Roadmap on computational methods in optical imaging and holography [invited].

Unlabelled: Computational methods have been established as cornerstones in optical imaging and holography in recent years. Every year, the dependence of optical imaging and holography on computational methods is increasing significantly to the extent that optical methods and components are being completely and efficiently replaced with computational methods at low cost. This roadmap reviews the current scenario in four major areas namely incoherent digital holography, quantitative phase imaging, imaging through scattering layers, and super-resolution imaging.

3D incoherent imaging using an ensemble of sparse self-rotating beams.

Interferenceless coded aperture correlation holography (I-COACH) is one of the simplest incoherent holography techniques. In I-COACH, the light from an object is modulated by a coded mask, and the resulting intensity distribution is recorded. The 3D image of the object is reconstructed by processing the object intensity distribution with the pre-recorded 3D point spread intensity distributions.

Scattering of Poincaré beams: polarization speckles.

Polarization speckle is a fine granular light pattern having spatially varying random polarization profile. We generate these speckle patterns by using the scattering of Poincaré beams, a special class of vector vortex beams, through a ground glass plate. Here, the Poincaré beams are generated using a polarization sensitive spatial light modulator displaying an on-axis hologram corresponding to an optical vortex phase profile.

Topological structures in vector speckle fields.

We here demonstrate on both theoretical and experimental bases a method to recover the topological structure of a monochromatic optical field that has suffered diffuse transmission. This method consists of two steps: first, a linearly polarized sample beam is mixed with a coaxial Gaussian beam in orthogonal polarization states resulting in a Poincaré beam; second, a polarization-related spatial correlation function is considered and measured for the overall speckle field arising by optical diffusion. The singularities of the sample beam turn out to be imaged into the correlation function of the vector speckle field.

Polarization state transformation using two quarter wave plates: application to Mueller polarimetry.

We show that there are a number of ways to transform an arbitrary polarization state into another with just two quarter wave plates (QWPs). We have verified this geometrically using the trajectories of the initial and final polarization states corresponding to all the fast axis orientations of a QWP on the Poincaré sphere. The exact analytical expression for the locus of polarization states has also been given, and describes the trajectory.

Non-coaxial superposition of vector vortex beams.

Vector vortex beams are classified into four types depending upon spatial variation in their polarization vector. We have generated all four of these types of vector vortex beams by using a modified polarization Sagnac interferometer with a vortex lens. Further, we have studied the non-coaxial superposition of two vector vortex beams.

Divergence of optical vortex beams.

We show, both theoretically and experimentally, that the propagation of optical vortices in free space can be analyzed by using the width [w(z)] of the host Gaussian beam and the inner and outer radii of the vortex beam at the source plane (z=0) as defined in [Opt. Lett.39, 4364 (2014)10.

Higher order optical vortices and formation of speckles.

We have experimentally generated higher order optical vortices and scattered them through a ground glass plate that results in speckle formation. Intensity autocorrelation measurements of speckles show that their size decreases with an increase in the order of the vortex. It implies an increase in the angular diameter of the vortices with their order.

Propagation of an arbitrary vortex pair through an astigmatic optical system and determination of its topological charge.

We embed a pair of vortices with different topological charges in a Gaussian beam and study its evolution through an astigmatic optical system, a tilted lens. The propagation dynamics are explained by a closed-form analytical expression. Furthermore, we show that a careful examination of the intensity distribution at a predicted position past the lens can determine the charge present in the beam.

Measuring the Mueller matrix of an arbitrary optical element with a universal SU(2) polarization gadget.

We propose a new method for determining the Mueller matrix of an arbitrary optical element and verify it with three known optical elements. This method makes use of two universal SU(2) polarization gadgets to obtain the projection matrix directly from the experiment. It allows us to determine the Mueller matrix without precalibration of the setup, since the generated polarization states are fully determined by the azimuths of the wave plates.

Experimental generation of ring-shaped beams with random sources.

We have experimentally reproduced ring-shaped beams from the scattered Laguerre-Gaussian and Bessel-Gaussian beams. A rotating ground glass plate is used as a scattering medium, and a plano-convex lens collects the scattered light to generate ring-shaped beams at the Fourier plane. The obtained experimental results are supported with the numerical results and are in good agreement with the theoretical results proposed by Wang et al.