Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus: erratum.

For J. Opt. Soc. Am. A33, 434 (2016)JOAOD60740-323210.1364/JOSAA.33.000434, a corrected version of Eq. (9) is provided owing to typographical errors in the original article. The original full article text and calculations are unchanged. Another typo is corrected in Eq. (A5) of Appendix A.

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus.

Polarimetric sensing by orthogonality breaking has been recently proposed as an alternative technique for performing direct and fast polarimetric measurements using a specific dual-frequency-dual-polarization (DFDP) source. Based on the instantaneous Stokes-Mueller formalism to describe the high-frequency evolution of the DFDP beam intensity, we thoroughly analyze the interaction of such a beam with birefringent, dichroic, and depolarizing samples. This allows us to confirm that orthogonality breaking is produced by the sample diattenuation, whereas this technique is immune to both birefringence and diagonal depolarization. We further analyze the robustness of this technique when polarimetric sensing is performed through a birefringent waveguide, and the optimal DFDP source configuration for fiber-based endoscopic measurements is subsequently identified. Finally, we consider a stochastic depolarization model based on an ensemble of random linear diattenuators, which makes it possible to understand the progressive vanishing of the detected orthogonality-breaking signal as the spatial heterogeneity of the sample increases, thus confirming the insensitivity of this method to diagonal depolarization. The fact that the orthogonality-breaking signal is exclusively due to the sample dichroism is an advantageous feature for the precise decoupled characterization of such an anisotropic parameter in samples showing several simultaneous effects.

Precision of polarization-resolved second harmonic generation microscopy limited by photon noise for samples with cylindrical symmetry.

The estimation of parameters in polarization-resolved two-photon microscopy response perturbed by photon noise is analyzed in the context of second harmonic generation for the distribution of molecules presenting cylindrical symmetry. The estimation task is investigated using the Cramer-Rao lower bound for Poisson photon noise. It is shown that a noniterative technique can lead to estimation results that have good efficiencies for most of the physical possible values of the sample parameters for sufficiently high photon levels. The trade-off, between the number of incident polarization states and the total number of measured photons, that can be obtained with the Cramer-Rao lower bound is also discussed.

Microscopic structural study of collagen aging in isolated fibrils using polarized second harmonic generation.

Polarization resolved second harmonic generation (PSHG) is developed to study, at the microscopic scale, the impact of aging on the structure of type I collagen fibrils in two-dimensional coatings. A ribose-glycated collagen is also used to mimic tissue glycation usually described as an indicator of aging. PSHG images are analyzed using a generic approach of the molecular disorder information in collagen fibrils, revealing significant changes upon aging, with a direct correlation between molecular disorder and fibril diameters.

Precision increase with two orthogonal analyzers in polarization-resolved second-harmonic generation microscopy.

We analyze the increase in precision of parameters estimation for polarization-resolved second-harmonic generation imaging microscopy when two intensities are measured with two orthogonal analyzers. The analysis is performed for measuring anisotropy parameters and molecule orientation for samples with cylindrical symmetry in the presence of photon noise with Poisson statistics. The improvement in comparison to global intensity measurement (i.e., without analyzer) is discussed.

Computational polarization imaging from a single speckle image.

We experimentally demonstrate that imaging of the degree of polarization (DOP) can be achieved from a single intensity image acquired under coherent illumination. This computational technique is based on the analysis of the speckle characteristics in a statistically homogeneous neighborhood of the pixel. Over a variety of samples obtained experimentally, we show that a simple calibration step allows this method to quickly and simply provide correct estimated values of the DOP, with precision in agreement with theoretical predictions. It is shown that unlike linear polarimetric contrast imaging, this method remains valid on birefringent samples.

Precision analysis in polarization-resolved second harmonic generation microscopy.

Polarization-resolved second harmonic generation (PSHG) imaging microscopy allows one to provide information such as anisotropy parameters and molecule orientation. We analyze the precision of parameter estimation for samples with cylindrical symmetry and a Gaussian additive noise model. We introduce improvements of existing techniques that can be useful to get rapid acquisition and processing of PSHG images, and we discuss the influence of photon noise.

Estimating the polarization degree of polarimetric images in coherent illumination using maximum likelihood methods.

We address the problem of estimating the polarization degree of polarimetric images in coherent illumination. It has been recently shown that the degree of polarization associated with polarimetric images can be estimated by the method of moments applied to two or four images assuming fully developed speckle. We show that the estimation can also be conducted by using maximum likelihood methods. The maximum likelihood estimators of the polarization degree are derived from the joint distribution of the image intensities. We show that the joint distribution of polarimetric images is a multivariate gamma distribution whose marginals are univariate, bivariate, or trivariate gamma distributions. This property is used to derive maximum likelihood estimators of the polarization degree using two, three, or four images. The proposed estimators provide better performance than the estimators of moments. These results are illustrated by estimations conducted on synthetic and real images.

Precision of moment-based estimation of the degree of polarization in coherent imagery without polarization device.

We propose and analyze a statistical method to estimate the degree of polarization of light from a single speckle intensity image by analyzing the statistical distribution of the light intensity. The optimal precision of such an estimation method is evaluated by computing the Cramer-Rao bounds for several speckle degrees. Two moment-based estimators of the square degree of polarization are introduced and characterized. For the first time to our knowledge, it is shown theoretically and through simulations that the estimators are almost efficient for high orders of speckle. The robustness of the method is discussed for the case when the intensity fluctuations do not follow the standard speckle model.

Parametric estimation of the square degree of polarization from two intensity images degraded by fully developed speckle noise.

Active polarimetric imagery systems allow one to reveal polarimetric characteristics of the scene. Among them, the degree of polarization allows one to have information about the polarizing nature of an imaged object. Its estimation is standardly done from four images of the scene. Reducing this number of images can be of great interest for industrial applications, allowing in particular reduction of cost in terms of money and acquisition time. We propose a parametric method to estimate the square degree of polarization from only two measurements when coherent illumination is considered and when the images are corrupted with fully developed speckle, and we characterize the performances of the estimation.

Estimation precision of the degree of polarization from a single speckle intensity image.

We address the problem of the estimation of the degree of polarization from a single intensity image. For that purpose, one considers the case of coherent active imagery that leads to speckle fluctuations and assumes that the measured intensity image corresponds to a fully developed speckle for each polarized component of the electric field. In particular, we determine the Cramer-Rao bound of the degree of polarization estimation and propose to illustrate this result by analyzing the variance of different simple estimators.

Preimplantation genetic diagnosis significantly improves the pregnancy outcome of translocation carriers with a history of recurrent miscarriage and unsuccessful pregnancies.

Preimplantation genetic diagnosis (PGD) for translocations has been shown to significantly reduce the risk of recurrent miscarriage, but because the majority of embryos produced are unbalanced, pregnancy rate is relatively low since 20% or more cycles have no normal or balanced embryos to transfer. The purpose of this study was to evaluate whether PGD could improve pregnancy outcome in translocation carriers with a history of two or more consecutive miscarriages and no live births. PGD for translocations was offered to translocation carriers with two or more previous miscarriages (average 3.5) and no live births (0/117 pregnancies) using a combination of distal and proximal probes to the breakpoints. After PGD, only 18.3% of embryos were normal or balanced. Only 5.3% of pregnancies were lost after PGD compared with 100% before PGD (P < 0.001). The cumulative pregnancy rate was 57.6% and the cumulative ongoing pregnancy rate was 54.5% in the short period of time of 1.24 IVF cycles, or 46.3% and 43.9% respectively per cycle. In conclusion, PGD significantly reduced losses and increased the number of viable pregnancies (P < 0.001). IVF plus PGD are a faster method of conceiving a live child than natural conception, at least for translocation carriers with recurrent miscarriages and no previous live births.

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

The 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 noise, by determining the Cramer-Rao lower bounds (CRLBs) when the illuminated materials are purely depolarizing. We demonstrate that the CRLBs are simply the sum of the CRLBs due to speckle noise and Poisson noise. We use this result to analyze the influence of different optical parameters on DOP estimation.

Invariant polarimetric contrast parameters of light with Gaussian fluctuations in three dimensions.

We propose a rigorous definition of the minimal set of parameters that characterize the difference between two partially polarized states of light whose electric fields vary in three dimensions with Gaussian fluctuations. Although two such states are a priori defined by eighteen parameters, we demonstrate that the performance of processing tasks such as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by three scalar functions of these parameters. These functions define a "polarimetric contrast" that simplifies the analysis and the specification of processing techniques on polarimetric signals and images. This result can also be used to analyze the definition of the degree of polarization of a three-dimensional state of light with Gaussian fluctuations in comparison, with respect to its polarimetric contrast parameters, with a totally depolarized light. We show that these contrast parameters are a simple function of the degrees of polarization previously proposed by Barakat [Opt. Acta 30, 1171 (1983)] and Setälä et al. [Phys. Rev. Lett. 88, 123902 (2002)]. Finally, we analyze the dimension of the set of contrast parameters in different particular situations.