Lensless Stokes holography with the Hanbury Brown-Twiss approach

Folded interferometer to measure coherence-polarization matrix

We present and experimentally demonstrate a new, to the best of our knowledge, technique to quantitatively measure coherence-polarization (BCP) matrix with correlations of only two Stokes fluctuations. The BCP matrix is a square matrix with four elements that involves two-point correlations among orthogonal polarization components. A theoretical framework of the technique is developed, and its viability is demonstrated by a proof of principle experiment. Experimental tests and measurement of the elements of the BCP matrix of statistically stationary beams are demonstrated.

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.

Lensless imaging of plant samples using the cross-polarized light

Lensless imaging has recently become an alternative and cost-effective choice for many macro and micro applications, like wave-front sensing, fluorescence imaging, holographic microscopy, and so on. However, the polarized imaging, especially the cross-polarized light, has rarely been explored and integrated in lensless imaging methods. In this paper, we introduce the cross-polarized illumination into the lensless system for high-contrast and background-free imaging of plant samples. We capture a snapshot measurement and apply the blind deconvolution for reconstruction, obtaining the depolarized imaging of plant samples. Experiments exhibit the specific and sparse structures of the root system and vessel distribution of samples. We also build a corresponding lens-based system for performance comparison. This proposed lensless system is believed to have the potential in studies on the root development and water transport mechanism of plants in the future.

Measuring complex correlation matrix of partially coherent vector light via a generalized Hanbury Brown-Twiss experiment

We introduce an effective method for measuring the spatial distribution of complex correlation matrix of a partially coherent vector light field obeying Gaussian statistics by extending our recently advanced generalized Hanbury Brown-Twiss experiment. The method involves a combination of the partially coherent vector light with a pair of fully coherent reference vector fields and a measurement of the intensity-intensity cross-correlation of the combined fields. We show the real and imaginary parts of the complex correlation matrix can be recovered through a judicious control of the phase delay between two reference fields. We test the feasibility of our method by measuring the complex correlation matrix of a specially correlated radially polarized vector beam and we find the consistence between the experimental results and our general theory. We further show that our complex correlation matrix measurement can be used in reconstructing the polarization states hidden behind a thin-layer diffuser.

Imaging of polarimetric-phase object through scattering medium by phase shifting

Light propagating through a scattering medium generates a random field, which is also known as a speckle. The scattering process hinders the direct retrieval of the information encoded in the light based on the randomly fluctuating field. In this study, we propose and experimentally demonstrate a method for the imaging of polarimetric-phase objects hidden behind a scattering medium based on two-point intensity correlation and phase-shifting techniques. One advantage of proposed method is that it does not require mechanical rotation of polarization elements. The method exploits the relationship between the two-point intensity correlation of the spatially fluctuating random field in the observation plane and the structure of the polarized source in the scattering plane. The polarimetric phase of the source structure is determined by replacing the interference intensity in traditional phase shift formula with the Fourier transform of the cross-covariance of the intensity. The imaging of the polarimetric-phase object is demonstrated by comparing three different phase-shifting techniques. We also evaluated the performance of the proposed technique on an unstable platform as well as using dynamic diffusers, which is implemented by replacing the diffuser with a new one during each phase-shifting step. The results were compared with that obtained with a fixed diffuser on a vibration-isolation platform during the phase-shifting process. A good match is found among the three cases, thus confirming that the proposed intensity-correlation-based technique is a useful one and should be applicable with dynamic diffusers as well as in unstable environments.

Generalized Hanbury Brown-Twiss effect for Stokes parameters

The classic experiments by Hanbury Brown and Twiss (HBT) were concerned with the correlation of intensity fluctuations at two different positions in a wave field. We generalize the HBT effect that occurs in random electromagnetic beams by examining its polarization-resolved version. This leads naturally to the concept of correlations of fluctuations of the four Stokes parameters. We calculate the correlations of such "Stokes fluctuations" for the case of Gaussian statistics. When the two points of observation coincide, these correlations reduce to "Stokes scintillations." Our work reveals a new layer of complexity in random beams by showing that the HBT effect and the scintillation coefficient are just two of many correlations that are present. We illustrate that, in general, the fluctuations of the various Stokes parameters are all correlated by studying beams and sources with different polarization states.