Vortex retarder-based Stokes polarimeters: optimal data processing and autocalibration capability.

We present a full Stokes polarimeter that utilizes a vortex retarder (VR) in conjunction with a polarization camera. We demonstrate its capability to estimate the full Stokes vector in a single shot with optimal precision and to autocalibrate the VR retardance, ensuring precise measurements even in dynamic environments where retardance is variable.

Impact of image registration errors on the quality of hyperspectral images in imaging static Fourier transform spectrometry.

Imaging static Fourier transform spectrometry (isFTS) is used for pushbroom airborne or spaceborne hyperspectral remote sensing. In isFTS, a static two-wave interferometer imprints linear interference fringes over the image of the scene, so that the spectral information is multiplexed over several instantaneous images, and numerical reconstruction is needed to recover the full spectrum for each pixel. The image registration step is crucial since insufficient accuracy leads to artefacts on the images and the estimated spectra. In order to investigate these artifacts, we performed a theoretical study and designed a simulation program. We established that registration errors create crenellated spatial patterns, the magnitude of which depends on the radiance gradient of the scene, the amplitude of the registration error, and the wavelength. In the case of sinusoidal perturbations, which may correspond for instance to mechanical vibrations of the carrier, we established that spurious peaks appear on the spectrum, similarly to what happens in dynamic FTS, but with spatial patterns specific to static interferometers.

Joint Denoising-Demosaicking Network for Long-Wave Infrared Division-of-Focal-Plane Polarization Images With Mixed Noise Level Estimation.

Denoising and demosaicking long-wave infrared (LWIR) division-of-focal-plane (DoFP) polarization images are crucial for various vision applications. However, existing methods rely on the sequential application of individual denoising and demosaicking processes, which may result in the accumulation of errors produced by each process. To address this issue, we propose a joint denoising and demosaicking method for LWIR DoFP images based on a three-stage progressive deep convolutional neural network. To ensure the generalization ability of this network, it is essential to have adequate training data that closely resembles real data. Therefore, we model the complex noise sources that affect LWIR DoFP images as mixed Poisson-Additive-Stripe noise and construct a least-squares problem based on the polarization measurement redundancy error to estimate the parameters of this model on real images. Subsequently, the estimated noise parameters are used to generate training data that enables the network to learn accurate polarization image statistics and improve its generalization ability. The experimental results demonstrate the effectiveness of the proposed method in enhancing the image restoration performance on real LWIR DoFP polarization data.

On the equivalence of binary phase masks optimized for localization or detection in extended depth-of-field localization microscopy.

Binary annular masks have recently been proposed to extend the depth of field (DoF) of single-molecule localization microscopy. A strategy for designing optimal masks has been introduced based on maximizing the emitter localization accuracy, expressed in terms of Fisher information, over a targeted DoF range. However, the complete post-processing pipeline to localize a single emitter consists of two successive steps: detection, where the regions containing emitters are determined, and localization, where the sub-pixel position of each detected emitter is estimated. Phase masks usually optimize only this second step. The presence of a phase mask also affecting detection, the purpose of this paper is to quantify and mitigate this effect. Using a rigorous framework built from a detection-oriented information theoretical criterion (Bhattacharyya distance), we demonstrate that in most cases of practical significance, annular binary phase masks maximizing Fisher information also maximize the detection probability. This result supports the common design practice consisting of optimizing a phase mask by maximizing Fisher information only.

Improved performance of a hybrid optical/digital imaging system with fast piecewise Wiener deconvolution.

We quantitatively investigate how spatially varying deblurring algorithms can improve the imaging performance of hybrid optical/digital systems affected by field aberrations. To this end, we validate a theoretical model of the maximal gain that linear and spatially varying deblurring can bring to any given lens, and derive a practical algorithm to implement this type of deblurring with low computational complexity. The results demonstrate the usefulness to properly coordinate and balance the roles of the imaging optical system and raw image post-processing: optimal final imaging quality can be obtained by a lens that has been optically designed to reduce field aberrations at the price of lower average raw optical quality, associated with a fast and "slightly" spatially varying piecewise Wiener deconvolution algorithm.

End-to-end optimization of optical systems with extended depth of field under wide spectrum illumination.

We study a way to take into account the scene illumination spectrum during end-to-end optimization of optical-digital hybrid systems that include annular binary phase masks to enhance their depth of field (DoF). We show that a phase mask specifically optimized for wide spectrum panchromatic imaging performs better under this type of illumination than phase masks optimized under monochromatic illumination assumption. Indeed, thanks to spectral averaging, the modulation transfer functions of such a phase mask are very close to each other. This guarantees a very homogeneous image quality across the DoF range, which we demonstrate theoretically and experimentally using a dedicated optical setup.

Error model for linear DoFP imaging systems perturbed by spatially varying polarization states.

Division of focal plane (DoFP) polarization sensors can perform linear polarimetric imaging in one shot. However, since they use several neighboring pixels to estimate the polarization state, fast spatial variations of the scene may lead to estimation errors. We investigate the influence of the spatial variations of the three polarimetric parameters of interest (intensity, degree of linear polarization, and angle of polarization) on these errors. Using theoretical derivations and imaging experiments, we demonstrate that the spatial variations of intensity are the main source of estimation errors, much more than variations in the polarization state. Building on this analysis, we show that compensating the intensity variations within a superpixel is sufficient to reach the estimation performance of state-of-the-art demosaicing methods.

Optimal nonlinear Stokes-Mueller polarimetry for multi-photon processes.

In this Letter, we present an optimization model for nonlinear Stokes-Mueller polarimetry (SMP) to improve the precision in estimating the nonlinear Mueller matrix (MM) for two- and three-photon processes. Although nonlinear polarimeters can measure the polarization properties of multi-photon processes or materials, existing methods are suboptimal, leading to low measurement precision. Based on the model and its solution, we have designed a new measurement strategy to substantially reduce the estimation variance of nonlinear MM coefficients by approximately 58.2% for second-harmonic generation polarimetry and 78.7% for third-harmonic generation polarimetry. The model and measurement method can be directly applied to multi-photon processes to improve the precision of SMP.

Comparison of methods for end-to-end co-optimization of optical systems and image processing with commercial lens design software.

We compare three different methods to co-optimize hybrid optical/digital imaging systems with a commercial lens design software: conventional optimization based on spot diagram minimization, optimization of a surrogate criterion based on a priori equalization of modulation transfer functions (MTFs), and minimization of the mean square error (MSE) between the ideal sharp image and the image restored by a unique deconvolution filter. To implement the latter method, we integrate - for the first time to our knowledge - MSE optimization to the software Synopsys CodeV. Taking as an application example the design of a Cooke triplet having good image quality everywhere in the field of view (FoV), we show that it is possible, by leveraging deconvolution during the optimization process, to adapt the spatial distribution of imaging performance to a prescribed goal. We also demonstrate the superiority of MSE co-optimization over the other methods, both in terms of quantitative and visual image quality.

Self-calibration for Mueller polarimeters based on DoFP polarization imagers.

Mueller polarimeters (MPs) based on division of focal plane (DoFP) polarization imagers can achieve fast measurements and significantly improve the effectiveness of Mueller polarimetry. In this Letter, we demonstrate a unique property of the DoFP sensor-based MPs: they can be calibrated without any extra polarizing reference element. We describe a self-calibration method that only requires six image acquisitions; based on our analysis, the calibration accuracy is only limited by the noise.

Definition of an error map for DoFP polarimetric images and its application to retardance calibration.

With the recent development of division of focal plane (DoFP) polarization sensors, it is possible to perform polarimetric analysis of a scene with a reduced number of acquisitions. One drawback of these sensors is that polarization estimation can be perturbed by the spatial variations of the scene. We thus propose a method to compute a map that indicates where polarization estimation can be trusted in the image. It is based on two criteria: the consistency between the intensity measurements inside a super-pixel and the detection of spatial intensity variations. We design both criteria so that a constant false alarm rate can be set. We demonstrate the benefit of this method to improve the precision of dynamic retardance calibration of DoFP-based full Stokes imaging systems.

On the validity domain of maximum likelihood estimators for depth-of-field extension in single-molecule localization microscopy.

Localization microscopy approaches with enhanced depth-of-field (EDoF) are commonly optimized using the Cramér-Rao bound (CRB) as a criterion. It is widely believed that the CRB can be attained in practice by using the maximum-likelihood estimator (MLE). This is, however, an approximation, of which we define in this paper the precise domain of validity. Exploring a wide range of settings and noise levels, we show that the MLE is efficient when the signal-to-noise ratio (SNR) is such that the localization standard deviation of a single molecule is less than 20 nm. Thus, our results provide an explicit and quantitative validity boundary for the use of the MLE in EDoF localization microscopy setups optimized with the CRB.

No-Reference Physics-Based Quality Assessment of Polarization Images and Its Application to Demosaicking.

Assessing the quality of polarization images is of significance for recovering reliable polarization information. Widely used quality assessment methods including peak signal-to-noise ratio and structural similarity index require reference data that is usually not available in practice. We introduce a simple and effective physics-based quality assessment method for polarization images that does not require any reference. This metric, based on the self-consistency of redundant linear polarization measurements, can thus be used to evaluate the quality of polarization images degraded by noise, misalignment, or demosaicking errors even in the absence of ground-truth. Based on this new metric, we propose a novel processing algorithm that significantly improves demosaicking of division-of-focal-plane polarization images by enabling efficient fusion between demosaicking algorithms and edge-preserving image filtering. Experimental results obtained on public databases and homemade polarization images show the effectiveness of the proposed method.

Influence of high numerical aperture on depth-of-field enhancing phase mask optimization in localization microscopy.

The depth-of-field (DoF) of localization microscopes can be extended by placing a phase mask in the aperture stop of the objective. To optimize these masks and characterize their performance, defocus is in general modeled by a simple quadratic pupil phase term. However, this model does not take into account two essential characteristics of localization microscopy setups: an extremely high numerical aperture (NA) and a mismatch between the refractive indices of the immersion liquid and sample. Using the more realistic high NA image formation model of Gibson & Lanni (GL), we show that the DoF extension is simply reduced by a NA-dependent scaling factor. We also show that, provided this scaled DoF extension factor is taken into account, masks optimized with the approximate quadratic model are still nearly optimal in the framework of the GL model. This result is important since it establishes that generic optimized masks can be used in setups with different NA and immersion indices.

Integration time optimization and starting angle autocalibration of full Stokes imagers based on a rotating retarder.

Full Stokes imaging can be performed with a continuously rotating retarder in front of a fixed polarizer and a standard camera (RRFP) or a division of a focal plane polarization camera (RRDOFP). We determine the optimal number and duration of intensity measurements through a cycle of the retarder for these two types of setups as a function of instrument and noise parameters. We show that this number mainly depends on the type of noise that corrupts the measurements. We also show that with these setups, the starting angle of the retarder need not be known precisely and can be autocalibrated, which facilitates synchronization of the rotating retarder with the camera. We investigate the precision and feasibility domain of this autocalibration and show the RRDOFP setup has more attractive properties compared with RRFP setup. These results are important to optimize and facilitate the operation of polarization imagers based on a rotating retarder.

Multispectral imaging detects gastritis consistently in mouse model and in humans.

Gastritis constitutes the initial step of the gastric carcinogenesis process. Gastritis diagnosis is based on histological examination of biopsies. Non-invasive real-time methods to detect mucosal inflammation are needed. Tissue optical properties modify reemitted light, i.e. the proportion of light that is emitted by a tissue after stimulation by a light flux. Analysis of light reemitted by gastric tissue could predict the inflammatory state. The aim of our study was to investigate a potential association between reemitted light and gastric tissue inflammation. We used two models and three multispectral analysis methods available on the marketplace. We used a mouse model of Helicobacter pylori infection and included patients undergoing gastric endoscopy. In mice, the reemitted light was measured using a spectrometer and a multispectral camera. We also exposed patient's gastric mucosa to specific wavelengths and analyzed reemitted light. In both mouse model and humans, modifications of reemitted light were observed around 560 nm, 600 nm and 640 nm, associated with the presence of gastritis lesions. These results pave the way for the development of improved endoscopes in order to detect real-time gastritis without the need of biopsies. This would allow a better prevention of gastric cancer alongside with cost efficient endoscopies.

Co-designed annular binary phase masks for depth-of-field extension in single-molecule localization microscopy.

Single-molecule localization microscopy has become a prominent approach to study structural and dynamic arrangements of nanometric objects well beyond the diffraction limit. To maximize localization precision, high numerical aperture objectives must be used; however, this inherently strongly limits the depth-of-field (DoF) of the microscope images. In this work, we present a framework inspired by "optical co-design" to optimize and benchmark phase masks, which, when placed in the exit pupil of the microscope objective, can extend the DoF in the realistic context of single fluorescent molecule detection. Using the Cramér-Rao bound (CRB) on localization accuracy as a criterion, we optimize annular binary phase masks for various DoF ranges, compare them to Incoherently Partitioned Pupil masks and show that they significantly extend the DoF of single-molecule localization microscopes. In particular we propose different designs including a simple and easy-to-realize two-ring binary mask to extend the DoF. Moreover, we demonstrate that a simple maximum likelihood-based localization algorithm can reach the localization accuracy predicted by the CRB. The framework developed in this paper is based on an explicit and general information theoretic criterion, and can thus be used as an engineering tool to optimize and compare any type of DoF-enhancing phase mask in high resolution microscopy on a quantitative basis.

When is retardance autocalibration of microgrid-based full Stokes imagers possible and useful?

Full Stokes polarimetric images can be obtained from two acquisitions with a microgrid polarization camera equipped with a retarder. When the retardance is imperfectly known, it can be calibrated from the measurements, but this requires three image acquisitions and may cause divergence of estimation variance at a low signal-to-noise ratio. We determine closed-form equations allowing one to decide in which experimental conditions autocalibration is possible and useful, and to quantify the performance gain obtained in practice. These results are validated by real-world experiments.

Optimal polarimeter structures for estimating polarization degree, angle, and ellipticity in the presence of additive noise.

In polarimetry, it is well known that measurement matrices based on spherical 2 designs optimize Stokes vector estimation in the presence of additive noise. We investigate the optimal matrices for estimation of the degree of polarization (DOP), the angle of polarization (AOP), and the ellipticity (EOP), which are nonlinear functions of the Stokes vector. We demonstrate that spherical 2 designs also optimize DOP and EOP estimation, but not AOP estimation, for which optimal structures consist of linear analyzers forming a regular polygon on the equator of the Poincaré sphere.