Efficient calculation of highly focused electromagnetic Schell-model beams.

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.

Roadmap on digital holography [Invited].

This Roadmap article on digital holography provides an overview of a vast array of research activities in the field of digital holography. The paper consists of a series of 25 sections from the prominent experts in digital holography presenting various aspects of the field on sensing, 3D imaging and displays, virtual and augmented reality, microscopy, cell identification, tomography, label-free live cell imaging, and other applications. Each section represents the vision of its author to describe the significant progress, potential impact, important developments, and challenging issues in the field of digital holography.

Three-dimensional polarimetric integral imaging in photon-starved conditions: performance comparison between visible and long wave infrared imaging.

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.

Roadmap on 3D integral imaging: sensing, processing, and display.

This Roadmap article on three-dimensional integral imaging provides an overview of some of the research activities in the field of integral imaging. The article discusses various aspects of the field including sensing of 3D scenes, processing of captured information, and 3D display and visualization of information. The paper consists of a series of 15 sections from the experts presenting various aspects of the field on sensing, processing, displays, augmented reality, microscopy, object recognition, and other applications. Each section represents the vision of its author to describe the progress, potential, vision, and challenging issues in this field.

Mueller matrix polarimetry with 3D integral imaging.

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.

Three-dimensional polarimetric integral imaging under low illumination conditions.

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.

Effect of linear polarizers on the behavior of partially coherent and partially polarized highly focused fields.

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.

Optical encryption in the longitudinal domain of focused fields.

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.

Authentication of gold nanoparticle encoded pharmaceutical tablets using polarimetric signatures.

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.

Security authentication with a three-dimensional optical phase code using random forest classifier.

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.

Polarimetric 3D integral imaging in photon-starved conditions.

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.

Optical encryption using photon-counting polarimetric imaging.

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.

Security authentication using phase-encoded nanoparticle structures and polarized light.

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.

Optical security verification by synthesizing thin films with unique polarimetric signatures.

This Letter reports the production and optical polarimetric verification of codes based on thin-film technology for security applications. Because thin-film structures display distinctive polarization signatures, this data is used to authenticate the message encoded. Samples are analyzed using an imaging ellipsometer able to measure the 16 components of the Mueller matrix. As a result, the behavior of the thin film under polarized light becomes completely characterized. This information is utilized to distinguish among true and false codes by means of correlation. Without the imaging optics the components of the Mueller matrix become noise-like distributions and, consequently, the message encoded is no longer available. Then, a set of Stokes vectors are generated numerically for any polarization state of the illuminating beam and thus, machine learning techniques can be used to perform classification. We show that successful authentication is possible using the k-nearest neighbors algorithm in thin-films codes that have been anisotropically phase-encoded with pseudorandom phase code.

Experimental implementation of tightly focused beams with unpolarized transversal component at any plane.

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. 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.

Synthesis of highly focused fields with circular polarization at any transverse plane.

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.

Design of highly focused fields that remain unpolarized on axis.

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.

3D integral imaging of acoustically trapped objects.

3D imaging provides crucial details about the objects and scenes that may not be obtained via 2D imaging methods. However, there are several applications in which the object to be 3D-imaged requires to be immobilized. The integrated digital holographic microscopy (DHM) and optical trapping (OT) system is a useful solution for such a task, but both DHM and OT are mostly suitable for microscopic specimens. Here, for the first time to the best of our knowledge and as an analogy to the DHM-OT system, we introduce integral imaging (InIm) and acoustic trapping (AT) integrated system for 3D imaging of immobilized mesoscopic and macroscopic objects. Post-processing of InIm data enables reconstructing the scene at any arbitrary plane, therefore, it re-focuses any particular depth of the object, which is a curtail task, especially when the object is trapped by AT. We demonstrate the capability of our system by simultaneous trapping and 3D imaging of single and multiple irregularly shaped objects with mm sizes.

Reconfigurable beams with arbitrary polarization and shape distributions at a given plane.

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.

On the physical realizability of highly focused electromagnetic field distributions.

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.