Experimental determination of generalized Stokes parameters

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.

Autocorrelation functions and power spectral densities of the Stokes parameters in a polarization speckle pattern

The concept of ensemble-average polarization and coherence has been applied to studying fluctuating Stokes parameters in a polarization speckle observed when coherent light is passed through a birefringent polarization scrambler. With the aid of the ensemble-average van Cittert-Zernike theorem for the propagation of ensemble-average polar-coherence, we invesitgate the autocorrelation functions and power spectra of the Stokes parameters to expose the dependence of the polarization-related scale-size distributions on the optical geometries in which the polarization speckle arises. A generalized concept of the Stokes ensemble-average coherence areas is introduced to deal with the polarization-related average areas associated with polarization speckle.

Modulation of coherence-polarization property of speckles using a birefringent scatterer

The change of the spatial coherence-polarization (CP) property of a speckle pattern due to the modulation of birefringence in a scattering medium is investigated experimentally. The birefringence is introduced to the scattering medium by attaching layers of overhead projector (OHP) sheets to it. It is shown that the spatial polarization distribution can be tuned from a uniformly polarized case to a randomly polarized case by increasing the number of OHP sheets. The change of the spatial CP property with the number of OHP sheets is investigated from the study of the spatial degree of coherence and the degree of polarization, and these variations are further confirmed from the probability density function of the intensity of the speckle pattern and from the measurement of the generalized Stokes parameters. The effect of the change of the number of OHP sheets on the visibility of the intensity correlation function and the quality of the object retrieved through the scattering medium are also investigated.

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.

Effect of the average number of reference speckles in speckle imaging using off-axis speckle holography

The propagation of a coherent beam of light through a random scattering medium results in the generation of a speckle pattern. Although the intensity distribution of the speckle pattern is random in nature, the information of the object hidden behind a scattering medium is scrambled into it. The scrambled object information can be retrieved using the off-axis speckle holographic technique, where the object retrieval is made from a recorded interferogram, formed by the superposition of the object speckles and a tilted reference speckle pattern. In the present paper, the effect of the average number of reference speckles on the signal-to-noise ratio of the retrieved object is investigated in two different random domains of the reference speckles, which are defined from the study of the Shannon entropy of the reference speckle patterns. The observed results can be useful in tuning the visibility and sharpness of the object, retrieved by employing the off-axis speckle holographic technique.

Focal shift in tightly focused hybridly polarized Laguerre-Gaussian vector beams with zero radial index

Hybridly polarized Laguerre-Gaussian vector beams (HPLGVBs) with zero radial index are obtained based on the third type of Laguerre-Gaussian vector beams. Polarization distributions of HPLGVBs are controlled by the phase retardation of a wave plate. The ellipticity angle and polarization orientation angle are used to describe the polarization distributions of the HPLGVBs. The electric field intensity distributions of tightly focused HPLGVBs are analyzed in the focal plane by the Richards-Wolf vectorial diffraction method. It is found that the tightly focused HPLGVBs have a focal shift phenomenon. The dependence of the focal shift of the HPLGVBs on the different parameters is discussed in detail. The simulation results show that the magnitude of the focal shift is related to the polarization distribution, and the focal shift is quite obvious for large azimuthal mode index, long focal length, large numerical aperture, and narrow beam waist. The effective control of the focal shift will have great potential applications in optical micromanipulation.

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.

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.

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.