In this review paper, we present a previously proposed approach for the estimation of degree of polarization under low illumination conditions. To avoid the saturation problems, zeros from the denominator of the Degree of polarization calculation are excluded which changes the distribution of the photon detection from Poisson to a Truncated Poisson distribution. 3D polarimetric imaging experiments had been conducted via light field under low illumination environments to verify the proposed approach.
KEYWORDS: Polarimetry, 3D image processing, Cameras, Integral imaging, Signal to noise ratio, Polarization, Stereoscopy, Sensors, Imaging systems, Image sensors
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.
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.
We recently reported that phase encoded samples produced with metallic components (e.g. gold nano-particles) can be distinguished by means of polarized light. Classification was carried out using data obtained from speckle distributions. Despite this approach is very successful, it cannot be used with codes made of materials that do not change the state of polarization of the illumination source. In the present communication we analyze the feasibility of using optical diffusers as polarizing phase encoders for optical security systems. Preliminary optical results seem to support our thesis.
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.
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.
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 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 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.
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 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.
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 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.
We analyze the behavior of complex information in the Fresnel domain, taking into account the limited capability to display complex values of liquid crystal devices when they are used as holographic displays. To do this analysis we study the reconstruction of Fresnel holograms at several distances using the different parts of the complex distribution. We also use the information adjusted with a method that combines two configurations of the devices in an adding architecture. The results of the error analysis show different behavior for the reconstructions when using the different methods. Simulated and experimental results are presented.
We present an educational resource based in a virtual optical laboratory for undergraduate students. It consists in a web-based textbook with several applets to illustrate the theory and simplify the teaching tasks in the classroom. These programs can also be used as a method for self-learning in an on-line environment. Applets are written in Java language using the Java Network Launching Protocol (JNPL) for avoiding problems related with the use of specific browsers or Java interpreters versions.
We study how the aberrations of the optical system affect the correlation peak heights in a joint transform correlator. A Meopta objective is evaluated as Fourier-transform system, and the correlation results taking into account its aberrations are presented. Finally, a simple method to minimize the effect of the aberrations is proposed.
On the basis of a representation of the general solution of the Maxwell equations in terms of the angular spectrum of the electromagnetic field, the concept of the so-called closest solution to a given field is analyzed. In particular, we investigate the spatial profile and the polarization structure of the closest field to a polarized Gaussian beam.
We propose an implementation to display full complex information using two ferroelectric liquid crystals spatial light modulators. We compare the simulated and experimental results obtained.
In this work we analyze the behavior of complex information in Fresnel domain taking into account the limited capability to display complex transmittance values of current liquid crystal devices, when used as holographic displays. In order to do this analysis we compute the reconstruction of Fresnel holograms at several distances using the different parts of the complex distribution (real and imaginary parts, amplitude and phase) as well as using the full complex information adjusted with a method that combines two configurations of the devices in an adding architecture. The RMS error between the amplitude of these reconstructions and the original amplitude is used to evaluate the quality of the information displayed. The results of the error analysis show different behavior for the reconstructions using the different parts of the complex distribution and using the combined method of two devices. Better reconstructions are obtained when using two devices whose configurations densely cover the complex plane when they are added. Simulated and experimental results are also presented.
In this work we present a generalization to complex transmittance objects of the Jared-Ennis algorithm for the generation of Synthetic Discriminant Function filters (SDFs). The original algorithm consists of the resolution of a nonlinear system of equations by means of an iterative procedure, including a phase adaptation of the filter. The method shown here takes into account the modulation of liquid crystal displays (LCD) both for scene and filter, generalizing the problem to the complex plane. Considering this new method gives a more realistic picture as the LCD modulation gives a complex distribution of the scenes instead of only real values as considered before. For instance, we use a high contrast configuration to display the scenes. Moreover, the addition of new parameters to the problem allows us to consider filters other than the phase-only one. In our case, we use a phase-mostly configuration to display the filter and the metric optimized is the maximum correlation intensity, as in the original method. Simulated results are presented for a two-class problem, as well as experimental results obtained in a VanderLugt correlator. The filters produce the desired correlation response in both cases.
The operation of a joint transform correlator is based on two Fourier transforms in cascade. The first one produces the joint power spectrum; the second one yields the correlation. In this work, we study the influence of the aberrations that affect the optical systems that produce the two Fourier transforms, by computing the wave aberration of the diffraction setups from data obtained by ray tracing. First, we consider the aberration only in the power spectrum, then only in the transformation of power spectrum to give the correlation and finally, in the two steps at the same time. In the study, real conditions have been reproduced and the dimensions and resolutions of real liquid crystal-displays have been used. The results show that the quality of the correlation is determined mostly by the aberrations of the first diffraction stage.
Optical correlators process two-dimensional images that come from a three-dimensional world. Filters designed for object recognition of three-dimensional scenes must have the information of all possible views. This implies a large quantity of filters, especially when the object is moving with respect to the observer. Although filters designed through the synthetic discriminant functions formalism can encode information of several images, there is a practical limit imposed by the noise appearing at the correlation plane. Fast correlators are one way of solving this problem. In this work we propose a global process for detecting 3-D objects based on fast sequential correlations with filters derived from the different possible views of the target. The acquisition of these views is accomplished in a fast and simple way by means of a three-dimensional scanner based on stereovision techniques. The 3-D model of the object thus obtained is then used to compute synthetic plane views from any desired viewpoint. A compact correlator has been developed which uses fast CCD cameras for input and output, and ferroelectric SLMs (spatial light modulators) to display the scene and the sequence of filters. The process of digitizing the 3-D coordinates is described in detail, from the acquisition of the stereopair of images, the stereo-matching algorithm we use and the final integration of all data sets into a common object-centered coordinate system. Also, general engineering problems involved in the design and construction of the correlator are analysed and discussed.
In this work we propose a method to obtain single centered correlations with an optical setup based on a joint transform correlator. This approach is a modification of a previous procedure that required displaying devices with a full 2(pi) phase modulation. The displaying requirements are less restrictive than before, allowing the use of many modulators and configurations. This new method is based on a binary power spectrum and it needs an interferometric process to obtain a single detection peak. To validate our new procedure, we propose an optical setup and we present the experimental results achieved.
The inclusion of optoelectronic displays has enabled optical correlators to improve radically and maintain the competitive edge of optical processors among information processing fields. In this work, an optical correlator has been implemented by using two VGA liquid crystal displays as spatial light modulators, both at the input and Fourier planes. These devices have been removed from a commercial videoprojector and have been characterized in order to operate in different configurations. This characterization is based on an interferometric procedure which includes amplitude and phase modulation measurements. For a phase-only modulation we have compared the use of linearly and elliptically polarized light. In this latter case we have found an operating curve with phase-only modulation which takes values from 0 to π radians. This is a limitation when a pure phase filter is required as in data security and encryption, in wavelet-based systems, and in optical pattern recognition, among others. An application in this latter field is presented in our work as a solution to overcome this limited phase depth. We propose a modification of the classical phase-only filter based on the use of the absolute value of the phase. Experimental correlation results using the optical setup and the modified filter have been obtained.
In this work we present the developments for the simulation of image formation through an ophthalmic lens. The procedure is, essentially an exact ray tracing taking into account the particular mobility conditions of the exit pupil. This leads to the computation of astigmatism as a function of the field angle considered. In the computer program, the use of a commercial glass with a gradient in the refractive index (GRIN material) is foreseen. This latter feature proves to be useful for two practical objectives: modifying the power and the astigmatism of the lens. To illustrate these points, an example based on a lens made by deforming a plane parallel plate of GRIN material will be presented.
The proposal of this work is the study of a method for characterization of the focal of ophthalmic lenses whose surface refraction index has been modified by diffusion techniques based on thermal ion exchange in glass. In particular the aim is the measurement of the variations in focal length of ophthalmic lenses after undergoing a diffusion process. An interferometric technique has been used and computer simulations have also been carried out.
The reduction of geometrical distances in optical correlators, in order to build miniaturized systems, has become a necessity for realistic applications [1]. In general, the scope of the studies carried out is only focused in some parts of the problem. Nowadays, liquid crystal devices (LCD), usually removed from commercial videoprojectors, are used to display images in optical setups. As a result of using pixelated panels, the viability study of building an optical correlator in a reduced space should not be only limited to a design of optical systems. It must include an analysis of the behaviour of the displaying devices. Another issue that has not been raised yet is the reduction of the material needed to control simultaneously two LCDs in a Vander Lugt correlator, which involves a duplication in the driving electronics. We analyze in depth several engineering problems regarding the construction of a Vander Lugt correlator with LCDs at the input and Fourier planes. In order to reduce the length of the setup we have designed two telephoto systems. An original method to control both devices with a single 8-bit frame grabber and a single videoprojector electronics is presented. We have solved the problems related to pixel-by-pixel control when displaying the data from the frame grabber on the LCDs. An accurate analysis of the phase modulation capability of the panels is also discussed. Experimental results obtained with this setup are presented.
The use of photorefractive materials such as Bi12SiO20 as a dynamic holographic medium is becoming an interesting alternative to current liquid crystal based modulators in real-time optical image processing. In this paper 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 deal with two possible ways to register the Fourier plane information: direct detection of the joint power spectrum or obtaining the spectrum from the phase-only distribution of the joint input. We also compare the latter case with the performance of a binary joint transform correlator. Analysis, simulations and experimental results are presented.
In this communication we present a method to correlate a scene with a filter using a binary joint transform correlator. The method consists in defining a suitable threshold function to binarize the joint power spectrum. By suitable binarizing the joint power spectrum it is possible to obtain correlations equivalent to those obtained with spatial correlation filters with a VanderLugt correlator. We analyze the problem theoretically and also provide some simulated results.
An experimental realization of optical correlation for pattern recognition by using phase only filters as a reference in a real-time joint transform correlation is presented. The correlator operates with a liquid crystal television as the input and a photorefractive crystal at the recording plane. The use of photorefractive materials such as Bi12SiO20 as a dynamic holographic medium is becoming an interesting alternative to current liquid crystal based modulators in real-time optical image processing. In order to improve the performance of detection, the phase-only filter has been taken into account. Usually, this filter is used in the frequency domain, although it can be employed in the object space, becoming the reference in a joint transform correlator. As this filter requires negative values, holographic codification methods are required to encode it. Experimental results are presented and compared with those obtained with the classical matched filter.
A method for the experimental realization of optical correlation for pattern recognition by using phase only filters as a reference in a real-time joint transform correlator is presented. The intensity of the interferences produced by the optical Fourier transform of both scene and reference is registered by means of a CCD camera and displayed through a liquid crystal device. A second Fourier transform accomplishes a real-time correlation. In our implementation we have used a videoprojector as a spatial light modulator. Non linear effects in the joint power spectrum have been shown as a technique for improving discrimination in a joint transform correlator. The design of spatial correlation filters is another technique to enhance discrimination. Usually, these filters are computed in the frequency domain, although they can be carried out in object space, by computing their inverse Fourier transform, becoming the reference in a joint transform correlator. In this case a codification is necessary because of the negative values. Another problem involved in the implementation is the filter normalization because usually the filters have a lower transmission than the scene. In this paper, the normalization factor has been chosen in order to optimize the optical efficiency of the process.
An implementation of a phase extractor Vander-Lugt correlator, which operates with a single spatial light modulator is suggested. Optical phase-retrieval manipulation, based on the symmetrization of the input scenes is proposed. As a consequence, the number of digital manipulations of the information is substantially reduced and spatial correlation filters can be used. Theoretical analysis and some simulated results are provided. The study also includes the results when the scenes are immersed into background or zero mean additive noise.
When real time optical pattern recognition is carried out by means of spatial light modulators (SLMs), 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 SLM allow it, an interesting possibility for improving the overall intensity in the Fourier plane is the replication of the scene. This procedure may be used in two different ways: regular along a lattice structure or non regular or random replication. In this work we analyze the usefulness of these methods, both to obtain diffraction images or cross-correlation between images in a joint transform correlator.
Phase-only filters are attractive designs because they provide good noise resistance and fairly narrow peaks together with optimum light efficiency. Since they contain only phase information they are easier to implement in current spatial light modulators. However, their extension to the synthetic discriminant function (SDF) formalism is troublesome owing to the nonlinear constraints involved. We developed a new procedure for computing phase-only SDF filters which is intended to overcome some of the pitfalls of previous methods.
The aim of this communication is to study one possible way of avoiding the limitations associated with mathematical poles and low optical efficiency of the inverse filter. In order to increase the performance characteristics of the filter, phase- only and inverse amplitude information are combined in a similar way to amplitude-compensated matched filter. A threshold value determines the ratio of filter frequencies in phase state or in inverse state. The behaviour of signal-to-noise ratio, discrimination and optical efficiency as a function of this threshold have been analyzed by digital simulation. According to the study, the median of the power spectrum reference histogram is an adequate threshold for filter design. By taking this value, satisfactory results of signal-to-noise ratio and discrimination have been obtained. With reference to optical efficiency, a significant increase has been observed by comparing with inverse filter or amplitude- compensated matched filter.
A simple method for optical implementation of a composite filter in a joint transform correlator is presented. A composite filter in object space is a real function, but by adding an appropriate constant value, only positive values are obtained. As a drawback, the bias introduced decreases the relative height of the correlation peaks in the recognition process. Non-linear effects in a joint transform correlator are used to increase discrimination by using positive composite filters. Digital simulation and optical implementation of the process has been carried out, achieving the non-linearities by means of saturation effects on the intensity detection process.
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