correlation optics & Imaging

We propose and experimentally demonstrate a noninterferometric method to quantitatively determine the topological charge and complete phase structure of a vortex beam scrambled by a random scattering medium. In the proposed technique, the vortex beam with an arbitrary topological charge coaxially enters into the scattering medium with another nonvortex beam with an orthogonal polarization state. This couples the spatial and polarization modes of the coherent light prior to entering the scattering medium. Correlation of the orthogonal polarization states of a random field encodes the signature of the twisted mode of the vortex beam. Recovery of the complex polarization correlation functions and hence twisted modes of the beam are retrieved from the Stokes parameters of a randomly scattered field. Two-point correlations of the Stokes parameters form a 4 × 4 matrix with a total of 16 elements. Out of these 16 elements, only four elements of the matrix are used to retrieve real and imaginary parts of the complex polarization correlation function and are subsequently applied in the reconstruction of twisted wavefronts. A complete theoretical basis is developed to retrieve the twisted wavefront of propagating light through random scattering media and is also supported by numerical simulation and experimental demonstration. As an application of the proposed technique, recovery of the complete phase maps of the different vortex beams from the random light is experimentally demonstrated and the twisted modes of the incident light are quantitatively analyzed using orthogonal projections. The experimental results are in good agreement with the theoretical basis and numerical results.

We discuss various new aspects of the Hanbury Brown-Twiss (HBT) approach. A possible extension of the HBT to the vectorial light is discussed and few imaging applications are highlighted.

Encoding information using the topological charge of vortex beams has been proposed for optical communications. The conservation of the topological charge on propagation and the detection of the topological charge by a receiver are significant in these applications and have been well established in free-space. However, when vortex beams enter a diffuser, the wavefront is distorted, leading to a challenge in the conservation and detection of the topological charge. Here, we present a technique to measure the value of the topological charge of a vortex beam obscured in the randomly scattered light. The results of the numerical simulations and experiments are presented and are in good agreement. In particular, only a single-shot measurement is required to detect the topological charge of vortex beams, indicating that the method is applicable to a dynamic diffuser.

Size and shape of laser speckle carries significant information of scatters and offer a solution to optical imaging challenge under spatially fluctuating media or highly random scattering media. Most prominently in area of astronomy, bio-medical science, metrology, optical tomography presence of speckle affects the image quality and could not be tolerated at a certain level. One of the solutions of this problem can be derived from the statistical optics which plays vital role in the study the speckle phenomena of light. One of the major contributions from statistical point of view is the Van Cittert-Zernike theorem which connects a relation to incoherence source of light with far field statistical properties of speckle. For the Gaussian random field like fully developed speckle, second order statistical properties of speckle is quantity of high interests which provides detailed spatial properties randomly fluctuation field at far field. The scope of this work to introduce the concept of two point intensity correlation i.e. forth orders field correlation and its application in static spatial random inhomogeneous media. The reported work is carried out by measuring the complex correlation function, i.e. second order field correlation, of spatially fluctuating speckle at far field using intensity covariance function and principle of Speckle Holography. A simple experimental geometry is suggested and demonstrated for application point of view of complex correlation function. A recovery of an off axis hologram through scattering media suggested here which enables to retrieve the depth information of complex three dimensional objects. Subsequently, we have also demonstrated the reconstruction of inline hologram through scattering media which may find numerous applications in optical imaging science mainly in biological tissue imaging.

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.

We report a phase shifting holography for coherence waves in the Hanbury Brown and Twiss approach. This technique relies on the wave nature and interference of the coherence waves in the two-point intensity correlation. Experimentation is carried out by recovery of the complex coherence using phase shifting in the intensity correlation. As an application, imaging of the phase target obscured by a random scattering medium is demonstrated, and the results are presented for three different cases. These results are also compared with imaging of the targets in absence of the scattering medium by a conventional phase shifting digital holography.

Optical coherence tomography (OCT) is being increasingly adopted as a label-free and non-invasive technique for biomedical applications such as cancer and ocular disease diagnosis. Diagnostic information for these tissues is manifest in textural and geometric features of the OCT images which are used by human expertise to interpret and triage. However, it suffers delays due to long process of conventional diagnostic procedure and shortage of human expertise. Here, a custom deep learning architecture, LightOCT, is proposed for classification of OCT images into diagnostically relevant classes. LightOCT is a convolutional neural network with only 2 convolutional layers and a fully connected layer, but it is shown to provide excellent training and test results for diverse OCT image datasets. We show that LightOCT provides > 99% accuracy in classifying 44 normal and 44 cancerous (invasive ductal carcinoma) breast tissues collected from 22 patients to perform the study. Also, ~99% accuracy in classifying public datasets of ocular OCT images as normal, age-related macular degeneration and diabetic macular edema. Additionally, we show ~96% test accuracy for classifying retinal images as belonging to choroidal neovascularization, diabetic macular edema, drusen and normal samples on a large public dataset of more than 100,000 images. Through this, we show that LightOCT can provide simultaneous significant diagnostic support for variety of OCT images with sufficient training and very little hyper-parameter tuning.

We developed a new quantitative phase microscopy technique, namely, spectrally resolved laser interference microscopy (SR-LIM), with which it is possible to quantify multi-spectral phase information related to biological specimens without color crosstalk using a color CCD camera. It is a single shot technique where sequential switched on/off of red, green, and blue (RGB) wavelength light sources are not required. The method is implemented using a three-wavelength interference microscope and a customized compact grating based imaging spectrometer fitted at the output port. The results of the USAF resolution chart while employing three different light sources, namely, a halogen lamp, light emitting diodes, and lasers, are discussed and compared. The broadband light sources like the halogen lamp and light emitting diodes lead to stretching in the spectrally decomposed images, whereas it is not observed in the case of narrow-band light sources, i.e. lasers. The proposed technique is further successfully employed for single-shot quantitative phase imaging of human red blood cells at three wavelengths simultaneously without color crosstalk. Using the present technique, one can also use a monochrome camera, even though the experiments are performed using multi-color light sources. Finally, SR-LIM is not only limited to RGB wavelengths, it can be further extended to red, near infra-red, and infra-red wavelengths, which are suitable for various biological applications.

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. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.

We propose a simple scheme for accurate state of polarization (SOP) mapping with an interferometric polarimeter using Fourier transform method of fringe analysis. In single shot polarimeters that use Fourier transform method of fringe analysis, a spatial carrier frequency is introduced in the fringes of recorded interferogram either by introducing the relative tilt between the sample beam under test and a reference beam, as demonstrated by Ohtsuka and Oka or by passing the sample beam through birefringent optical components such as Wollaston prisms as demonstrated by Oka and Kaneko. In this technique, the amount of spatial carrier frequency that enabled to filter different terms in the Fourier spectrum of the recorded interferogram had to be calibrated with the use of light with a known SOP. Even in this case, the spatial carrier frequency introduced in the recorded interferogram is influenced by the relative tilt of the beam used for calibration. To eliminate the linear phase introduced by spatial carrier frequency, usually the spectrum around the carrier frequency location in the Fourier transform is shifted and brought to the centre. During this process an error of a fraction of a pixel in the shifting of the spectrum after filtering to remove the linear phase introduced by spatial carrier frequency will drastically change the measured SOP of light. For accurate SOP mapping, it is important that we eliminate the artifacts and errors due to the spatial carrier frequency in the single shot polarimeter that are otherwise very promising. In the present work, we propose a Mach-Zehnder interferometric polarimeter that uses a common path Sagnac interferometer to generate reference beams with orthogonal state of polarization. By taking advantage of the inherent stability of the proposed common path Sagnac interferometer against surrounding vibrations and air turbulences, a simple calibration scheme using a light of known state of polarization is used to map the state of polarization with better accuracy.

Lens-less digital holography for quantitative phase contrast imaging is established with a cyclic lateral shearing interferometer and non-collimated light beam. In a self-reference type configuration, the object and reference beams are generated from the same spherical wavefront after the light beam has passed through the sample plane. The experimental configuration is implemented with simple optical components involving beam splitter and mirrors. This proposed architecture has the advantage that the system does not require any special optical element such as pinhole, gratings, and other customized optical components and hence can be easily realized with significantly simplified alignment procedure. Experimental results for both amplitude and phase objects are presented as a proof of concept.

Generation of in-homogeneously polarized beams, namely radial and azimuthal polarization is demonstrated using holography and results are presented for the same. This technique can be used to generate even higher order cylindrically polarized vector beams.

We have demonstrated use of holography for controlled generation of polarized light. This permits easy generation of desired spatial polarization structure, of course under limitation of holography, in comparison to conventional polarization optics method.

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.

We experimentally demonstrate the generation of two dimensional spatially varying coherence points using Dammann grating. The experimental result is presented for the case of 3×3 array of coherence points. The principle of the technique is based on van Cittert Zernike theorem and the coherence is controlled by using a phase grating.

A phase-sharing scheme using the Mach-Zehnder interferometric set up is demonstrated. Two coherent light fields of the same wavelength which have orthogonal polarizations are used as sources at the two ends of a Mach-Zehnder interferometer. They are made to interfere independently at the opposing ends of the interferometer so that the phase estimated by two observers at the two opposing ends of the interferometer is nearly identical. The scheme could be in principle used by two observers to simultaneously monitor and study a phase object inserted in one of the arms of the interferometer. A pseudo random phase plate which mimics atmospheric turbulence is inserted in one of the arms of the interferometer to demonstrate that such a phase-sharing scheme could be converted to a secret-key sharing scheme. Shared secret key generation is demonstrated through evaluation of the phase correlates of the shared phase samples available their respective ends. The shared random phases could also be used in a more direct manner by the respective observers for random phase encryption of images.

We propose an experimental technique for two dimensional Jones matrix imaging of transparent and anisotropic sample using polarization interferometer. Employing this technique, the Jones matrix components are measured for polarizer and quarter wave plate and results are compared with theoretical results of the samples.

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.

Phase information recovered through interferometric techniques is mathematically wrapped in the interval (-π, π). Obtaining the original unwrapped phase is very important in numerous number of applications. This paper discusses a Fourier transform based phase unwrapping method. Kalman filter is proposed for denoising in post processing step to restore the unwrapped phase without any noise. The proposed method is highly robust to noise and performs better even at lower SNR values (5-10dB) with a very less value of RMS error. Also, the time taken for execution is very less compared to the many available methods in the literature.

Optical imaging through complex scattering media is one of the major technical challenges with important applications in many research fields, ranging from biomedical imaging, astronomical telescopy, and spatially multiplex optical communications. Although various approaches for imaging though turbid layer have been recently proposed, they had been limited to two-dimensional imaging. Here we propose and experimentally demonstrate an approach for three-dimensional single-shot imaging of objects hidden behind an opaque scattering layer. We demonstrate that under suitable conditions, it is possible to perform the 3D imaging to reconstruct the complex amplitude of objects situated at different depths.

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.

We propose and experimentally demonstrate a technique to quantitatively determine the topological structure of the vortex beam coaxially launched into the random scattering media with another non-vortex beam of the orthogonal polarization component. The proposed technique applies the coherent superposition of the random electromagnetic fields and a priori knowledge of correlation of one of the random fields to determine the polarization correlation of the other. The polarization correlation of the random field is used to determine the topological charge and phase structure of the vortex beam from the laser speckle. The application of the proposed technique is demonstrated by determining the helicity and topological charge of the vortex beam for three different cases.

Non-invasive and single-shot holographic imaging through complex media is technically challenging due to random light scattering which significantly scrambles optical information. Recently, several methods have been presented to address this issue. However, they require complicated measurements of optical transmission matrices, or existing techniques do only retrieve intensity information. Here we propose and experimentally demonstrate a holographic approach for single-shot imaging through a scattering layer based on digital in-line holography in combination with the autocorrelation of the speckle intensity. Using a simple optical configuration and experimental procedure, the proposed method enables to retrieve the complex amplitude image of an object located at arbitrary planes behind scattering media. The technique has potential applications in biomedical imaging, deep tissue microscopy, and 3D imaging through turbid media.

Propagation of a coherent light through an anisotropic random medium generates randomly polarized field, known as polarization speckle. In this paper, an experimental technique is proposed and demonstrated to recover the transmittance of a polarized object from polarization speckle. Recovery of the polarized object from polarization speckle is made possible by combining the far-field intensity correlation of the object speckle with off-axis holography to determine the complex coherence function of the speckle. The desired object speckle which is uniformly polarized is filtered from the polarization speckle using a polarizer. The results are compared with the case where the complex coherence function is determined in the absence of the polarizer.

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 demonstrated both theoretically and experimentally 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 also 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 applications in sensing, biomedical studies, and in determining the rotation of the electric field vector after passing through a scattering medium.

Propagation of a coherent light through a random birefringent scatterer generates a speckle pattern with spatially varying polarization called polarization speckle. The spatial polarization distribution of the polarization speckle is random in nature making zero net polarization. In this paper, we experimentally characterize the memory effect of the polarization speckle from a birefringent scatterer for different orientations of an analyzing polarizer using far-field intensity correlation measurements.

Coherence functions behave like a wave and follow two-four dimensional wave equations. Utilizing this feature, we propose a lensless Fourier transform holography for coherence waves. Experimental demonstration is carried out by synthesizing the coherence function of a stationary random field as a superposition of two independent coherence functions in the Fresnel domain. Using the connection between two point intensity correlation and coherence function for the Gaussian random field, the application of this technique is demonstrated in imaging through a random scatterer in a lensless geometry from a single measurement of the speckle field.

Effect of coma on the intensity distribution and encircled energy of a singular beam, at the focal plane of a lens, is evaluated numerically by using Fresnel–Kirchhoff diffraction integral for two different values of topological charge. Results show lateral shift and flattening of the dark core. It is noticed that the singular beam with double topological charge is affected more by comatic aberration in comparison to the beam with single topological charge. We also verified our results by using optical transfer function approach.

Optical imaging through complex scattering media is one of the major technical challenges with important applications in many research fields, ranging from biomedical imaging to astronomical telescopy to spatially multiplexed optical communications. Various approaches for imaging through a turbid layer have been recently proposed that exploit the advantage of object information encoded in correlations of the random optical fields. Here we propose and experimentally demonstrate an alternative approach for single-shot imaging of objects hidden behind an opaque scattering layer. The proposed technique relies on retrieving the interference fringes projected behind the scattering medium, which leads to complex field reconstruction, from far-field laser speckle interferometry with two-point intensity correlation measurement. We demonstrate that under suitable conditions, it is possible to perform imaging to reconstruct the complex amplitude of objects situated at different depths.

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.

We propose and experimentally demonstrate lensless complex amplitude image retrieval through a visually opaque scattering medium from spatially fluctuating fields using intensity measurement and a phase-retrieval algorithm. The complex amplitude information of the hidden object is encoded in the form of a real and nonnegative amplitude function represented as an interference pattern. A single charge coupled device (CCD) image of the scattered light collected through a visually opaque optical diffuser contains enough information to digitally regenerate the interference pattern. Furthermore, a lensless configuration is implemented which eliminates any possible aberration effects associated with optical components, and this further has promising applications where the use of imaging optics is not feasible. Experimental results for the recovery of complex fields corresponding to optical vortices of two different topological charges are presented.

The tight focusing of vortex carrying beams is studied using the Debye-Wolf diffraction integral in the presence of primary astigmatism. The roles of topological charge, polarization distribution of the input beam, and handedness of the beam polarization are investigated in the intensity distribution of the focal plane of a high-numerical-aperture lens. The effect of tight focusing in the presence of astigmatism on the dark core of the azimuthally polarized beam is also investigated and compared with the dark core of a circularly polarized vortex beam. The effect of an aberration has been discussed in the context of the fluorescent spot size in the focal plane of a stimulated emission depletion microscope for two different polarization setups.

A non-interferometric technique for imaging from laser speckle using speckle autocorrelation assisted with sparsity enhanced iterative phase reconstruction is proposed and demonstrated in this paper. The use of sparsity assisted approach in combination with speckle correlation provides the potential to retrieve the complex correlation function from random speckle pattern. Imaging through random scattering medium is demonstrated by recovery of a circular and an annular aperture from the laser speckle.

Measurement of optical activity of anisotropic sample in the visible domain is employed as a routine task in wide range of applications. In this paper, we propose a new scheme to measure anisotropy of the sample using Jones matrix elements. This is implemented by making use of polarization and angular multiplexing. The technique offers retrieval of all Jones matrix elements from a single measurement. Basic principle of proposed technique is described and as a proof of the proposed scheme, preliminary results are presented.

A relation between vectorial source structure and coherence-polarization of the fluctuating field is established. This relation connects the source structure to the degree of coherence by Fourier relation, and this is extension of the van Cittert-Zernike theorem to the vectorial regime. Experimental verification of the proposed theorem is presented by making use of space averages as replacement of ensemble averages for Gaussian stochastic field. Both experimental and analytical results are obtained for different polarized sources, and good agreements between two justify use of space average as replacement of ensemble average in the spatially fluctuating field.

A relation between vectorial source structure and coherence-polarization of the fluctuating field is established. This relation connects the source structure to the degree of coherence by Fourier relation, and this is extension of the van Cittert-Zernike theorem to the vectorial regime. Experimental verification of the proposed theorem is presented by making use of space averages as replacement of ensemble averages for Gaussian stochastic field. Both experimental and analytical results are obtained for different polarized sources, and good agreements between two justify use of space average as replacement of ensemble average in the spatially fluctuating field.

The van Cittert-Zernike theorem is extended to the vectorial regime based on spatial averaging over the observation plane, and experimental demonstrations are presented. The theorem connects complex vectorial source structure to the degree of coherence and polarization of the spatially fluctuating vectorial field in the far field. Experimentation is carried out by making use of the space averages as a replacement of ensemble averages for the Gaussian stochastic field. For quantitative comparison with the theorem, analytical and experimental results are presented for a rectangular aperture with different vectorial source structures.

A new holographic method for viewing the object through scatterer is described, and preliminary experimental result for a 2-D object reconstruction is presented. This method is expected to play important role in imaging of the objet lying behind the scatterer.

We propose and experimentally demonstrate a technique for the recovery of the wavefront from spatially fluctuating fields using the two point intensity correlation, i.e., fourth order correlation. Assuming spatial ergodicity and Gaussian statistics for the speckle field, we connect the fourth order correlation to the modulus of the corresponding second order correlation. The idea is to retrieve the complex coherence function and consequently the wavefront using the off-axis holography. Application of this technique is demonstrated in the reconstruction of complex field of the object lying behind a weak scatterer. Experimental results of recovery of the complex field of phase objects “vortices” with three values of topological charges are presented

We propose and experimentally demonstrate a technique for the recovery of the wavefront from spatially fluctuating fields using the two point intensity correlation, i.e., fourth order correlation. Assuming spatial ergodicity and Gaussian statistics for the speckle field, we connect the fourth order correlation to the modulus of the corresponding second order correlation. The idea is to retrieve the complex coherence function and consequently the wavefront using the off-axis holography. Application of this technique is demonstrated in the reconstruction of complex field of the object lying behind a weak scatterer. Experimental results of recovery of the complex field of phase objects “vortices” with three values of topological charges are presented.

We report a new technique for the recovery of quantitative phase and amplitude information of an object hidden behind a scattering medium. Two-point intensity correlation measurement together with digital holography principles are utilized for this purpose. The hologram information of the object and a reference beam is scrambled by the presence of a scattering medium in its path. A direct digital holographic recording of this scattered light does not lead to the reconstruction of actual object information. We propose the idea of recovering this hologram information from the spatially fluctuating field of a laser speckle pattern using the intensity correlation, and subsequently apply digital reconstruction of the hologram for recovery of quantitative phase and amplitude information of objects hidden by a random diffuser.