Georges Nehmetallah

Applications of Digital and Analog Holography in Three-Dimensional Imaging

Digital and analog holography, along with its many variations, viz., holographic interferometry, holographic microscopy, holographic tomography, multiwavelength digital holography, phase-shifting holography, compressive holography, coherence holography, etc., have become the methods of choice for various metrological applications in three-dimensional (3D) imaging. In this review, we discuss the basic principles of analog and digital holography and the various topics mentioned above, with selected applications to real-world problems. We also discuss other related topics such as dynamic holography, non-Bragg orders, and compressive holographic tomography, nonlinear holography, holographic TV, as well as a nonholographic technique for 3D visualization, viz., transport of intensity imaging. Finally, we expose interested readers to contemporary topics in the area, viz., nonlinear holography and real-time holographic TV.

Digital tomographic compressive holographic reconstruction of three-dimensional objects in transmissive and reflective geometries

In this work compressive holography (CH) with multiple projection tomography is applied to solve the inverse ill-posed problem of reconstruction of three-dimensional (3D) objects with high axial accuracy. To visualize the 3D shape, we propose digital tomographic CH, where projections from more than one direction, as in tomographic imaging, can be employed, so that a 3D shape with improved axial resolution can be reconstructed. Also, we propose possible schemes for shadow elimination when the same object is illuminated at multiple angles using a single illuminating beam and using a single CCD. Finally, we adapt CH designed for a Gabor-type setup to a reflective geometry and apply the technique to reflective objects.

Linear and Nonlinear Propagation in Negative Index Materials

We analyze linear propagation in negative index materials by starting from a dispersion relation and by deriving the underlying partial differential equation. Transfer functions for propagation are derived in temporal and spatial frequency domains for unidirectional baseband and modulated pulse propagation, as well as for beam propagation. Gaussian beam propagation is analyzed and reconciled with the ray transfer matrix approach as applied to propagation in negative index materials. Nonlinear extensions of the linear partial differential equation are made by incorporating quadratic and cubic terms, and baseband and envelope solitary wave solutions are determined. The conditions for envelope solitary wave solutions are compared with those for the standard nonlinear Schrodinger equation in a positive index material.

Determination of model airplane attitudes using dynamic holographic interferometry.

We demonstrate how real-time holographic interferometry yielding two-dimensional fringes can be recorded and used to determine changes in three-dimensional attitude of a model airplane through digital image processing. A simple bench-top experiment with a model airplane as a test object is conducted to demonstrate interference fringes superposed on the image due to changes in attitudes (pitch, yaw, and roll) as well as distortion. A novel second-generation thermoplastic camera suitable for dynamic multiple reversible registration of thin-phase holograms using thermoplastic and semiconductor film on glass substrate is used for in situ recording and readout during real-time holographic interferometry. Thin-phase holograms also offer the advantage of exact image reconstruction from forward-phase conjugation.

SHOT: single-beam holographic tomography

A novel single-beam holographic tomography (SHOT) based technique is used for the recording and reconstruction of 3D shapes of water droplets, leading to quantification of the radii of curvatures along the surface, droplet separation, and number density.

Multilayer Periodic and Random Metamaterial Structures: Analysis and Applications

In recent years, multilayer photonic bandgap structures comprising stacks of alternating layers of positive and negative index have been proposed for a variety of applications, such as perfect imaging, filters, sensors, coatings for tailored emittance, absorptance, etc. Following a brief review of the history of negative index materials, the performance of such stacks is reviewed, with emphasis on analysis of plane wave and beam propagation, and possible applications in sensing. First, the use of the transfer matrix method to analyze plane wave propagation in such structures to determine the transmittance and reflectance is developed. Examples of cases where the Bragg bandgap and the so-called zero <;\(n \) > gap can be used for possible applications in sensing are illustrated. Next, the transfer matrix approach is extended to simulate the spatial evolution of a collection of propagating and nonpropagating TE and TM plane waves (or plane wave spectra) incident on such multilayer structures. The use of the complex Poynting theorem in checking the computations, as well as monitoring powers and the stored electric or magnetic energy in any section of the multilayer stack, is illustrated, along with its use in designing alternating positive and negative index structures with optimal gain to compensate for losses in the negative index material. Finally, the robustness of PIM-NIM stacks with respect to randomness in the dimensions of the PIM-NIM structure is examined. This should be useful in determining the performance of such structures when they are physically fabricated.

Numerical modeling of (D+1)-dimensional solitons in a sign-alternating nonlinear medium with an adaptive fast Hankel split-step method

We present a novel technique to numerically solve transverse and pulsed optical beam or light bullet propagation in a layered alternating self-focusing and self-defocusing medium based on the scalar nonlinear Schrodinger equation in two and three dimensions with cylindrical and spherical symmetry, respectively. Using fast algorithms for Hankel transform along with adaptive longitudinal stepping and transverse grid management in a symmetrized split-step technique, it is possible to accurately study many nonlinear effects, including the possibility of spatiotemporal collapse, or the collapse-arresting mechanism due to a sign-alternating nonlinearity coefficient. Also, by using the variational approximation technique, we can prove that stable (D+1)-dimensional soliton beams and optical bullets exist in these media.

Multi-Wavelength Digital Holographic Microscopy Using A Telecentric Reflection Configuration

A telecentric recording configuration for multi-wavelength digital holographic microscopy (MW-DHM) is proposed. The advantage of this configuration is to optically remove, without post-processing, the parabolic phase distortion caused by the microscope objective in traditional MW-DHM.

Tunable metamaterial binary nano-particle dispersed liquid crystal cells

Metamaterials with tunable properties are of great importance due to potential applications in super-resolution lensing and sensors. In this paper we study the feasibility of the fabrication of a metamaterial using binary nanoparticle-dispersed liquid crystal cell (NDLCC). Depending on the angle between the director axis of the LCC and the incident beam, types, radii, and volume filling fractions of the nanoparticles, a negative index of refraction cell is obtained in a certain range of frequencies. The effective index of refraction is calculated using the effective medium theory. The scattering, extinction, and absorption of such a NDLCC cell is also found. Finally, the influence of the various parameters to obtain such a negative index metamaterial has been investigated.

An imaging system detectivity metric using energy and power spectral densities

The purpose of this paper is to construct a robust modeling framework for imaging systems in order to predict the performance of detecting small targets such as Unmanned Aerial Vehicles (UAVs). The underlying principle is to track the flow of scene information and statistics, such as the energy spectra of the target and power spectra of the background, through any number of imaging components. This information is then used to calculate a detectivity metric. Each imaging component is treated as a single linear shift invariant (LSI) component with specified input and output parameters. A component based approach enables the inclusion of existing component-level models and makes it directly compatible with image modeling software such as the Night Vision Integrated Performance Model (NV-IPM). The modeling framework also includes a parallel implementation of Monte Carlo simulations designed to verify the analytic approach. However, the Monte Carlo simulations may also be used independently to accurately model nonlinear processes where the analytic approach fails, allowing for even greater extensibility. A simple trade study is conducted comparing the modeling framework to the simulation.