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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.

An object with a unique three-dimensional (3D) optical phase mask attached is analyzed for security and authentication. These 3D optical phase masks are more difficult to duplicate or to have a mathematical formulation compared with 2D masks and thus have improved security capabilities. A quick response code was modulated using a random 3D optical phase mask generating a 3D optical phase code (OPC). Due to the scattering of light through the 3D OPC, a unique speckle pattern based on the materials and structure in the 3D optical phase mask is generated and recorded on a CCD device. Feature extraction is performed by calculating the mean, variance, skewness, kurtosis, and entropy for each recorded speckle pattern. The random forest classifier is used for authentication. Optical experiments demonstrate the feasibility of the authentication scheme.

We develop a method for encoding information in the longitudinal component of a focused field. Focused beams display a non-zero contribution of the electric field in the direction of propagation. However, the associated irradiance is very weak and difficult to isolate from the transverse part of the beam. For these reasons, the longitudinal component of a focused field could be a good choice for encoding and securing information. Using the Richards and Wolf formalism we show how to encrypt information in the longitudinal domain of the focal area. In addition, we use quantum imaging techniques to enhance the security and to prevent unauthorized access to the information. To the best of our knowledge, this is the first report on using the longitudinal component of the focused fields in optical security.

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 investigate the contributions of the propagating and the evanescent waves associated to freely-propagating nonparaxial light beams whose transverse component at some plane is azimuthally polarized. In terms of the plane-wave angular spectrum of these fields, analytical expressions are given for determining both the spatial shape of the above components and their relative weight integrated over the whole transverse plane. The results are applied to a kind of doughnut-like beams with transverse azimuthal polarization.

A comparison is established between the contributions of transverse and longitudinal components of both the propagating and the evanescent waves associated to freely propagating radially polarized nonparaxial beams. Attention is focused on those fields that remain radially polarized upon propagation. In terms of the plane-wave angular spectrum of these fields, analytical expressions are given for determining both the spatial shape of the above components and their relative weight integrated over the whole transverse plane. The results are applied to two kinds of doughnut-like beams with radial polarization, and we compare the behavior of such fields at two transverse planes.

A computational imaging system based on wavefront coding is presented. Wavefront coding provides an extension of the depth-of-field at the expense of a slight reduction of image quality. This trade-off results from the amount of coding used. By using spatial light modulators, a flexible coding is achieved which permits it to be increased or decreased as needed. In this paper a computational method is proposed for evaluating the output of a wavefront coding imaging system equipped with a spatial light modulator, with the aim of thus making it possible to implement the most suitable coding strength for a given scene. This is achieved in an unsupervised manner, thus the whole system acts as a dynamically selfadaptable imaging system. The program presented here controls the spatial light modulator and the camera, and also processes the images in a synchronised way in order to implement the dynamic system in real time. A prototype of the system was implemented in the laboratory and illustrative examples of the performance are reported in this paper. Program summary Program title: DynWFC (Dynamic WaveFront Coding) Catalogue identifier: AEKC_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKC_v1_0.html Program obtainable from: CPC Program Library, Queenʼs 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.: 10 483 No. of bytes in distributed program, including test data, etc.: 2 437 713 Distribution format: tar.gz Programming language: Labview 8.5 and NI Vision and MinGW C Compiler Computer: Tested on PC Intel ® Pentium ® Operating system: Tested on Windows XP Classification: 18 Nature of problem: The program implements an enhanced wavefront coding imaging system able to adapt the degree of coding to the requirements of a specific scene. The program controls the acquisition by a camera, the display of a spatial light modulator and the image processing operations synchronously. The spatial light modulator is used to implement the phase mask with flexibility given the trade-off between depth-of-field extension and image quality achieved. The action of the program is to evaluate the depth-of-field requirements of the specific scene and subsequently control the coding established by the spatial light modulator, in real time.

An optical recognition process using real functions in a joint transform correlation is presented. We propose a new method to implement real filters in object space by using positive-only displays. Two alternatives have been tested: the filters have been recorded by means of holographic methods based on detour phase techniques, and we also propose a simple method to obtain a non-negative filter, based on the addition of a constant in order to simplify the encoding procedure. In this case, to improve discrimination in correlation, non-linear saturation effects on joint power spectrum are used. Finally, as an example, optical detection and digital simulation results are compared using composite filters as references.

Optical trapping is an attractive and multidisciplinary topic that has become the center of attention to a large number of researchers. Moreover, it is a suitable subject for advanced students that requires a knowledge of a wide range of topics. As a result, it has been incorporated into some syllabuses of both undergraduate and graduate programs. In this paper, basic concepts in laser trapping theory are reviewed. To provide a better understanding of the underlying concepts for students, a Java application for simulating the behavior of a dielectric particle trapped in a highly focused beam has been developed. The program illustrates a wide range of theoretical results and features, such as the calculation of the force exerted by a beam in the Mie and Rayleigh regimes or the calibration of the trap stiffness. Some examples that are ready to be used in the classroom or in the computer lab are also supplied.

A new phase mask typology for wavefront-coding is proposed, the meshed phase mask (MPM). It is intended to be a flexible form in order to be easily adaptable. The use of an evaluating criterion to measure the performance of the MPM is used to optimize its shape. The MPM is uniquely defined by the fixed phase in a number of control points equally spaced in the pupil area. These control points define a regular mesh, and the continuous MPM phase surface is obtained from cubic spline interpolation. A global search algorithm is used to optimize the values at the control points, thus optimizing the MPM. The preliminary results show an improvement over the conventional cubic phase mask, especially in reducing the undesired artefacts in the final restored images.

A digital simulation of frequency limitations and saturation effects in the power spectrum of a real time joint transform correlator (JTC) has been carried out. The results of optical image recognition using a real time JTC with a liquid crystal television to display the power spectrum are compared with the simulation, for different images. The resemblance between optical and simulated results confirms the good agreement obtained by the analysis.

Micron-sized particles can be trapped by means of a highly focused beam; light is concentrated in a tiny spot using a high numerical aperture objective. In this communication we describe a numerical tool we have developed for obtaining the force exerted by a beam on a spherical dielectric particle in realistic conditions. The system (a water immersion microscope objective) is simulated using an optical system design software that provides the required information to feed the application. The calculation of the force is carried out using the ray-optics (Mie) approach.

The analysis of the importance of the amplitude and the phase of Fourier transform has been carried out by means of combining these functions between two images and observing the reconstructed image after a second transform. This processing has been studied by taking into account several possibilities, especially for very structurally different images. It is proved that the phase carries the most relevant information, but when common images are combined with images constituted by strongly marked geometric forms it is not so evident and the amplitude could play a more important role.

In terms of the Fourier spectrum, a simple but general analytical expression is given for the evanescent field associated to a certain kind of non-paraxial exact solutions of the Maxwell equations. This expression enables one to compare the relative weight of the evanescent wave with regard to the propagating field. In addition, in those cases in which the evanescent term is significant, the magnitude of the field components across the transverse profile (including the evanescent features) can be determined. These results are applied to some illustrative examples.

This work presents an application that generates real-time holograms to be displayed on a holographic optical tweezers setup; a technique that allows the manipulation of particles in the range from micrometres to nanometres. The software is written in Java, and uses random binary masks to generate the holograms. It allows customization of several parameters that are dependent on the experimental setup, such as the specific characteristics of the device displaying the hologram, or the presence of aberrations. We evaluate the software's performance and conclude that real-time interaction is achieved. We give our experimental results from manipulating 5 micron-diametre microspheres using the program., 17 pages, 6 figures

The paper describes the design of an inexpensive holographic optical tweezers setup. The setup is accompanied by software that allows real-time manipulation of the sample and takes into account the experimental features of the setup, such as aberration correction and LCD modulation. The LCD, a HoloEye LCR-2500, is the physical support of the holograms, which are calculated using the fast random binary mask algorithm. The real-time software achieves 12 fps at full LCD resolution (including aberration correction and modulation) when run on a Pentium IV HT, 3.2 GHz computer.

We present an educational resource based in an optical software package for undergraduate students. It consists in a web based textbook with several applets for illustrating the theory and simplify the teaching tasks in the classroom. These programs are also used as a method for self-learning in an on-line environment. Applets are written in Java language using the Java Network Launching Protocol (JNLP) for avoiding problems related with the use of specific browsers or java interpreter's versions.

Due to a low environmental impact, phytoremediation could become an attractive method to remove heavy metals from contaminated soils. The work reported here describes preliminary results for the recovery of mercury from contaminated soils by phytoextraction. This process involves the removal of mercury by plants followed by combustion of the plant biomass to recover the extracted mercury. Three agricultural crop plants, barley, wheat and yellow lupin, were tested in a field experiment. Mean Hg content of the soil were 29.17 µg g−1 for the 0–10 cm horizon and 20.32 eg g−1 for 10–40 cm horizon with less than 2% of the total Hg being bioavailable. The results of a field experiment showed that all the crops extracted mercury with Hg concentration reaching up to 0.479 eg g−1 for wheat. The low Hg uptake by the plants was attributed to the low availability of the mercury in the soils. The best Hg phytoextraction yield was obtained for barley reaching up to 719 mg ha−1. Further efforts are being made to improve the fraction of bioavailable mercury (by means of solubilization agents) and the biomass crop yields.

We present a simple method of constructing synthetic discriminant function filters optimized to take into account the modulation of liquid-crystal devices. This relaxation algorithm, a generalization of the Jared and Ennis method, is an iterative method that includes arbitrary modulations for both scene and filter, extending the problem to the complex plane. Simulated and experimental results obtained in a VanderLugt correlator are presented for a two-class recognition problem. The optimal number of images needed to describe an object in a filter generated in this way is discussed, and the influence of the spatial light modulation resolution on the correlation is studied.

We report the study of the influence of optical aberrations in a joint-transform correlator: The wave aberration of the optical system is computed from data obtained by ray tracing. Three situations are explored: We consider the aberration only in the first diffraction stage (generation of power spectrum), then only in the second (transformation of the power spectrum into correlation), and finally in both stages simultaneously. The results show that the quality of the correlation is determined mostly by the aberrations of the first diffraction stage and that we can optimize the setup by moving the cameras along the optical axis to a suitable position. The good agreement between the predicted data and the experimental results shows that the method explains well the behavior of optical diffraction systems when aberrations are taken into account.

An original method used to detect images in defocused scenes by means of a binary joint transform correlation is presented. The optical transfer function of the imaging lens, which presents positive and negative values, introduces sign errors in the joint power spectrum. The goal of this study is to detect the sign of the optical transfer function starting from the defocused image by means of a digital algorithm, to compensate the sign errors in the binary joint power spectrum and to obtain invariant correlations with respect to defocusing. Theoretical analysis and digital experiments to test the procedure are provided.

In this paper we present a method for reconstructing Fresnel holograms using two liquid crystal devices, one to display the amplitude information and the other to display the phase. The theoretical approach has been adapted to real configurations of VGA panels removed from a commercial video projector. The optical setup is based on the projection of the phase plane into the amplitude plane by means of an imaging lens. Simulated and experimental results are presented.

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.

As regards some objections raised with regard to a recent paper (Martinez-Herrero et al 2006 J. Opt. A: Pure Appl. Opt. 8 524–30), several clarifications are reported. They refer, on the one hand, to the criterion used to establish a limit for the validity of the paraxial approach, and, on the other hand, to the kinds of solutions of the Maxwell equations that we considered in the paper.

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.

Laser diffraction (LD) and static image analysis (SIA) of rectangular particles [United States Pharmacopeia, USP30-NF25, General Chapter , Optical Miroscopy.] have been systematically studied. To rule out sample dispersion and particle orientation as the root cause of differences in size distribution profiles, we immobilize powder samples on a glass plate by means of a dry disperser. For a defined region of the glass plate, we measure the diffraction pattern as induced by the dispersed particles, and the 2D dimensions of the individual particles using LD and optical microscopy, respectively. We demonstrate a correlation between LD and SIA, with the scattering intensity of the individual particles as the dominant factor. In theory, the scattering intensity is related to the square of the projected area of both spherical and rectangular particles. In traditional LD the size distribution profile is dominated by the maximum projected area of the particles (A). The diffraction diameters of a rectangular particle with length L and breadth B as measured by the LD instrument approximately correspond to spheres of diameter OL and OB respectively. Differences in the scattering intensity between spherical and rectangular particles suggest that the contribution made to the overall LD volume probability distribution by each rectangular particle is proportional to A2/L and A2/B. Accordingly, for rectangular particles the scattering intensity weighted diffraction diameter (SIWDD) explains an overestimation of their shortest dimension and an underestimation of their longest dimension. This study analyzes various samples of particles whose length ranges from approximately 10 to 1000 μm. The correlation we demonstrate between LD and SIA can be used to improve validation of LD methods based on SIA data for a variety of pharmaceutical powders all with a different rectangular particle size and shape.

The contribution of the propagating and the evanescent waves associated with freely propagating non-paraxial light fields whose transverse component is azimuthally polarized at some plane is investigated. Analytic expressions are derived for describing both the spatial shape and the relative weight of the propagating and the evanescent components integrated over the transverse plane. The analysis is carried out within the framework of the plane-wave angular spectrum approach. These results are used to illustrate the behavior of a kind of donut-like beams with transverse azimuthal polarization at some plane.

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.

Phase-encoded nanostructures such as quick response (QR) codes made of metallic nanoparticles are suggested to be used in security and authentication applications. We present a polarimetric optical method able to authenticate random phase-encoded QR codes. The system is illuminated using polarized light, and the QR code is encoded using a phase-only random mask. Using classification algorithms, it is possible to validate the QR code from the examination of the polarimetric signature of the speckle pattern. We used Kolmogorov–Smirnov statistical test and Support Vector Machine algorithms to authenticate the phase-encoded QR codes using polarimetric signatures.

A practical activity designed to introduce wavefront coding techniques as a method to extend the depth of field in optical systems is presented. The activity is suitable for advanced undergraduate students since it combines different topics in optical engineering such as optical system design, aberration theory, Fourier optics, and digital image processing. This paper provides the theoretical background and technical information for performing the experiment. The proposed activity requires students able to develop a wide range of skills since they are expected to deal with optical components, including spatial light modulators, and develop scripts to perform some calculations.

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.

The use of photorefractive materials such as Bi12SiO20 as dynamic holographic media is becoming an interesting alternative to that of the current liquid-crystal-based modulators in real-time optical image processing. We present an experimental realization of optical correlation for pattern recognition by means of a photorefractive joint transform correlator. The correlator operates with a liquid-crystal television as the input and a photorefractive crystal at the recording plane. We consider two possible ways of registering the Fourier plane information: conventional detection of the joint power spectrum, and utilization of only phase information at the Fourier plane by suitable preprocessing of the scene and the reference at the object plane. We compare the latter case with the performance of a binary joint transform correlator. Analysis, simulations, and experimental results are presented.

We develop a method for obtaining 3D polarimetric integral images from elemental images recorded in low light illumination conditions. Since photon-counting images are very sparse, calculation of the Stokes parameters and the degree of polarization should be handled carefully. In our approach, polarimetric 3D integral images are generated using the Maximum Likelihood Estimation and subsequently reconstructed by means of a Total Variation Denoising filter. In this way, polarimetric results are comparable to those obtained in conventional illumination conditions. We also show that polarimetric information retrieved from photon starved images can be used in 3D object recognition problems. To the best of our knowledge, this is the first report on 3D polarimetric photon counting integral imaging.