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The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task. Although in recent years several methods have been reported in the literature, this measure is still not routinely performed. This paper describes a method that allows us to estimate and visualize the longitudinal component of the field in a relatively simple way. First, we measure the transverse components of the focused field in several planes normal to the optical axis. Then, we determine the complex amplitude of the two transverse field components: the phase is obtained using a phase recovery algorithm, while the phase difference between the two components is determined from the Stokes parameters. Finally, the longitudinal component is estimated using the Gauss’s theorem. Experimental results show an excellent agreement with theoretical predictions.

Cryo-electron microscopy has become one of the most important tools in biological research to reveal the structural information of macromolecules at near-atomic resolution. In single-particle analysis, the vitrified sample is imaged by an electron beam and the detectors at the end of the microscope column produce movies of that sample. These movies contain thousands of images of identical particles in random orientations. The data need to go through an image processing workflow with multiple steps to obtain the final 3D reconstructed volume. The goal of the image processing workflow is to identify the acquisition parameters to be able to reconstruct the specimen under study. Scipion provides all the tools to create this workflow using several image processing packages in an integrative framework, also allowing the traceability of the results. In this article the whole image processing workflow in Scipion is presented and discussed with data coming from a real test case, giving all the details necessary to go from the movies obtained by the microscope to a high resolution final 3D reconstruction. Also, the power of using consensus tools that allow combining methods, and confirming results along every step of the workflow, improving the accuracy of the obtained results, is discussed.

Cryo-electron microscopy has established as a mature structural biology technique to elucidate the three-dimensional structure of biological macromolecules. The Coulomb potential of the sample is imaged by an electron beam, and fast semi-conductor detectors produce movies of the sample under study. These movies have to be further processed by a whole pipeline of image-processing algorithms that produce the final structure of the macromolecule. In this chapter, we illustrate this whole processing pipeline putting in value the strength of "meta algorithms," which are the combination of several algorithms, each one with different mathematical rationale, in order to distinguish correctly from incorrectly estimated parameters. We show how this strategy leads to superior performance of the whole pipeline as well as more confident assessments about the reconstructed structures. The "meta algorithms" strategy is common to many fields and, in particular, it has provided excellent results in bioinformatics. We illustrate this combination using the workflow engine, Scipion.

International audience; Xmipp is an open-source software package consisting of multiple programs for processing data originating from electron microscopy and electron tomography, designed and managed by the Biocomputing Unit of the Spanish National Center for Biotechnology, although with contributionsfrom many other developers over the world. During its 25 years of existence, Xmipp underwent multiple changes and updates. While there were many publications related to new programs and functionality added to Xmipp, there is no single publication on the Xmipp as a package since 2013.In this article, we give an overview of the changes and new work since 2013, describe technologies and techniques used during the development, and take a peek at the future of the package.

We introduce an algorithm able to map arbitrary complex values into an arbitrary modulation curve using the K-Nearest Neighbor algorithm. The proposed algorithm is around 80 times faster than the conventional calculation.

The presence of preferred orientations in single particle analysis (SPA) by cryo-Electron Microscopy (cryoEM) is currently one of the hurdles preventing many structural analyses from yielding high-resolution structures. Although the existence of preferred orientations is mostly related to the grid preparation, in this technical note, we show that some image processing algorithms used for angular assignment and three-dimensional (3D) reconstruction are more robust than others to these detrimental conditions. We exemplify this argument with three different data sets in which the presence of preferred orientations hindered achieving a 3D reconstruction without artifacts or, even worse, a 3D reconstruction could never be achieved, We acknowledge support from “la Caixa” Foundation (Fellowship LCF/BQ/DI18/11660021. This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 713673. We also thank the financial support from the Spanish Ministry of Economy and Competitiveness through Grants BIO2016-76400-R(AEI/FEDER, UE) and SEV 2017-0712, the “Comunidad Autónoma de Madrid” through Grant: S2017/BMD-3817, Instituto de Salud Carlos III, PT17/ 0009/0010 (ISCIII-SGEFI/ERDF), European Union (EU) and Horizon 2020 through grants: CORBEL (INFRADEV-1-2014-1, Proposal: 654248), INSTRUCT-ULTRA (INFRADEV-03-2016-2017, Proposal: 731005), EOSC Life (INFRAEOSC-04-2018, Proposal: 824087), High- ResCells (ERC-2018-SyG, Proposal: 810057), IMpaCT (WIDESPREAD-03-2018 – Proposal: 857203), EOSC-Synergy (EINFRA-EOSC-5, Proposal: 857647), and iNEXT-Discovery (Proposal: 871037). The authors acknowledge the support and the use of resources of Instruct, a Landmark ESFRI project

In recent years, advances in cryoEM have dramatically increased the resolution of reconstructions and, with it, the number of solved atomic models. It is widely accepted that the quality of cryoEM maps varies locally; therefore, the evaluation of the maps-derived structural models must be done locally as well. In this article, a method for the local analysis of the map-to-model fit is presented. The algorithm uses a comparison of two local resolution maps. The first is the local FSC (Fourier shell correlation) between the full map and the model, while the second is calculated between the half maps normally used in typical single particle analysis workflows. We call the quality measure “FSC-Q”, and it is a quantitative estimation of how much of the model is supported by the signal content of the map. Furthermore, we show that FSC-Q may be helpful to detect overfitting. It can be used to complement other methods, such as the Q-score method that estimates the resolvability of atoms., Here, the authors present a cryo-EM validation method for the local analysis of the map-to-model fit and introduce FSC-Q as a quality measure. FSC-Q provides a quantitative estimation of how much of the model is supported by the signal content of the map.

The analysis of structure factors in 3D cryo-EM Coulomb potential maps and their “enhancement” at the end of the reconstruction process is a well-established practice, normally referred to as sharpening. The aim is to increase contrast and, in this way, to help tracing the atomic model. The most common way to accomplish this enhancement is by means of the so-called B-factor correction, which applies a global filter to boost high frequencies with some dampening considerations related to noise amplification. The results are maps with a better visual aspect and a quasiflat spectrum at medium and high frequencies. This practice is so widespread that most map depositions in the Electron Microscopy Data Base (EMDB) only contain sharpened maps. Here, the use in cryoEM of global B-factor corrections is theoretically and experimentally analyzed. Results clearly illustrate that protein spectra present a falloff. Thus, spectral quasi-flattening may produce protein spectra with distortions when compared with experimental ones, this fact, combined with the practice of reporting only sharpened maps, generates a sub-optimal situation in terms of data preservation, reuse and reproducibility. Now that the field is more advanced, we put forward two suggestions: (1) to use methods which keep more faithfully the original experimental signal properties of macromolecules when “enhancing” the map, and (2) to further stress the need to deposit the original experimental maps without any postprocessing or sharpening, not only the enhanced maps. In the absence of access to these original maps data is lost, preventing their future analysis with new methods., The authors would like to acknowledge economical support from The Spanish Ministry of Economy and Competitiveness through Grants BIO2016-76400-R(AEI/FEDER, UE), the “Comunidad Autónoma de Madrid” through Grant: S2017/BMD-3817.

Cryo-EM Single Particle Analysis workflows require tens of thousands of high-quality particle projections to unveil the three-dimensional structure of macromolecules. Conventional methods for automatic particle picking tend to suffer from high false-positive rates, hampering the reconstruction process. One common cause of this problem is the presence of carbon and different types of high-contrast contaminations. In order to overcome this limitation, we have developed MicrographCleaner, a deep learning package designed to discriminate, in an automated fashion, between regions of micrographs which are suitable for particle picking, and those which are not. MicrographCleaner implements a U-net-like deep learning model trained on a manually curated dataset compiled from over five hundred micrographs. The benchmarking, carried out on approximately one hundred independent micrographs, shows that MicrographCleaner is a very efficient approach for micrograph preprocessing. MicrographCleaner (micrograph_cleaner_em) package is available at PyPI and Anaconda Cloud and also as a Scipion/Xmipp protocol. Source code is available at, The authors would like to acknowledge economical support from: The Spanish Ministry of Economy and Competitiveness through Grants BIO2016-76400-R(AEI/FEDER, UE) and the “Comunidad Autónoma de Madrid and Ministry of Education of Spain” through Grant: S2017/BMD-3817. Ruben Sanchez-Garcia is recipient of an FPU fellowship.

[Motivation]: Cryo electron microscopy (EM) is currently one of the main tools to reveal the structural information of biological macromolecules. The re-construction of three-dimensional (3D) maps is typically carried out following an iterative process that requires an initial estimation of the 3D map to be refined in subsequent steps. Therefore, its determination is key in the quality of the final results, and there are cases in which it is still an open issue in single particle analysis (SPA). Small angle X-ray scattering (SAXS) is a well-known technique applied to structural biology. It is useful from small nanostructures up to macromolecular ensembles for its ability to obtain low resolution information of the biological sample measuring its X-ray scattering curve. These curves, together with further analysis, are able to yield information on the sizes, shapes and structures of the analyzed particles. [Results]: In this paper, we show how the low resolution structural information revealed by SAXS is very useful for the validation of EM initial 3D models in SPA, helping the following refinement process to obtain more accurate 3D structures. For this purpose, we approximate the initial map by pseudo-atoms and predict the SAXS curve expected for this pseudo-atomic structure. The match between the predicted and experimental SAXS curves is considered as a good sign of the correctness of the EM initial map., This work was supported by the Spanish Ministry of Economy and Competitiveness through Grants BIO2016-76400-R(AEI/FEDER, UE), Comunidad Autonoma de Madrid through Grant: S2017/BMD-3817, Instituto de Salud Carlos III, PT13/0001/0009, PT17/0009/0010 and European Union (EU) and Horizon 2020 through Grants: Elixir—EXCELERATE (INFRADEV-3-2015, Proposal: 676559), iNEXT (INFRAIA-1-2014-2015, Proposal: 653706) and INSTRUCT—ULTRA (INFRADEV-03-2016-2017, Proposal: 731005).

Deep Consensus performs particle pruning in cryo-EM image-processing workflows using a smart consensus., Single-particle cryo-electron microscopy (cryo-EM) has recently become a mainstream technique for the structural determination of macromolecules. Typical cryo-EM workflows collect hundreds of thousands of single-particle projections from thousands of micrographs using particle-picking algorithms. However, the number of false positives selected by these algorithms is large, so that a number of different ‘cleaning steps’ are necessary to decrease the false-positive ratio. Most commonly employed techniques for the pruning of false-positive particles are time-consuming and require user intervention. In order to overcome these limitations, a deep learning-based algorithm named Deep Consensus is presented in this work. Deep Consensus works by computing a smart consensus over the output of different particle-picking algorithms, resulting in a set of particles with a lower false-positive ratio than the initial set obtained by the pickers. Deep Consensus is based on a deep convolutional neural network that is trained on a semi-automatically generated data set. The performance of Deep Consensus has been assessed on two well known experimental data sets, virtually eliminating user intervention for pruning, and enhances the reproducibility and objectivity of the whole process while achieving precision and recall figures above 90%.

Linear polarizers are commonly used for projecting the direction of the electric field of a transverse paraxial beam on the direction of the polarizer axis. However, the use of these devices with highly convergent field poses a practical problem because the non transversal character of electric field. In this article, we discuss the behavior of highly focused beams with spiral polarization when they pass through a polarizer. Interestingly, beams with azimuthal polarization display a non negligible irradiance in the direction of propagation after passing through a polarizer. On top of that, we found that the irradiance of a highly focused radially polarized beam after a polarizer is notably different from the projection of the field on the direction of the polarizer axis.

Electron microscopy of macromolecular structures is an approach that is in increasing demand in the field of structural biology. The automation of image acquisition has greatly increased the potential throughput of electron microscopy. Here, the focus is on the possibilities in Scipion to implement flexible and robust image-processing workflows that allow the electron-microscope operator and the user to monitor the quality of image acquisition, assessing very simple acquisition measures or obtaining a first estimate of the initial volume, or the data resolution and heterogeneity, without any need for programming skills. These workflows can implement intelligent automatic decisions and they can warn the user of possible acquisition failures. These concepts are illustrated by analysis of the well known 2.2 angstrom resolution beta-galactosidase data set., Spanish Ministry of Economy and Competitiveness through the BIO2016-76400-R (AEI/FEDER, UE) grant, the Comunidad Auto ´noma de Madrid through grant S2017/BMD3817, the Instituto de Salud Carlos III (PT17/0009/0010), the European Union (EU) and Horizon 2020 through the CORBEL

© The Author(s) 2019., [Motivation]: Recent technological advances and computational developments have allowed the reconstruction of Cryo-Electron Microscopy (cryo-EM) maps at near-atomic resolution. On a typical workflow and once the cryo-EM map has been calculated, a sharpening process is usually performed to enhance map visualization, a step that has proven very important in the key task of structural modeling. However, sharpening approaches, in general, neglects the local quality of the map, which is clearly suboptimal. [Results]: Here, a new method for local sharpening of cryo-EM density maps is proposed. The algorithm, named LocalDeblur, is based on a local resolution-guided Wiener restoration approach of the original map. The method is fully automatic and, from the user point of view, virtually parameter-free, without requiring either a starting model or introducing any additional structure factor correction or boosting. Results clearly show a significant impact on map interpretability, greatly helping modeling. In particular, this local sharpening approach is especially suitable for maps that present a broad resolution range, as is often the case for membrane proteins or macromolecules with high flexibility, all of them otherwise very suitable and interesting specimens for cryo-EM. To our knowledge, and leaving out the use of local filters, it represents the first application of local resolution in cryo-EM sharpening., The authors would like to acknowledge economical support from: the Comunidad de Madrid through grant CAM (S2017/BMD-3817), the Spanish Ministry of Economy and Competitiveness (BIO2016-76400-R) and the European Union and Horizon 2020 through grants INSTRUCT-ULTRA (INFRADEV-03-2016-2017, Proposal: 731005) and iNEXT (INFRAIA-1-2014-2015, Proposal: 653706).

In the present communication, we describe how to produce long light distributions in the focal area of a high numerical aperture optical system using a custom modulation function with spiral charge. This analysis expands our previous developments in the field. We analyze the effect of this new element on the behavior of light along the optical axis.

According to intensity consideration along the propagation axis, we derived mathematical conditions for a family of modulating functions able to produce needles of arbitrary length, sub-wavelength width and almost constant irradiance. These functions are derived by introducing mathematical constrains on the on-axis power content. As a result, the modulating distribution is continuous with no jumps within or at the edge of the pupil. Numerical results suggests that the proposed approach is suitable for producing high quality needles.

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed., Spanish Ministry of Economy and Competitiveness through grants BIO2013-44647-R and BIO2016-76400-R (AEI/FEDER, UE), Comunidad Autonoma de Madrid through grant S2017/BMD-3817, Instituto de Salud Carlos III through grants PT13/0001/0009 and PT17/0009/0010, the European Union (EU) and Horizon 2020 through West-Life (EINFRA-2015-1, Proposal 675858), CORBEL (INFRADEV-1-2014-1, Proposal 654248), ELIXIR–EXCELERATE (INFRADEV-3-2015, Proposal 676559), iNEXT (INFRAIA-1-2014-2015, Proposal 653706), EOSCpilot (INFRADEV-04-2016, Proposal 739563) and the National Institutes of Health (P41GM 103712) (IB).

Recent technological advances and computational developments, have allowed the reconstruction of cryo-EM maps at near-atomic resolution structures. Cryo-EM maps benefit significantly of a “postprocessing” step, normally referred to as “sharpening”, that tends to increase signal at medium/high resolution. Here, we propose a new method for local sharpening of volumes generated by cryo-EM. The algorithm (LocalDeblur) is based on a local resolution-guided Wiener restoration approach, does not need any prior atomic model and it avoids artificial structure 1 factor corrections. LocalDeblur is fully automatic and parameter free. We show that the new method significantly and quantitatively improving map quality and interpretability, especially in cases of broad local resolution changes (as is often the case of membrane proteins).

The Map Challenge organized by the Electron Microscopy Data Bank has prompted the development of an Xmipp high resolution reconstruction protocol (which we will refer to as highres) that is integrated in the software platform Scipion . In this work we describe the details of the image angular alignment and map reconstruction steps in our new method. This algorithm is similar to the standard projection matching approach with some important modifications, especially in the area of detecting significant features in the reconstructed volume. We show that the new method is able to produce higher resolution maps than the current de facto standard as measured by the Fourier Shell Correlation, the Monogenic Local Resolution and EMRinger.

We introduce a new method for producing optical needles with tunable length and almost constant irradiance based on the evaluation of the on-axis power content of the light distribution at the focal area. According to theoretical considerations, we propose an adaptive modulating continuous function that presents a large derivative and a zero value jump at the entrance pupil of the focusing system. This distribution is displayed on liquid crystal devices using holographic techniques. In this way, a polarized input beam is shaped and subsequently focused using a high numerical aperture (NA) objective lens. As a result, needles with variable length and nearly constant irradiance are produced using conventional optics components. This procedure is experimentally demonstrated obtaining a 53λ-long and 0.8λ-wide needle.

Three dimensional electron microscopy is becoming a very data-intensive field in which vast amounts of experimental images are acquired at high speed. To manage such large-scale projects, we had previously developed a modular workflow system called Scipion (de la Rosa-Trevín et al., 2016). We present here a major extension of Scipion that allows processing of EM images while the data is being acquired. This approach helps to detect problems at early stages, saves computing time and provides users with a detailed evaluation of the data quality before the acquisition is finished. At present, Scipion has been deployed and is in production mode in seven Cryo-EM facilities throughout the world., Spanish Ministry of Economy and Competitiveness through Grants BIO2016-76400R(AEI/FEDER, UE) and AEI/FEDER BFU 2016 74868P, the Comunidad Autónoma de Madrid through Grant: S2017/BMD-3817, European Union (EU) and Horizon 2020 through grant Corbel (INFRADEV-1-2014-1, Proposal: 654248). The “Knut & Alice Wallenberg Foundation”, and “A Pilot Facility development grant from Science for Life Laboratory”. European Union (EU) and Horizon 2020 through grant EOSCpilot (INFRADEV-04-2016, Proposal: 739563).This work used the EGI Infrastructure and is co-funded by the EGIEngage project (Horizon 2020) under Grant No. 654142. European Union (EU) and Horizon 2020 through grant West-Life (EINFRA-2015-1, Proposal: 675858) European Union (EU) and Horizon 2020 through grant Elixir - EXCELERATE (INFRADEV-3-2015, Proposal: 676559) European Union (EU) and Horizon 2020 through grant iNEXT (INFRAIA-1-2014-2015, Proposal: 653706).

An experiment is presented in which a partially coherent source endowed with circular coherence is generated. The source is synthesized through a time averaging procedure, so that the mutual intensity is used as the basic correlation function. The correlation between points at different radial distances from the source center is tested by means of a Young interferometer. To confirm the perfect coherence among points along a circle concentric with the source center, the Young mask is replaced by an array of equally spaced pinholes arranged along a circle. The observed pattern is identical to that produced by the same mask, illuminated by perfectly coherent light.

Linear polarizers are present in all kind of optical systems. These devices behave as vector projectors in the polarization direction assuming quasi-transverse beams in the paraxial domain. Nevertheless, the performance of polarizers used in combination with focused beams requires a more in-depth analysis. Understanding this behavior is essential in microscopy applications because of the non-negligible longitudinal irradiance in the focal plane. In this talk, we discuss the effect of polarizers on the focused electric field. Experimental results show a good agreement with theoretical predictions based on considering linear polarizers as anisotropic plates.

In this communication we analyze the light field distribution of a highly focused radially polarized beam when passes through a linear polarizer. The polarizer is modeled as a plane-parallel uniaxial absorbing medium with the optical axis parallel to the plate surfaces of the polarizer. Analytical results and numerical calculations are provided.

© 2019 Optical Society of America, Optical needles produced by means of diffractive technology might display limited quality and uniformity. It has been suggested that the bulky optical elements present on these setups can be responsible of such behavior. In particular, issues such as the lack of flatness of the optical components, modulation errors in the holographic displays, and optical aberrations might degrade the quality of the needle. In this paper, we model how these variables affect the uniformity of the irradiance of the needle on the propagation axis. A comparison between experimental and computationally estimated results is provided., Ministerio de Economía y Competitividad (MINECO) (FIS2016-75147-C3-1-P)

Recently, a variety of applications requiring the use of non-uniformly polarized beams have been described. Moreover, digital holography using liquid crystal displays has provided a way of implementing in practice such beams. In particular, in the field of optical security, this type of beams has become very important since information can be encrypted using polarization keys. Moreover, focusing a non uniform polarized beam using a high numerical aperture lens provides a way of encoding information in the longitudinal component of the field. Security can be improved when the system works in low light illumination conditions.

We propose a method for tailoring light spots in the focal region with tunable polarization and shape using a single high focusing system. The proposed method is based in the relationship between the polarization distribution in the input beam and the filed distribution in the focal region. We introduce an incident vortex field with two arbitrary parameters that enable us modifying the transverse polarization and the size in both transverse and longitudinal directions.

In this work a physically realizable pseudo Schell-model planar light source with optical vortex is proposed. The characteristics of irradiance and coherence of the beam radiated by this type of source are analysed at the source plane and upon free paraxial propagation.

Dark plasmon modes in metal nanoparticle systems are usually excited by non-optical means. We show that strongly focused illumination can lead to excitation of dark modes. We first use rigorous vectorial diffraction theory to compute the distribution of light at the focus and then numerically calculate the response of single particles and particle dimers. Controlling the distribution of light arriving at the focusing lens by pupil filters enables enhancing the excitation of dark modes. Overall, these results present guidelines for the excitation of dark plasmon modes using standard optical instrumentation.

A new class of partially coherent light sources is introduced. At the source plane, they exhibit perfect coherence along any annulus that is concentric to the source center. Between two points at different distances from the center, coherence can be partial or even vanishing. Such sources can be synthesized by using a generalized form of van Cittert Zernike theorem where axial sources are used. Beams radiated by this type of source are analyzed at the source plane and upon free propagation for some simple cases. (C) 2017 Optical Society of America

The aim of this paper is to provide a formal framework for designing highly focused fields with specific transversal features when the incoming beam is partially polarized. More specifically, we develop a field with a transversal component that remains unpolarized in the focal area. Moreover, its longitudinal component exhibits non-zero values on axis. Special attention is paid to the design of the input beam and the development of the experiment. The implementation of such fields is possible by using an interferometric setup combined with the use of digital holography techniques. Experimental results are compared with those obtained numerically.

The target of this communication is to present a method for tailoring the complex amplitude and the polarization at the entrance pupil of a high numerical aperture objective lens in order to obtain focused fields with transverse circular polarization at any plane. Analytical expressions within the framework of the Richards-Wolf vectorial model are derived and some numerical results are presented.

In this communication we analyze the feasibility of experimentally implementing arbitrary three-dimensional vectorial distributions in the focal area of a converging lens. The analysis is carried out using the framework of the closest electromagnetic field to a target vectorial function. An optical setup based on the use of liquid crystal devices and an objective lens is also discussed.

Methods for generating beams with arbitrary polarization based on the use of liquid crystal displays have recently attracted interest from a wide range of sources. In this paper we present a technique for generating beams with arbitrary polarization and shape distributions at a given plane using a Mach-Zehnder setup. The transverse components of the incident beam are processed independently by means of spatial light modulators placed in each path of the interferometer. The modulators display computer generated holograms designed to dynamically encode any amplitude value and polarization state for each point of the wavefront in a given plane. The steps required to design such beams are described in detail. Several beams performing different polarization and intensity landscapes have been experimentally implemented. The results obtained demonstrate the capability of the proposed technique to tailor the amplitude and polarization of the beam simultaneously.

Recently, the development of optical setups capable of generating beams with arbitrary polarization have attracted broad interest. One possible way to implement such devices is by taking advantage of the properties of liquid crystal spatial light modulators, which act as optical phase retarders controlled by computer. In this communication we present the design of an alternative experimental setup for the generation of light beams with arbitrary spatially-variant polarization distribution. The objective is to develop a flexible optical device capable of dynamically encode any elliptical polarization state in each point of the wavefront. Our approach is based on a Mach-Zehnder setup combined with a translucent modulator in each path of the interferometer. The transverse beam components of the incident light beam are processed independently, and modified by means of their respective modulator displaying a specifically tailored computer generated phase hologram.

We develop a method for generating focused vector beams with circular polarization at any transverse plane. Based on the Richards-Wolf vector model, we derive analytical expressions to describe the propagation of these set of beams near the focal area. Since the polarization and the amplitude of the input beam are not uniform, an interferometric system capable of generating spatially-variant polarized beams has to be used. In particular, this wavefront is manipulated by means of spatial light modulators displaying computer generated holograms and subsequently focused using a high numerical aperture objective lens. Experimental results using a NA = 0.85 system are provided: irradiance and Stokes images of the focused field at different planes near the focal plane are presented and compared with those obtained by numerical simulation.

A new model of physically realizable electromagnetic source is proposed. The source is partially coherent and non-uniformly totally polarized. The coherence and polarization characteristics of this new source are analyzed. The spatial coherence area of the source can be easily modified at will. The state of polarization is linear across the transverse plane of the source with an azimuth that varies from point to point in a different way depending on the selected values of the parameters that define the source.

In this Letter, we describe the behavior of partially coherent, partially polarized focused vector beams after passing a linear polarizer placed at the focal plane of a high numerical aperture microscope lens. In particular, we develop a mathematical framework for such beams that helps the understanding of the performance of polarizers when interact with non-paraxial beams. The features of the focused field after the polarizer are numerically evaluated for some illustrative examples.

A method for generating beams with arbitrary polarization and shape is proposed. Our design requires the use of a Mach-Zehnder set-up combined with translucent liquid crystal displays in each arm of the interferometer; in this way, independent manipulation of each transverse beam components is possible. The target of this communication is to develop a numerical procedure for calculating the holograms required for dynamically encode any amplitude value and polarization state in each point of the wavefront. Several examples demonstrating the capabilities of the method are provided.

We present a polarimetric-based optical encoder for image encryption and verification. A system for generating random polarized vector keys based on a Mach-Zehnder configuration combined with translucent liquid crystal displays in each path of the interferometer is developed. Polarization information of the encrypted signal is retrieved by taking advantage of the information provided by the Stokes parameters. Moreover, photon-counting model is used in the encryption process which provides data sparseness and nonlinear transformation to enhance security. An authorized user with access to the polarization keys and the optical design variables can retrieve and validate the photon-counting plain-text. Optical experimental results demonstrate the feasibility of the encryption method.