it suffices to add a special matrix to [G][M](T)[G][M]. Consequently, it is possible to check experimental Mueller matrices with a more flexible tool. Application to the emblematic case of the Mueller images of the free space shows that more than 99% of the pixels are in fact physical, while only 2% initially passed the test.

One can explicitly retrieve physically realizable Mueller matrices from quantified intensity data even in the presence of noise. This is done by integrating the physical realizability criterion obtained by Givens and Kostinski, [J. Mod. Opt. 40, 471 (1993)], as an active constraint in a global optimization process. Among different global optimization techniques, two of them have been tested and their robustness analyzed: a deterministic approach based on sequential quadratic programming and a stochastic approach based on constrained simulated annealing algorithms are implemented for this purpose. We illustrate the validity of both methods on experimental data and on the inadmissible Mueller matrix given by Howell, [Appl. Opt. 18, No. 6, 808-812 (1979)]. In comparison, the constrained simulated annealing method produced higher accuracy with similar computing time.

Two methods used to retrieve Mueller matrices from intensity measurements are revisited. It is shown that with symmetry or orthogonality considerations, numerical inversions of polarimetric equations can be avoided. With the obtained analytical formulas, noise propagation can be analyzed. If the intensity noise is a Gaussian white noise, the noise of Mueller matrices features remarkable properties. Mueller components are mutually correlated according to a scheme that involves decomposition into four blocks of 2x2 matrices. Variances are unequally distributed: the middle 2x2 block has the highest variance, the element on the bottom right has the lowest. These characteristics have been validated on experimental Mueller images of the free space.

Retrieval of Mueller matrices from intensity measurements is a noise-sensitive process. In addition, the choice of the method used for extracting Mueller matrix elements greatly influences the precision of the final results. Among available procedures, three have been tested and their robustness analyzed by adding Gaussian noise to computer synthesized data and have been verified by comparing experimental data. As expected, the methods based on classical matrix inversion reach their noise reduction limit even if more data are considered. In contrast, the discrete Fourier transform approach features a remarkable stability. The identified reason is that the retrieval process corresponds to filtering with a periodic kernel.

By focusing light with a sphere several wavelengths in diameter, we can obtain a photonic nanojet [Opt. Express 13, 526 (2005)]: if light is focused on the surface of the sphere, the width of the beam stays smaller than the wavelength along a distance of propagation of approximately two wavelengths and reaches a high intensity. We use the rigorous Mie theory to analyze the basic properties of the photonic jet in the general three-dimensional polarized case. This fast algorithm allows us to determine the influence of the radius and the refractive index of the sphere on the photonic jet. The polarization response is also studied. We observe that high-intensity concentrations and subwavelength focusing are two different effects. Their basic properties are analyzed, and explanations are proposed.

This paper extends and refines previous work on clustering of polarization-encoded images. The polarization-encoded images used in this work are considered as multidimensional parametric images where a clustering scheme based on Markovian Bayesian inference is applied. Hidden Markov Chains Model (HMCM) and Hidden Hierarchical Markovian Model (HHMM) show to handle effectively Mueller images and give very good results for biological tissues (vegetal leaves). Pretreatments attempting to reduce the image dimensionality based on the Principal Component Analysis (PCA) turns out to be useless for Mueller matrix images.

Polarization-encoded imaging consists of the distributed measurements of polarization parameters for each pixel of an image. We address clustering of multidimensional polarization-encoded images. The spatial coherence of polarization information is considered. Two methods of analysis are proposed: polarization contrast enhancement and a more-sophisticated image-processing algorithm based on a Markovian model. The proposed algorithms are applied and validated with two different Mueller images acquired by a fully polarimetric imaging system.

We present an imaging system that measures the polarimetric state of the light coming from each point of a scene. This system, which determines the four components of the Stokes vector at each spatial location, is based on a liquid-crystal polarization modulator, which makes it possible to acquire four-dimensional Stokes parameter images at a standard video rate. We show that using such polarimetric images instead of simple intensity images can improve target detection and segmentation performance.