Spectral pre-modulation of training examples enhances the spatial resolution of the Phase Extraction Neural Network (PhENN)

The Phase Extraction Neural Network (PhENN) is a computational architecture, based on deep machine learning, for lens-less quantitative phase retrieval from raw intensity data. PhENN is a deep convolutional neural network trained through examples consisting of pairs of true phase objects and their corresponding intensity diffraction patterns; thereafter, given a test raw intensity pattern PhENN is capable of reconstructing the original phase object robustly, in many cases even for objects outside the database where the training examples were drawn from. Here, we show that the spatial frequency content of the training examples is an important factor limiting PhENN's spatial frequency response. For example, if the training database is relatively sparse in high spatial frequencies, as most natural scenes are, PhENN's ability to resolve fine spatial features in test patterns will be correspondingly limited. To combat this issue, we propose "flattening" the power spectral density of the training examples before presenting them to PhENN. For phase objects following the statistics of natural scenes, we demonstrate experimentally that the spectral pre-modulation method enhances the spatial resolution of PhENN by a factor of 2.Comment: 12 pages, 10 figure

Tapered Simplified Modal Method for Analysis of Non-rectangular Gratings

The Simplified Modal Method (SMM) provides a quick and intuitive way to analyze the performance of gratings of rectangular shapes. For non-rectangular shapes, a version of SMM has been developed, but it applies only to the Littrow-mounting incidence case and it neglects reflection. Here, we use the theory of mode-coupling in a tapered waveguide to improve SMM so that it applies to non-rectangular gratings at arbitrary angles of incidence. Moreover, this new 'Tapered Simplified Modal Method' (TSMM) allows us to properly account for reflected light. We present here the analytical development of the theory and numerical simulations, demonstrating the validity of the method.Comment: 13 pages, 8 figure

Hamiltonian and Phase-Space Representation of Spatial Solitons

We use Hamiltonian ray tracing and phase-space representation to describe the propagation of a single spatial soliton and soliton collisions in a Kerr nonlinear medium. Hamiltonian ray tracing is applied using the iterative nonlinear beam propagation method, which allows taking both wave effects and Kerr nonlinearity into consideration. Energy evolution within a single spatial soliton and the exchange of energy when two solitons collide are interpreted intuitively by ray trajectories and geometrical shearing of the Wigner distribution functions.Comment: 12 pages, 5 figure

Volume Holographic Hyperspectral Imaging

A volume hologram has two degenerate Bragg-phase-matching dimensions and provides the capability of volume holographic imaging. We demonstrate two volume holographic imaging architectures and investigate their imaging resolution, aberration, and sensitivity. The first architecture uses the hologram directly as an objective imaging element where strong aberration is observed and confirmed by simulation. The second architecture uses an imaging lens and a transmission geometry hologram to achieve linear two-dimensional optical sectioning and imaging of a four-dimensional (spatial plus spectral dimensions) object hyperspace. Multiplexed holograms can achieve simultaneously three-dimensional imaging of an object without a scanning mechanism

Shift multiplexing with spherical reference waves

Shift multiplexing is a holographic storage method particularly suitable for the implementation of holographic disks. We characterize the performance of shift-multiplexed memories by using a spherical wave as the reference beam. We derive the shift selectivity, the cross talk, the exposure schedule, and the storage density of the method. We give experimental results to verify the theoretical predictions

Coherence retrieval using trace regularization

The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from measurements through a process called coherence retrieval, otherwise known as phase-space tomography. As practical considerations often rule out the availability of a complete set of measurements, coherence retrieval is usually a challenging high-dimensional ill-posed inverse problem. In this paper, we propose a trace-regularized optimization model for coherence retrieval and a provably-convergent adaptive accelerated proximal gradient algorithm for solving the resulting problem. Applying our model and algorithm to both simulated and experimental data, we demonstrate an improvement in reconstruction quality over previous models as well as an increase in convergence speed compared to existing first-order methods.Comment: 28 pages, 10 figures, accepted for publication in SIAM Journal on Imaging Science

3-D measurements using conoscopy and application to ophthalmology

In this paper we present a novel method to measure 3-D quasi planar or quasi spherical reflective surfaces with submicron depth accuracy. Two implementations are presented: a scanning and a non-scanning system. The non-scanning device allows fast measurements and can be applied for eye-shape measurements. The paper is organized as follows: in the introductory section, we first demonstrate the principle of the conoscopic effect leading to the formation of the interferogram. The second and third sections explain respectively. the scanning and non-scanning methods based on the conoscopic effect. We present the experimental results from a simple measurement and show how they conform with theory

Diffraction from deformed volume holograms: perturbation theory approach

We derive the response of a volume grating to arbitrary small deformations, using a perturbative approach. This result is of interest for two applications: (a) when a deformation is undesirable and one seeks to minimize the diffracted field's sensitivity to it and (b) when the deformation itself is the quantity of interest and the diffracted field is used as a probe into the deformed volume where the hologram was originally recorded. We show that our result is consistent with previous derivations motivated by the phenomenon of shrinkage in photopolymer holographic materials. We also present the analysis of the grating's response to deformation due to a point indenter and present experimental results consistent with theory

Holographic storage using shift multiplexing

We demonstrate theoretically and experimentally a new multiplexing method for volume holographic storage using a single reference beam that is composed of multiple plane waves or is a spherical wave. We multiplex the holograms by shifting the recording material or the recording/readout head. The volume properties of the recording medium allow selective readout of holograms stored in successive overlapping locations. High storage densities can be achieved with a relatively simple implementation by use of the new method