Comparison of the estimation of the degree of polarization from four or two intensity images degraded by speckle noise

Active polarimetric imagery is a powerful tool for accessing the information present in a scene. Indeed, the polarimetric images obtained can reveal polarizing properties of the objects that are not avalaible using conventional imaging systems. However, when coherent light is used to illuminate the scene, the images are degraded by speckle noise. The polarization properties of a scene are characterized by the degree of polarization. In standard polarimetric imagery system, four intensity images are needed to estimate this degree . If we assume the uncorrelation of the measurements, this number can be decreased to two images using the Orthogonal State Contrast Image (OSCI). However, this approach appears too restrictive in some cases. We thus propose in this paper a new statistical parametric method to estimate the degree of polarization assuming correlated measurements with only two intensity images. The estimators obtained from four images, from the OSCI and from the proposed method, are compared using simulated polarimetric data degraded by speckle noise

Cramer-Rao lower bound for the estimation of the degree of polarization in active coherent imagery at low photon level

International audienceThe degree of polarization (DOP) is an important tool in many optical measurement and imaging applications. We address the problem of its estimation in images that are perturbed with both speckle and photon noises, by determining the Cramer-Rao Lower Bound (CRLB) when the illuminated materials are purely depolarizing. We demonstrate that the CRLB is simply the sum of the CRLBs due to speckle noise and to Poisson noise. We use this result to analyze the influence of different optical parameters on DOP estimation

Quantum limits in image processing

We determine the bound to the maximum achievable sensitivity in the estimation of a scalar parameter from the information contained in an optical image in the presence of quantum noise. This limit, based on the Cramer-Rao bound, is valid for any image processing protocol. It is calculated both in the case of a shot noise limited image and of a non-classical illumination. We also give practical experimental implementations allowing us to reach this absolute limit.Comment: 4 pages, two figure

Implementation of arbitrary real-valued correlation filters for the shadow-casting incoherent correlator

International audienceWe describe an incoherent correlator, based on the shadow-casting principle, that is able to implement any real-valued linear correlation filter. The correlation filter and the input image are displayed on commercial liquid-crystal television ~LCTV! panels. Although it cannot handle high-resolution images, the incoherent correlator is lensless, compact, low cost, and uses a white-light source. A bipolar technique is devised to represent any linear filter, computed from a single reference image or composite, in the correlator. We demonstrate experimentally the efficiency of the design in the case of optimal trade-off ~OT! filters and optimal trade-off synthetic discriminant function ~OT-SDF! filter

Optical snake-based segmentation processor using a shadow casting incoherent correlator.

What is believed to be the first incoherent snake-based optoelectronic processor that is able to segment an object in a real image is described. The process, based on active contours (snakes), consists of correlating adaptive binary references with the scene image. The proposed optical implementation of algorithms that are already operational numerically opens attractive possibilities for faster processing. Furthermore, this experiment has yielded a new, versatile application for optical processors

Entropy of partially polarized light and application to statistical processing techniques

International audienceWe have analyzed entropy properties of coherent and partially polarized light in an arbitrary number of spatial dimensions. We show that for Gaussian fields, the Shannon entropy is a simple function of the intensity and of the Barakat degree of polarization. In particular, we provide a probabilistic interpretation of this definition of the degree of polarization. Using information theory results, we also deduce some physical properties of partially polarized light such as additivity of the entropy and depolarization effects induced by mixing partially polarized states of light. Finally, we demonstrate that entropy measures can play an important role in segmentation and detection task

An analysis of complexity and randomness in a few different optical examples

International audienc

Irreversible effects of random modulation on coherence properties of partially polarized light

International audienceThe effect of random modulations of two electric vector fields on their coherence properties is investigated by analyzing their interference fringes. It is shown that random modulations cannot increase the maximal visibility obtained when the polarization states of the two analyzed electric fields are optimized. This new result generalizes a standard property of perfectly polarized light to unpolarized light and is representative of the irreversible effects of random modulations. It is also proved that another quantity related to coherence properties is also non increasing if the modulations applied to each electric field are uncorrelated