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

Validation of optical codes based on 3D nanostructures

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

Optical security and authentication using nanoscale and thin-film structures

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

Estimation of Zernike polynomials for a highly focused electromagnetic field using polarimetric mapping images and neural networks

In this communication, we present a method to estimate the aberrated wavefront at the focal plane of a vectorial diffraction system. In contrast to the phase, the polarization state of optical fields is simply measurable. In this regard, we introduce an alternative approach for determining the aberration of the wavefront using polarimetric information. The method is based on training a convolutional neural network using a large set of polarimetric mapping images obtained by simulating the propagation of aberrated wavefronts through a high-NA microscope objective; then, the coefficients of the Zernike polynomials could be recovered after interrogating the trained network. On the one hand, our approach aims to eliminate the necessity of phase retrieval for wavefront sensing applications, provided the beam used is known. On the other hand, the approach might be applied for calibrating the complex optical system suffering from aberrations. As proof of concept, we use a radially polarized Gaussian-like beam multiplied by a phase term that describes the wavefront aberration. The training dataset is produced by using Zernike polynomials with random coefficients. Two thousand random combinations of polynomial coefficients are simulated. For each one, the Stokes parameters are calculated to introduce a polarimetric mapping image as the input of a neural network model designed and trained for predicting the polynomial coefficients. The accuracy of the neural network model is tested by predicting an unseen dataset (test dataset) with a high success rate

Optical visual encryption using focused beams and convolutional neural networks

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

Multi-spectral imaging: a tool for the study of the area burned in wildfires.

Multi-spectral images provide powerful information to assess the effects of wildfires. Data can be processed, combined and analyzed in such a way that can contribute to suggest a protocol of action to help recover devastated areas. The objective of this paper is to describe methods to evaluate the surface burned in a forest fire. Combining the information recorded by the visible and infrared sensors of the Landsat 8 satellite, we can estimate the temperature of the surface after the wildfire. Finally, by comparing images recorded before and after the fire, we can estimate the surface burned

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

3D polarimetric integral imaging in low illumination conditions

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

Behavior of propagating and evanescent components in azimuthally polarized non-paraxial fields

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

On how thick diffusers can contribute to the design of optical security systems

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