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The target of this paper is to implement an optically-based visual encryption system able to work with a large set of optical codes. The optical setup comprises a holographic system designed to generate spirally-polarized highly focused fields and an imaging module able to perform polarimetric analysis. In a previous stage, the optical system is numerically simulated in order to produce synthetic polarimetric distributions that are used to train a convolutional neural network. Interestingly, the way the network is trained depends on the selected state of polarization. Then, secret codes are split in two XOR-connected ones that are optically processed. The corresponding experimental polarimetric distribution is obtained and transmitted to the corresponding recipients, that can recover the code by interrogating the neural network. Finally, combining the two pieces of information, the encrypted message can be decoded.

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.

In this work we develop a partially-coherent spirally-polarized imaging system for generating gradual edge detection images. A rotating diffuser is used for producing illumination sources with tunable degree of coherence. Using a 4f configuration, the frequency content of the image is modified by means of a vortex half-wave retarder as a spatial filter. Accordingly, we analytically describe a spirally-polarized imaging system illuminated with a Gauss–Schell source using paraxial coherence-polarization theory. Numerical simulations and experimental results demonstrate the validity of our approach. We use a referenceless spatial content descriptor to assess the quality of the recorded images as a function of the coherence state of the source.

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.

We explore the detection limits of the Degree of Polarization by capturing Light Fields and introducing a semi-empirical formula to model its behaviour as the mean amount of detected photons in the sensor decreases.

A new version of the code system pengeom , which provides a complete set of tools to handle different geometries in Monte Carlo simulations of radiation transport, is presented. The distribution package consists of a set of Fortran subroutines and a Java graphical user interface that allows building and debugging the geometry-definition file, and producing images of the geometry in two- and three-dimensions. A detailed description of these tools is given in the original paper [ Comput. Phys. Commun. 199 (2016) 102–113] and in the code manual included in the distribution package. The present new version corrects a bug in the Fortran subroutines, and it includes various improvements of the Java graphical user interface. New Version Program Summary Program Title: pengeom CPC Library link to program files: https://doi.org/10.17632/zgswr8kyf5.1 Licensing provisions: CC BY NC 3.0 Programming language: Fortran 90, Java Journal reference of previous version: Comput. Phys. Commun. 199 (2016) 102–113 Does the new version supersede the previous version?: Yes Reasons for the new version: The original Fortran code contained a subtle bug, which had an effect only when (1) a particle moving within a void region entered a material body, and (2) the particle was left in the void volume because of numerical roundoff errors (undershot). In such case, the steering main program erroneously concluded that the particle was in the external vacuum and, consequently, it discontinued the simulation of the particle trajectory. This anomalous behavior has been corrected by shifting the position of the particle a small distance, determined by the parameters of the master ray equation, which places the particle a small distance inside the material body. In the original Fortran subroutines, inconsistencies in the geometry-definition file resulted in a stop of the program; this reaction was hard to control from a graphical user interface. The present new version has been verified to work correctly under Java 8, Java 11, and Java 13. Summary of revisions: In the new version the tracking bug is corrected. In addition, any apparent syntax error is now resolved by returning the control to the calling program with an error flag activated and with an error message. Various aspects of the Java user interface have been improved: the text editor now includes line numbers, which are used to locate possible inconsistencies and errors in the geometry definition file; the size of the application window can now be modified, and the possible sizes of the graphics windows are adapted to the actual resolution of the monitor; the action of keystroke commands under Windows, Linux, and macOS is now the same. Nature of problem: The Fortran subroutines perform all geometry operations in Monte Carlo simulations of radiation transport with arbitrary interaction models. They track particles through complex quadric geometries, i.e., through material systems consisting of homogeneous bodies limited by quadric surfaces. Particles are moved in steps (free flights) of a given length, which is dictated by the simulation program, and are halted when they cross an interface between media of different compositions or when they enter selected bodies. At the end of each step, pengeom returns the indices of the material and body where the particle is. Solution method: pengeom is tailored to optimize simulation speed and accuracy. Fast tracking is accomplished by the use of quadric surfaces, which facilitate the calculation of ray intersections , and of modules (connected volumes limited by quadric surfaces) organized in a hierarchical structure. Optimal accuracy is obtained by considering fuzzy surfaces, with the aid of a simple algorithm that keeps control of multiple intersections of a ray and a surface. The 64-bit Java GUI PenGeomJar provides a complete geometry toolbox; it allows building and debugging of the geometry definition file, as well as visualizing the resulting geometry in two and three dimensions. Additional comments including restrictions and unusual features: All geometrical operations are performed internally. The connection between the steering main program and the tracking routines is through a Fortran module, which contains the state variables of the transported particle, and the input-output arguments of subroutine STEP . Rendering of two- and three-dimensional images is performed by using the pengeoem subroutines, so that what we see in the images is what is passed to the simulation program. By default pengeom can handle systems with up to 5,000 bodies and 10,000 surfaces. These numbers can be increased by editing the source file. [1] J. Almansa, F. Salvat-Pujol, G. Diaz-Londono, A. Carnicer, A.M. Lallena, and Francesc Salvat, Comput. Phys. Commun. 199 (2016) 102–113.

The calculation of the propagation of partially coherent and partially polarized optical beams involves using 4D Fourier Transforms. This poses a major drawback, taking into account memory and computational capabilities of nowadays computers. In this paper we propose an efficient calculation procedure for retrieving the irradiance of electromagnetic Schell-model highly focused beams. We take advantage of the separability of such beams to compute the cross-spectral density matrix by using only 2D Fourier Transforms. In particular, the number of operations depends only on the number of pixels of the input beam, independently on the coherence properties. To provide more insight, we analyze the behavior of a beam without a known analytical solution. Finally, the numerical complexity and computation time is analyzed and compared with some other algorithms.

We overview a previously reported three-dimensional (3D) polarimetric integral imaging method and algorithms for extracting 3D polarimetric information in low light environment. 3D integral imaging reconstruction algorithm is first performed to the originally captured two-dimensional (2D) polarimetric images. The signal-to-noise ratio (SNR) of the 3D reconstructed polarimetric image is enhanced comparing with the 2D images. The Stokes polarization parameters are measured and applied for the calculation of the 3D volumetric degree of polarization (DoP) image of the scene. Statistical analysis on the 3D DoP can extract the polarimetric properties of the scene. Experimental results verified the proposed method out performs the conventional 2D polarimetric imaging in low illumination environment.

Three-dimensional (3D) polarimetric integral imaging (InIm) to extract the 3D polarimetric information of objects in photon-starved conditions is investigated using a low noise visible range camera and a long wave infrared (LWIR) range camera, and the performance between the two sensors is compared. Stokes polarization parameters and degree of polarization (DoP) are calculated to extract the polarimetric information of the 3D scene while integral imaging reconstruction provides depth information and improves the performance of low-light imaging tasks. An LWIR wire grid polarizer and a linear polarizer film are used as polarimetric objects for the LWIR range and visible range cameras, respectively. To account for a limited number of photons per pixel using the visible range camera in low light conditions, we apply a mathematical restoration model at each elemental image of visible camera to enhance the signal. We show that the low noise visible range camera may outperform the LWIR camera in detection of polarimetric objects under low illumination conditions. Our experiments indicate that for 3D polarimetric measurements under photon-starved conditions, visible range sensing may produce a signal-to-noise ratio (SNR) that is not lower than the LWIR range sensing. We derive the probability density function (PDF) of the 2D and 3D degree of polarization (DoP) images and show that the theoretical model demonstrates agreement to that of the experimentally obtained results. To the best of our knowledge, this is the first report comparing the polarimetric imaging performance between visible range and infrared (IR) range sensors under photon-starved conditions and the relevant statistical models of 3D polarimetric integral imaging.

Under low light conditions, sensor noise perturbs the photodetection distribution. Using light field cameras, we present a biased estimator that reduces sensor noise and is equivalent to the maximum likelihood estimator under high illumination conditions.

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.

Optical diffusers have been widely investigated from both theoretical and practical points of view.1 In particular, a large number of papers focus on numerical models related to the behavior of light interacting with such devices (see, for instance,2, 3). Despite diffusers have been investigated from multiples points of view, polarization is not a particularly interesting property in the present analysis.4 The objective of this communication is to evaluate to what extent a thick diffuser modifies and reinforces the uniqueness of the optical signature of the sample. In order to achieve this objective, we develop a ray-tracing calculation in order to determine polarization changes; data from a real diffuser surface is used. Then, experimental results validate the proposed model. Recent developments in optical authentication and validation demonstrate the ability of the properties of light to distinguish among counterfeit and true samples.5 Sometimes, metallic nanoparticles or thin films technology is used during the fabrication process in order to provide a strong polarimetric signature. In particular, the combined examination of the state of polarization of light after interacting with the sample and the statistical analysis of the speckle patterns provide enough information to train machine learning methods. In this way, these techniques would be able to predict whether the sample is true or fake.6-8 On the other hand, phase-encoding masks using cello-type diffusers provide an extra security layer. After propagation, phase encoded information becomes a Poisson-like noise distribution and thus, any attempt to access to the original signal is very difficult. In a recent paper we studied the capacity of three-dimensional phase coders using thick diffusers to enrich the amount of information for training machine learning algorithms.9 The paper is organized as follows. In section 2, we describe the numerical approach used and present several experimental results that validate the model. Finally, our conclusions are presented in section 3

Conventional polarimetric imaging may perform poorly in photon-starved environments. In this Letter, we demonstrate the potential of integral imaging and dedicated algorithms for extracting three-dimensional (3D) polarimetric information in low light, and reducing the effects of measurement uncertainty. In our approach, the Stokes polarization parameters are measured and statistically analyzed in low illumination conditions through 3D-reconstructed polarimetric images with dedicated algorithms to improve the signal-to-noise ratio (SNR). The 3D volumetric degree of polarization (DoP) of the scene is calculated by statistical algorithms. We show that the 3D polarimetric information of the object can be statistically extracted from the Stokes parameters and 3D DoP images. Experimental results along with a novel statistical analysis verify the feasibility of the proposed approach for polarimetric 3D imaging in photon-starved environments and show that it outperforms its two-dimensional counterpart in terms of SNR. To the best of our knowledge, this is the first report of novel optical experiments along with novel statistical analysis and dedicated algorithms to recover 3D polarimetric imaging signatures in low light.

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.

An overview of multidimensional integral imaging for sensing, visualization, and recognition in degraded environments is presented. Applications include 3D visualization, photon starved imaging, material inspection, IR imaging, passive depth estimation, automated human gesture recognition, and long-range imaging.

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.

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.

We present an overview of our work on multidimensional integral imaging systems. Integral-imaging-based multidimensional optical sensing and imaging will be described for 3-D visualization, seeing through obscurations, material inspection, augmented reality, biomedical applications, and object recognition from microscales to long-range imaging.

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.

We overview our recent work [1] on utilizing three-dimensional (3D) optical phase codes for object authentication using the random forest classifier. A simple 3D optical phase code (OPC) is generated by combining multiple diffusers and glass slides. This tag is then placed on a quick-response (QR) code, which is a barcode capable of storing information and can be scanned under non-uniform illumination conditions, rotation, and slight degradation. A coherent light source illuminates the OPC and the transmitted light is captured by a CCD to record the unique signature. Feature extraction on the signature is performed and inputted into a pre-trained random-forest classifier for authentication.

Image information encoding using random phase masks produce speckle-like noise distributions when the sample is propagated in the Fresnel domain. As a result, information cannot be accessed by simple visual inspection. Phase masks can be easily implemented in practice by attaching cello-tape to the plain-text message. Conventional 2D-phase masks can be generalized to 3D by combining glass and diffusers resulting in a more complex, physical unclonable function. In this communication, we model the behavior of a 3D phase mask using a simple approach: light is propagated trough glass using the angular spectrum of plane waves whereas the diffusor is described as a random phase mask and a blurring effect on the amplitude of the propagated wave. Using different designs for the 3D phase mask and multiple samples, we demonstrate that classification is possible using the k-nearest neighbors and random forests machine learning algorithms.

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.

Authentication of encoded information is a popular current trend in optical security. Recent research has proposed the production of secure unclonable ID tags and devices with the use of nanoscale encoding and thin-film deposition fabrication techniques, which are nearly impossible to counterfeit but can be verified using optics and photonics instruments. Present procedures in optical encryption provide secure access to the information, and these techniques are improving daily. Nevertheless, a rightful recipient with access to the decryption key may not be able to validate the authenticity of the message. In other words, there is no simple way to check whether the information has been counterfeited. Metallic nanoparticles may be used in the fabrication process because they provide distinctive polarimetric signatures that can be used for validation. The data is encoded in the optical domain, which can be verified using physical properties with speckle analysis or ellipsometry. Signals obtained from fake and genuine samples are complex and can be difficult to distinguish. For this reason, machine-learning classification algorithms are required in order to determine the authenticity of the encoded data and verify the security of unclonable nanoparticle encoded or thin-film-based ID tags. In this paper, we review recent research on optical validation of messages, ID tags, and codes using nanostructures, thin films, and 3D optical codes. We analyze several case scenarios where optically encoded devices have to be authenticated. Validation requires the combined use of a variety of multi-disciplinary approaches in optical and statistical techniques, and for this reason, the first five sections of this paper are organized as a tutorial.

In this paper, we introduce the Mueller matrix imaging concepts for 3D Integral Imaging Polarimetry. The Mueller matrix of a complex scene is measured and estimated with 3D integral imaging. This information can be used to analyze the complex polarimetric behavior of any 3D scene. In particular, we show that the degree of polarization can be estimated at any selected plane for any arbitrary synthetic illumination source which may be difficult to produce in practice. This tool might open new perspectives for polarimetric analysis in the 3D domain. Also, we illustrate that 2D polarimetric images are noisier than 3D reconstructed polarimetric integral imaging. To the best of our knowledge, this is the first report on Mueller matrix polarimetry in 3D Integral Imaging.

© 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)

In this invited paper, we present an overview of our recently published work on 3D imaging, visualization and displays, including optical security using quantum imaging principles, 3D microscopy, healthcare, automated disease identification with 3D imaging, fatigue free augmented reality 3D glasses, and optical security and authentication using photon counting for IC inspection, polarimetric photon counting 3D imaging, and 3D human gesture recognition

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.

The calculation of the Stokes Parameters and the Degree of Polarization in 3D integral images requires a careful manipulation of the polarimetric elemental images. This fact is particularly important if the scenes are taken in low-light conditions. In this paper, we show that the Degree of Polarization can be effectively estimated even when elemental images are recorded with few photons. The original idea was communicated in [A. Carnicer and B. Javidi, 'Polarimetric 3D integral imaging in photon-starved conditions,' Opt. Express 23, 6408-6417 (2015)]. First, we use the Maximum Likelihood Estimation approach for generating the 3D integral image. Nevertheless, this method produces very noisy images and thus, the degree of polarization cannot be calculated. We suggest using a Total Variation Denoising filter as a way to improve the quality of the generated 3D images. As a result, noise is suppressed but high frequency information is preserved. Finally, the degree of polarization is obtained successfully.

The Fortran subroutine package pengeom provides a complete set of tools to handle quadric geometries in Monte Carlo simulations of radiation transport. The material structure where radiation propagates is assumed to consist of homogeneous bodies limited by quadric surfaces. The pengeom subroutines (a subset of the penelope code) track particles through the material structure, independently of the details of the physics models adopted to describe the interactions. Although these subroutines are designed for detailed simulations of photon and electron transport, where all individual interactions are simulated sequentially, they can also be used in mixed (class II) schemes for simulating the transport of high-energy charged particles, where the effect of soft interactions is described by the random-hinge method. The definition of the geometry and the details of the tracking algorithm are tailored to optimize simulation speed. The use of fuzzy quadric surfaces minimizes the impact of round-off errors. The provided software includes a Java graphical user interface for editing and debugging the geometry definition file and for visualizing the material structure. Images of the structure are generated by using the tracking subroutines and, hence, they describe the geometry actually passed to the simulation code. Program summary Program title: Pengeom Catalogue identifier: AEYH_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEYH_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 89390 No. of bytes in distributed program, including test data, etc.: 5062646 Distribution format: tar.gz Programming language: Fortran, Java. Computer: PC with Java Runtime Environment installed. Operating system: Windows, Linux. RAM: 210 MiB Classification: 21.1, 14. Nature of problem: The Fortran subroutines perform all geometry operations in Monte Carlo simulations of radiation transport with arbitrary interaction models. They track particles through material systems consisting of homogeneous bodies limited by quadric surfaces. Particles are moved in steps (free flights) of a given length, which is dictated by the simulation program, and are halted when they cross an interface between media of different compositions or when they enter selected bodies. Solution method: The pengeom subroutines are tailored to optimize simulation speed and accuracy. Fast tracking is accomplished by the use of quadric surfaces, which facilitate the calculation of ray intersections, and of modules (connected volumes limited by quadric surfaces) organized in a hierarchical structure. Optimal accuracy is obtained by considering fuzzy surfaces, with the aid of a simple algorithm that keeps control of multiple intersections of a ray and a surface. The Java GUI PenGeomJar provides a geometry toolbox; it allows building and debugging the geometry definition file, as well as visualizing the resulting geometry in two and three dimensions. Restrictions: By default pengeom can handle systems with up to 5000 bodies and 10,000 surfaces. These numbers can be increased by editing the Fortran source file. Unusual features: All geometrical operations are performed internally. The connection between the steering main program and the tracking routines is through a Fortran module, which contains the state variables of the transported particle, and the input-output arguments of the subroutine step. Rendering of two- and three-dimensional images is performed by using the pengeom subroutines, so that displayed images correspond to the definitions passed to the simulation program. Additional comments: Java editor and viewer (PenGeomJar), geometry examples, translator to POV-Ray™ format, detailed manual. The Fortran subroutine package pengeom is part of the penelope code system [1]. Running time: The running time much depends on the complexity of the material system. The most complicated example provided, phantom, an anthropomorphic phantom, has 264 surfaces and 169 bodies and modules, with different levels of grouping; the largest module contains 51 daughters. The rendering of a 3D image of phantom with 1680x1050 pixels takes about 25 s (i.e., about 1.5⋅10 −5 seconds per ray) on an Intel Core I7-3520M CPU, with Windows 7 and subroutines compiled with gfortran. References: [1] F. Salvat, PENELOPE-2014: A Code System for Monte Carlo Simulation of Electron and Photon Transport, OECD/NEA Data Bank, Issy-les-Moulineaux, France, 2015. Available from http://www.nea.fr/lists/penelope.html .

The counterfeiting of pharmaceutical products represents concerns for both industry and the safety of the general public. Falsification produces losses to companies and poses health risks for patients. In order to detect fake pharmaceutical tablets, we propose producing film-coated tablets with gold nanoparticle encoding. These coated tablets contain unique polarimetric signatures. We present experiments to show that ellipsometric optical techniques, in combination with machine learning algorithms, can be used to distinguish genuine and fake samples. To the best of our knowledge, this is the first report using gold nanoparticles encoded with optical polarimetric classifiers to prevent the counterfeiting of pharmaceutical products.

Recently, a cryptosystem based on the analysis of light in the focal area of a high numerical aperture system has been proposed. A key element in the design of this device is the selection of the polarization of the input beam. In this paper we analyze how polarization influences the performance of the encoded message. In order to avoid attacks and enhance security, the system is assumed to work in photon-counting illumination conditions.

A method for optimizing the strength of a parametric phase mask for a wavefront coding imaging system is presented. The method is based on an optimization process that minimizes a proposed merit function. The goal is to achieve modulation transfer function invariance while quantitatively maintaining final image fidelity. A parametric filter that copes with the noise present in the captured images is used to obtain the final images, and this filter is optimized. The whole process results in optimum phase mask strength and optimal parameters for the restoration filter. The results for a particular optical system are presented and tested experimentally in the laboratory. The experimental results show good agreement with the simulations, indicating that the procedure is useful.

The resolution concept in connection with the Fabry–Perot interferometer is difficult to understand for undergraduate students enrolled in physical optics courses. The resolution criterion proposed in textbooks for distinguishing equal intensity maxima and the deduction of the resolving power equation is formal and non-intuitive. In this paper, we study the practical meaning of the resolution criterion and resolution power using a computer simulation of a Fabry–Perot interferometer. The light source in the program has two monochromatic components, the wavelength difference being tunable by the user. The student can also adjust other physical parameters so as to obtain different simulation results. By analysing the images and graphics of the simulation, the resolving power concept becomes intuitive and understandable.

Research on the properties of highly focused fields mainly involved fully polarized light, whereas partially polarized waves received less attention. The aim of this Letter is to provide an appropriate framework, for designing some features of the focused field, when dealing with incoming partially polarized beams. In particular, in this Letter, we describe how to get an unpolarized field on the axis of a high numerical aperture objective lens. Some numerical results that corroborate theoretical predictions are provided.

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.

We analyze in depth several engineering problems regarding the construction of a VanderLugt correlator. Two liquid crystal devices are used in the input and Fourier planes, and the large distances involved are reduced with the help of telephoto systems. An original method to control both modulators with a single 8-bit frame grabber and a single videoprojector electronics is presented. Problems related to pixel-by-pixel addressing and the phase modulation in the panels are also discussed. All the solutions proposed in this paper have been implemented and experimental correlation results using the setup have been obtained.

A new phase modulation spatial light modulator (SLM) characterization procedure is presented, based on the analysis of the interference fringes of a Mach - Zender interferometer arrangement, by means of correlation and Fourier transform methods. This, accompanied by an amplitude calibration technique that makes use of the same experimental set-up, gives a general measurement procedure for SLM full complex characterization. As an experimental application, two different operation curves of an Epson LCTV are determined, in order to use these configurations for an optical pattern recognition procedure: a phase-only high-efficient joint transform correlator.

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.

A method to evaluate the physical realizability of an arbitrary three-dimensional vectorial field distribution in the focal area is proposed. A parameter that measures the similarity between the designed (target) field and the physically achievable beam is provided. This analysis is carried out within the framework of the closest electromagnetic field to a given vectorial function, and the procedure is applied to two illustrative cases.

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.

When real time optical pattern recognition is carried out by means of spatial light modulators, a practical situation may arise in which the size of the Fourier transform and the intensity of the light source are fixed. Then, provided the input scene and the size of the spatial light modulator allow it, an interesting possibility for improving the overall intensity in the Fourier plane is the replication of the scene, either along a regular lattice structure or a random replication. In this work we analyse the usefulness of these methods, both to obtain diffraction images or cross-correlation between images in a joint transform correlator.

The concept of the so-called closest field to a given vector function is extended to the non-polarized case. Attention is focused on transverse field solutions of the Maxwell equations whose transverse character is preserved under free propagation. The coherence matrix of the non-paraxial transverse field that is closest to a paraxial unpolarized transverse beam is given. It is shown that the intensity matrix of this closest field can be written as the sum of the intensity matrices of a non-polarized field and a totally polarized beam.

Using a binary joint transform correlator, the height of the detection peaks is not well controlled. In order to avoid this problem a method to predetermine the value of the correlation is discussed. To guarantee the success of the method, a frequency variant threshold to binarize the joint power spectrum and a suitable peak weight should he used. An experimental implementation of the method has been carried out, showing a good agreement with theoretical previsions.