Phase retrieval algorithm using edge point referencing.

In the past few decades, extensive research and efforts have been made for developing a phase retrieval iterative algorithm (PRA) for reconstructing a complex object from far-field intensity equivalently from the object autocorrelation. Since most of the existing PRA techniques employ a random initial guess, the reconstruction output sometimes changes in different trials leading to a non-deterministic output. Additionally, the output of such algorithm occasionally either shows non-convergence, needs a longer time to converge, or shows the twin-image problem. Due to these problems, PRA methods are unsuitable for cases where consecutive reconstructed outputs need to be compared. In this Letter, a novel, to the best of our knowledge, method is developed and discussed using edge point referencing (EPR). In the EPR scheme, in addition to illuminating a region of interest (ROI) of the complex object, a small area near the periphery of the complex object within the ROI is illuminated with an additional beam. Such illumination creates an imbalance in the autocorrelation that can be used to improve the initial guess for achieving unique deterministic output free from the aforementioned problems. Furthermore, by introducing the EPR, one can also achieve faster convergence. To support our theory, derivation, simulations, and experiment are performed and presented.

Single-shot and twin-image free unique phase retrieval using an aspect of autocorrelation that considers the object asymmetry.

A phase-retrieval algorithm can reconstruct the phase of an object from an intensity image of a diffraction pattern recorded at the Fourier plane, provided one makes a right initial guess. For the algorithms that are based on an initial random guess, at times, the output either becomes nondeterministic, becomes nonconvergent, or develops a twin image. For improving the performance of the algorithms by eliminating the twin image and for bringing uniqueness to the output, prior information about the object or more intensity measurements are needed. In order to achieve this using only a single acquisition of the intensity pattern recorded at the Fourier plane for an object, we propose a method in which object support, along with the object information in the case in which the object has a direction of asymmetry, can be measured from the object autocorrelation and utilized as an initial guess in the phase-retrieval algorithm. In the process, we explore how even a partial asymmetry in the object distribution can lead to a good solution in the phase-retrieval algorithm. This method is beneficial for unique phase detection without any twin artifact in various fields of optics. We theoretically analyze the proposed method and validate it by carrying out the simulations and experiment.

Characterization of a spatial light modulator using polarization-sensitive digital holography.

We show a digital holographic approach for polarimetric characterization of a twisted nematic liquid crystal spatial light modulator (TNLC-SLM). An experimental scheme is designed to perform polarization analysis of the SLM with gray levels. This is realized by simultaneous detection of the polarization states of the light from the SLM for a given gray level with the help of a specially designed spatial-frequency multiplex polarization interferometer. This provides amplitude and phase characteristics of the SLM in a single shot. In order to characterize the SLM, we perform Jones matrix imaging at its various gray values (driving voltages), and corresponding results are presented. These results are expected to be useful in designing and developing various SLM-based experiments in the scalar and vectorial domain.

Ultrashort vortex from a Gaussian pulse - An achromatic-interferometric approach.

The more than a century old Sagnac interferometer is put to first of its kind use to generate an achromatic single-charge vortex equivalent to a Laguerre-Gaussian beam possessing orbital angular momentum (OAM). The interference of counter-propagating polychromatic Gaussian beams of beam waist ωλ with correlated linear phase (ϕ 0 ≥ 0.025 λ) and lateral shear (y 0 ≥ 0.05 ωλ) in orthogonal directions is shown to create a vortex phase distribution around the null interference. Using a wavelength-tunable continuous-wave laser the entire range of visible wavelengths is shown to satisfy the condition for vortex generation to achieve a highly stable white-light vortex with excellent propagation integrity. The application capablitiy of the proposed scheme is demonstrated by generating ultrashort optical vortex pulses, its nonlinear frequency conversion and transforming them to vector pulses. We believe that our scheme for generating robust achromatic vortex (implemented with only mirrors and a beam-splitter) pulses in the femtosecond regime, with no conceivable spectral-temporal range and peak-power limitations, can have significant advantages for a variety of applications.

Exploiting scattering media for exploring 3D objects.

Scattering media, such as diffused glass and biological tissue, are usually treated as obstacles in imaging. To cope with the random phase introduced by a turbid medium, most existing imaging techniques recourse to either phase compensation by optical means or phase recovery using iterative algorithms, and their applications are often limited to two-dimensional imaging. In contrast, we utilize the scattering medium as an unconventional imaging lens and exploit its lens-like properties for lensless three-dimensional (3D) imaging with diffraction-limited resolution. Our spatially incoherent lensless imaging technique is simple and capable of variable focusing with adjustable depths of focus that enables depth sensing of 3D objects that are concealed by the diffusing medium. Wide-field imaging with diffraction-limited resolution is verified experimentally by a single-shot recording of the 1951 USAF resolution test chart, and 3D imaging and depth sensing are demonstrated by shifting focus over axially separated objects.

Isogyres - Manifestation of Spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference.

Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.

Generation of optical vortex dipole from superposition of two transversely scaled Gaussian beams.

We propose a distinct concept on the generation of optical vortex through coupling between the amplitude and phase differences of the superposing beams. For the proof-of-concept demonstration, we propose a simple free-space optics recipe for the controlled synthesis of an optical beam with a vortex dipole by superposing two transversely scaled Gaussian beams. The experimental demonstration using a Sagnac interferometer introduces the desired amount of radial shear and linear phase difference between the two out-of-phase Gaussian beams to create a vortex pair of opposite topological charge in the superposed beam. Flexibility to tune their location and separation using the choice of direction of the linear phase difference and the amount of amplitude difference between the superposing beams has potential applications in optical tweezers and traps utilizing the local variation in angular momentum across the beam cross section.

Effect of residual phase gradients in optical null interference.

A scheme to study the effect of residual phase gradients in an optical interference between two out-of-phase Gaussian beams is proposed. In a Sagnac interferometer configured to provide a null output, a variable linear phase swept across the null point unfolds an optical field rotation due to an apparently negligible residual phase gradient present orthogonal to the linear phase sweep. As the optical beam that rotates around its propagation axis carries orbital angular momentum, the experimental results presented in this Letter could provide an insight into the momentum change associated with the energy redistribution in the fundamental phenomenon of optical interference.

Looking through a diffuser and around an opaque surface: a holographic approach.

Retrieving the information about the object hidden around a corner or obscured by a diffused surface has a vast range of applications. Over the time many techniques have been tried to make this goal realizable. Here, we are presenting yet another approach to retrieve a 3-D object from the scattered field using digital holography with statistical averaging. The methods are simple, easy to implement and allow fast image reconstruction because they do not require phase correction, complicated image processing, scanning of the object or any kind of wave shaping. The methods inherit the merit of digital holography that the micro deformation and displacement of the hidden object can also be detected.

Spectrally resolved incoherent holography: 3D spatial and spectral imaging using a Mach-Zehnder radial-shearing interferometer.

Spatial and spectral information holds the key for characterizing incoherently illuminated or self-luminous objects, as well as for imaging fluorescence. We propose spectrally resolved incoherent holography using a multifunctional Mach-Zehnder interferometer that can introduce both a radial shear and a variable time delay between the interfering optical fields and permits the measurement of both spatial and temporal coherence functions, from which a 3D spatial and spectral image of the object is reconstructed. We propose and demonstrate the accurate 3D imaging of the object spectra by in situ calibration.

Vectorial van Cittert-Zernike theorem based on spatial averaging: experimental demonstrations.

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.

Recording of incoherent-object hologram as complex spatial coherence function using Sagnac radial shearing interferometer and a Pockels cell.

The ideas of incoherent holography were conceived after the invention of coherent-light holography and their concepts seems indirectly related to it. In this work, we adopt an approach based on statistical optics to describe the process of recording of an incoherent-object hologram as a complex spatial coherence function. A Sagnac radial shearing interferometer is used for the correlation of optical fields and a Pockels cell is used to phase shift the interfering fields with the objective to quantify and to retrieve the spatial coherence function.

Coherence holography by achromatic 3-D field correlation of generic thermal light with an imaging Sagnac shearing interferometer.

We propose a new technique for achromatic 3-D field correlation that makes use of the characteristics of both axial and lateral magnifications of imaging through a common-path Sagnac shearing interferometer. With this technique, we experimentally demonstrate, for the first time to our knowledge, 3-D image reconstruction of coherence holography with generic thermal light. By virtue of the achromatic axial shearing implemented by the difference in axial magnifications in imaging, the technique enables coherence holography to reconstruct a 3-D object with an axial depth beyond the short coherence length of the thermal light.

Single-shot full-field interferometric polarimeter with an integrated calibration scheme.

A simple interferometric polarimeter with an integrated calibration scheme is proposed for accurate and fast mapping of the state of polarization (SOP). Conventional single-shot polarimeters that detect the amplitude and phase of orthogonally polarized field components by interferometry using Fourier fringe analysis suffers from errors caused by the imperfect reference beam and ambiguity in the spatial carrier frequency in the fringe pattern. In the proposed system, the integrated calibration scheme eliminates those error sources and enables accurate measurement of SOP without prior knowledge of the reference beam and the spatial carrier frequency.

Interferometer setup for the observation of polarization structure near the unfolding point of an optical vortex beam in a birefringent crystal.

We propose a novel birefringent interferometer setup for the study of unfolding points, and obtain for the first time to our knowledge the spatial polarization structure very near the unfolding point of a uniformly polarized optical vortex beam propagating in a birefringent crystal. The unfolding point is reconstructed by folding back the two separated eigen-beams at the output of the birefringent crystal into a single beam using another identical birefringent crystal, resulting in a birefringent interferometer of Mach-Zehnder type. We also demonstrate that the separation near the unfolding point can be varied by a small rotation of the second crystal.

Laser speckle reduction by multimode optical fiber bundle with combined temporal, spatial, and angular diversity.

We report significant speckle reduction in a laser illumination system using a vibrating multimode optical fiber bundle. The optical fiber bundle was illuminated by two independent lasers simultaneously. The beams from both lasers were first expanded and collimated and were further divided into multiple beams to illuminate the fiber optic bundle with normal and oblique incidence. Static diffusers were also placed at the input and output faces of the fiber bundle, thus introducing the spatial as well as angular diversity of illumination. Experiments were carried out both in free space and in imaging geometry configuration. Standard deviation, speckle contrast and signal-to-noise ratio of the images were computed, and the results were compared with those of white light illumination. Speckle contrast close to that of white light was obtained using a vibrating fiber bundle with combined temporal, spatial, and angular diversities of the illumination.

Stokes holography.

A new technique, referred to as Stokes holography, is proposed and experimentally demonstrated for controlled synthesis of generalized Stokes parameters in 3D space using Stokes fringes. Stokes fringes are polarization fringes which permit to record and reconstruct complete wavefront. Full use of Stokes fringes in a single step is realized by scattering complex field and subsequently reconstructing using spatial averaging of the randomly scattered field. Mathematical formulations are derived and supported by experimental results of 3D object reconstruction in generalized Stokes parameters.

Vectorial coherence holography.

Extension of coherence holography to vectorial regime is investigated. A technique for controlling and synthesizing optical fields with desired elements of coherence-polarization matrix is proposed and experimentally demonstrated. The technique uses two separate coherence holograms, each of which is assigned to one of the orthogonal polarization components of the vectorial fields.

Photon correlation holography.

Unconventional holography called photon correlation holography is proposed and experimentally demonstrated. Using photon correlation, i.e. intensity correlation or fourth order correlation of optical field, a 3-D image of the object recorded in a hologram is reconstructed stochastically with illumination through a random phase screen. Two different schemes for realizing photon correlation holography are examined by numerical simulations, and the experiment was performed for one of the reconstruction schemes suitable for the experimental proof of the principle. The technique of photon correlation holography provides a new insight into how the information is embedded in the spatial as well as temporal correlation of photons in the stochastic pseudo thermal light.

Real-time coherence holography.

Coherence holography capable of real-time recording and reconstruction is proposed and experimentally demonstrated with a generic Leith-type coherence hologram. The coherence hologram is optically generated in real-time using a Mach-Zehnder interferometer and reconstructed using a Sagnac radial shearing interferometer. With this method one can create an optical field distribution with a desired spatial coherence function, and visualize the coherence function in real-time as the contrast and phase variations in an interference fringe pattern. The reconstructed image of the complex coherence function has been quantified with the Fourier transform method of fringe-pattern analysis.