Stokes holography

Detecting topological index of randomly scattered V-point singularities using Stokes correlations

Topological defects in vector fields constitute polarization singularities that have numerous applications in classical and quantum optics. These beams are inhomogeneously polarized and are shown to self-heal under symmetric amplitude perturbations. Polarization singular beams are characterized using a singularity index that can be detected using Stokes polarimetry or other interferometric and diffraction approaches. However, the information about the singularity index is lost when these beams travel through random scattering media; this results in a spatially fluctuating polarization pattern known as polarization speckle. This paper proposes and experimentally demonstrates a new method to detect the topological index of these randomly scattered V-point singularities using higher-order Stokes correlations in a lensless condition. A detailed theoretical basis is developed, and the performance of the technique is demonstrated by retrieving the signature of polarization singularities with Poincaré-Hopf index |η|=1 and |η|=2. We also demonstrate that by studying the intensity-intensity correlations of the polarization speckle, it is possible to differentiate between different vector beams having the same magnitude as the Poincaré-Hopf index.

Real-time Jones phase microscopy for studying transparent and birefringent specimens

Tissue birefringence is an intrinsic marker of potential value for cancer diagnosis. Traditionally, birefringence properties have been studied by using intensity-based formalisms, through the Mueller matrix algebra. On the other hand, the Jones matrix description allows for a direct assessment of the sample's anisotropic response. However, because Jones algebra is based on complex fields, requiring measurements of both phase and amplitude, it is less commonly used. Here we propose a real-time imaging method for measuring Jones matrices by quantitative phase imaging. We combine a broadband phase imaging system with a polarization-sensitive detector to obtain Jones matrices at each point in a megapixel scale image, with near video rate capture speeds. To validate the utility of our approach, we measured standard targets, partially birefringent samples, dynamic specimens, and thinly sliced histopathological tissue.

Three-dimensional vectorial holography based on machine learning inverse design

The three-dimensional (3D) vectorial nature of electromagnetic waves of light has not only played a fundamental role in science but also driven disruptive applications in optical display, microscopy, and manipulation. However, conventional optical holography can address only the amplitude and phase information of an optical beam, leaving the 3D vectorial feature of light completely inaccessible. We demonstrate 3D vectorial holography where an arbitrary 3D vectorial field distribution on a wavefront can be precisely reconstructed using the machine learning inverse design based on multilayer perceptron artificial neural networks. This 3D vectorial holography allows the lensless reconstruction of a 3D vectorial holographic image with an ultrawide viewing angle of 94° and a high diffraction efficiency of 78%, necessary for floating displays. The results provide an artificial intelligence-enabled holographic paradigm for harnessing the vectorial nature of light, enabling new machine learning strategies for holographic 3D vectorial fields multiplexing in display and encryption.

Single-shot quantitative birefringence microscopy for imaging birefringence parameters

A method for realizing 2D single-shot measurements of birefringence parameters (including both retardation and optic axis orientation) of anisotropic materials using a simple recording setup and an efficient processing algorithm is proposed. The recording setup can be built simply by inserting a circular polarizer and a polarization beam splitter, respectively, in the object path and reference path of a conventional off-axis holographic imaging system, with no need for other adjustments. An algorithm for quantitatively retrieving the birefringence parameters from one single-shot hologram is proposed and demonstrated, in which a new quantity describing the birefringence, called complex birefringence parameter, is introduced, and a set of formulas used to extract the birefringence parameters is derived. Some experimental results are given for demonstrating the feasibility of the method that reveal that the method may provide another effective approach for investigating the birefringence properties of dynamic anisotropic materials, especially the birefringence induced by ultrafast pulse lasers.

Lensless Stokes holography with the Hanbury Brown-Twiss approach

The recording and reconstruction of the Stokes parameter is of paramount importance for the description of the vectorial interference of light. Polarization holography provides a complete vectorial wavefront, however, direct recording and reconstruction of the hologram is not possible in a situation where the object is located behind the random scattering layer. The Stokes holography plays an important role in such situations and makes use of the Fourier transform relation between the Stokes parameters (SPs) at the scattering plane and the generalized Stokes parameters (GSPs) of the random field. In this paper, we propose and experimentally demonstrate the Stokes holography with the Hanbury Brown-Twiss (HBT) interferometer. We also propose and implement a lensless Fourier configuration for the Stokes holography. This permits us to reconstruct the wavefront from the GSPs at any arbitrary distance from the scattering plane. The application of the proposed technique is experimentally demonstrated for the 3D imaging of two different objects lying behind the random scattering medium. Depth information of the 3D objects is obtained by digitally propagating the generalized Stokes parameters to a different longitudinal distance. The quality of the reconstruction is assessed by measuring the overall visibility, efficiency, and PSNR of the reconstruction parameters.

Jones matrix microscopy from a single-shot intensity measurement

Quantitative measurement of Jones matrix elements is crucial for the study of light polarization with the wide range of applications. Here, we propose and experimentally demonstrate a novel method of Fourier space sharing to determine spatially resolved all four elements of the Jones matrix from a single-intensity frame. This is achieved by applying a holographic approach and making use of two triangular polarization Sagnac interferometers in the sample and reference arms. The proposed technique is flexible to adjust carrier frequencies in order to meet the varying demand of different anisotropic samples. A Jones matrix microscopy system is developed and applied to transparent samples. Experimental implementation of the proposed technique is demonstrated by determining the Jones matrix elements of commercially available known samples and liquid crystal droplets.

Controlled modulation of depolarization in laser speckle

A new technique based on superposition of two speckle patterns is proposed and demonstrated for controlled modulation of the spatial polarization distribution of the resultant speckle. It is theoretically and experimentally demonstrated that controlled modulation of the spatial polarization distribution of laser speckle can be achieved by proper choice of the polarization states as well as the average spatial intensity of the constituent speckles. It is shown that the proposed technique is useful to generate different speckle patterns with sinusoidal variation in their degree of polarization, which can be tuned from zero to unity. This technique can find application in sensing, biomedical studies, and in determining the rotation of an electric field vector after passing through a scattering medium.

Hybrid correlation holography with a single pixel detector

Correlation holography reconstructs three-dimensional (3D) objects as a distribution of two-point correlations of the random field detected by two-dimensional detector arrays. Here, we describe a hybrid method, a combination of optical and computational channels, to reconstruct the objects from only a single pixel detector. An experimental arrangement is proposed as a first step to realizing the technique; we have simulated the experimental model for both scalar and vectorial objects. The proposed technique provides depth focusing and 3D reconstruction with digital suppression of unwanted frequency spectrum.

Single-shot digital holographic microscopy for quantifying a spatially-resolved Jones matrix of biological specimens

Field-based polarization measurements are essential for the completeness of information when exploiting the complex nature of optical responses of target objects. Here, we demonstrate digital holographic microscopy for quantifying a polarization-sensitive map of an object with a single-shot measurement. Using the image-splitting device generating four different copies of an object image and a separate reference beam of an off-axis configuration enables single-shot and multi-imaging capability. With the use of two polarization filters, four complex field images containing an object's polarization response are obtained simultaneously. With this method, we can construct a complete set of 2-by-2 Jones matrix at every single point of the object's images, and thus clearly visualize the anisotropic structures of biological tissues with low level of birefringence. This method will facilitate the high-precision measurements for fast dynamics of the polarization properties of biological specimens.

Single-shot dual-wavelength phase reconstruction in off-axis digital holography with polarization-multiplexing transmission

A new system for single-shot dual-wavelength digital holographic microscopy with polarization-multiplexing path-shared transmission is presented. The key feature of the optical configuration is that the interference waves of two wavelengths having orthogonal polarization can transmit in the same interferometer paths at the same time, and two polarizers orthogonal to each other are placed in front of the CCD to realize single-shot recording of two holograms. The correlative filtering algorithm of the spatial-frequency spectrum for dual-wavelength digital holograms is reliable and efficient in the dual-wavelength path-shared configuration. The phase reconstruction in dual-wavelength digital holographic imaging is achieved by using this filtering algorithm. The experiment results of phase reconstruction of a groove grating demonstrate the reliability and validity of this optical configuration and the correlative filtering algorithm. This polarization-multiplexing configuration for dual-wavelength digital holography is compact and has more flexibility for the replacement of different-wavelength lasers.

Polarization modulation for imaging behind the scattering medium

We propose and experimentally demonstrate a technique, based on polarization modulation, for imaging of the polarization discriminating object hidden behind a scattering medium. This is realized by making use of the relation between the complex correlation function of the randomly scattered orthogonal polarization components in the far field and polarized source structure at the scattering plane. Full use of a polarimetric parameter at the scattering plane is realized in the object plane reconstruction behind the scattering medium using a backpropagation approach. To demonstrate application of the technique, imaging of two different objects lying behind the scattering media is presented.

Synthesis of statistical properties of a randomly fluctuating polarized field

An experimental technique for the synthesis of statistical properties of a randomly fluctuating polarized field is investigated and experimentally demonstrated. The technique offers the controlled synthesis of coherence and polarization and subsequent analysis of the synthesized field is carried out by making use of two-point intensity correlation and the speckle holographic technique. The controlled synthesis is achieved by using an aperture of specific size at the source plane and generating a vortex in one of the orthogonal polarization components of the polarized field, thereby producing a singularity in off-diagonal elements of the coherence-polarization matrix.

Experimental determination of generalized Stokes parameters

A new technique to determine generalized Stokes parameters by making use of the speckle holographic technique and the two-point intensity correlation is proposed and experimentally demonstrated. Assuming Gaussian statistics and spatial stationarity, a speckle hologram is generated prior to the fourth-order correlation, i.e., the two-point intensity correlation. This measurement technique offers a complete retrieval of complex generalized Stokes parameters. The application of the proposed technique is experimentally demonstrated for two different, random source structures.

One-step Jones matrix polarization holography for extraction of spatially resolved Jones matrix of polarization-sensitive materials

We propose, for the first time to our knowledge, a method for realizing one-step measurement of two-dimensional Jones matrix parameters of polarization-sensitive materials. This method could be called one-step Jones matrix polarization holography (JMPH). Our theoretical analysis and the experimental results demonstrate that a double-source polarization interferometer combined with angular multiplexing holography make it possible to realize one-step holographic measurements of four spatially resolved Jones matrix parameters. Compared with the existing methods, our one-step JMPH has a simpler optical arrangement and easier measuring procedure. We believe that it will provide a new approach for development of an integrated system suitable for measuring, in real-time, a Jones matrix or transmittance matrix, as well as dynamic polarization imaging.

LCD panel characterization by measuring full Jones matrix of individual pixels using polarization-sensitive digital holographic microscopy

We present measurements of the full Jones matrix of individual pixels in a liquid-crystal display (LCD) panel. Employing a polarization-sensitive digital holographic microscopy based on Mach-Zehnder interferometry, the complex amplitudes of the light passing through individual LCD pixels are precisely measured with respect to orthogonal bases of polarization states, from which the full Jones matrix components of individual pixels are obtained. We also measure the changes in the Jones matrix of individual LCD pixels with respect to an applied bias. In addition, the complex optical responses of a LCD panel with respect to arbitrary polarization states of incident light were characterized from the measured Jones matrix.

Generation of spatial coherence comb using Dammann grating

A new technique to generate a spatially varying coherence field, such as a coherence comb using a Dammann grating, is proposed and experimentally demonstrated. The principle of the technique lies with the vectorial van Cittert-Zernike theorem, which connects vectorial source structure with the coherence-polarization of the light. The Dammann grating is encoded into one of the polarization components of the light to shape the vectorial source structure and, consequently, the coherence-polarization of the light. Experimental results on the generation of a spatial coherence comb by the Dammann grating are presented for different orders.

Polarization holographic microscopy for extracting spatio-temporally resolved Jones matrix

We present a high-speed holographic microscopic technique for quantitative measurement of polarization light-field, referred to as polarization holographic microscopy (PHM). Employing the principle of common-path interferometry, PHM quantitatively measures the spatially resolved Jones matrix components of anisotropic samples with only two consecutive measurements of spatially modulated holograms. We demonstrate the features of PHM with imaging the dynamics of liquid crystal droplets at a video-rate.