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DOE OSTI2021

Exactly unitary discrete representations of the metaplectic transform for linear-time algorithms

The metaplectic transform (MT), a generalization of the Fourier transform sometimes called the linear canonical transform, is a tool used ubiquitously in modern optics, for example, when calculating the transformations of light beams in paraxial optical systems. The MT is also an essential ingredient of the geometrical-optics modeling of caustics that we recently proposed. In particular, this application relies on the near-identity MT (NIMT); however, the NIMT approximation used so far is not exactly unitary and leads to numerical instability. Here, we develop a discrete MT that is exactly unitary, and approximate it to obtain a discrete NIMT that is also unitary and can be computed in linear time. We prove that the discrete NIMT converges to the discrete MT when iterated, thereby allowing the NIMT to compute MTs that are not necessarily near-identity. Finally, we then demonstrate the new algorithms with a series of examples.

47 OTHER INSTRUMENTATION↗

NASA NTRS1972

Improved methods of performing coherent optical correlation

Coherent optical correlators are described in which complex spatial filters are recorded by a quasi-Fourier transform method. The high-pass spatial filtering effects (due to the dynamic range of photographic films) normally encountered in Vander Lugt type complex filters are not present in this system. Experimental results for both transmittive as well as reflective objects are presented. Experiments are also performed by illuminating the object with diffused light. A correlator using paraboloidal mirror segments as the Fourier-transforming element is also described.

Husain-Abidi, A. S.↗

NASA NTRS1972

Solar system applications of Mie theory and of radiative transfer of polarized light

A theory of the multiple scattering of polarized light is discussed using the doubling method of van de Hulst. The concept of the Stokes parameters is derived and used to develop the form of the scattering phase matrix of a single particle. The diffuse reflection and transmission matrices of a single scattering plane parallel atmosphere are expressed as a function of the phase matrix, and the symmetry properties of these matrices are examined. Four matrices are required to describe scattering and transmission. The scattering matrix that results from the addition of two identical layers is derived. Using the doubling method, the scattering and transmission matrices of layers of arbitrary optical thickness can be derived. The doubling equations are then rewritten in terms of their Fourier components. Computation time is reduced since each Fourier component doubles independently. Computation time is also reduced through the use of symmetry properties.

Whitehill, L. P.↗

NASA NTRS1990

Real-time image processing II; Proceedings of the Meeting, Orlando, FL, Apr. 16-18, 1990

The present conference discusses topics in the fields of feature extraction and implementation, filter and correlation algorithms, optical correlators, high-level algorithms, and digital image processing for ranging and remote driving. Attention is given to a nonlinear filter derived from topological image features, IR image segmentation through iterative thresholding, orthogonal subspaces for correlation masking, composite filter trees and image recognition via binary search, and features of matrix-coherent optical image processing. Also discussed are multitarget tracking via hybrid joint transform correlator, binary joint Fourier transform correlator considerations, global image processing operations on parallel architectures, real-time implementation of a differential range finder, and real-time binocular stereo range and motion detection.

Juday, Richard D.↗

NASA NTRS2004

Adaptive DIT-Based Fringe Tracking and Prediction at IOTA

An automatic fringe tracking system has been developed and implemented at the Infrared Optical Telescope Array (IOTA). In testing during May 2002, the system successfully minimized the optical path differences (OPDs) for all three baselines at IOTA. Based on sliding window discrete Fourier transform (DFT) calculations that were optimized for computational efficiency and robustness to atmospheric disturbances, the algorithm has also been tested extensively on off-line data. Implemented in ANSI C on the 266 MHZ PowerPC processor running the VxWorks real-time operating system, the algorithm runs in approximately 2.0 milliseconds per scan (including all three interferograms), using the science camera and piezo scanners to measure and correct the OPDs. Preliminary analysis on an extension of this algorithm indicates a potential for predictive tracking, although at present, real-time implementation of this extension would require significantly more computational capacity.

Wilson, Edward↗

NASA NTRS2006

Distributed Computing Architecture for Image-Based Wavefront Sensing and 2 D FFTs

Image-based wavefront sensing (WFS) provides significant advantages over interferometric-based wavefi-ont sensors such as optical design simplicity and stability. However, the image-based approach is computational intensive, and therefore, specialized high-performance computing architectures are required in applications utilizing the image-based approach. The development and testing of these high-performance computing architectures are essential to such missions as James Webb Space Telescope (JWST), Terrestial Planet Finder-Coronagraph (TPF-C and CorSpec), and Spherical Primary Optical Telescope (SPOT). The development of these specialized computing architectures require numerous two-dimensional Fourier Transforms, which necessitate an all-to-all communication when applied on a distributed computational architecture. Several solutions for distributed computing are presented with an emphasis on a 64 Node cluster of DSPs, multiple DSP FPGAs, and an application of low-diameter graph theory. Timing results and performance analysis will be presented. The solutions offered could be applied to other all-to-all communication and scientifically computationally complex problems.

Smith, Jeffrey S.↗

NASA NTRS2006

Quantum Entanglement Molecular Absorption Spectrum Simulator

Quantum Entanglement Molecular Absorption Spectrum Simulator (QE-MASS) is a computer program for simulating two photon molecular-absorption spectroscopy using quantum-entangled photons. More specifically, QE-MASS simulates the molecular absorption of two quantum-entangled photons generated by the spontaneous parametric down-conversion (SPDC) of a fixed-frequency photon from a laser. The two-photon absorption process is modeled via a combination of rovibrational and electronic single-photon transitions, using a wave-function formalism. A two-photon absorption cross section as a function of the entanglement delay time between the two photons is computed, then subjected to a fast Fourier transform to produce an energy spectrum. The program then detects peaks in the Fourier spectrum and displays the energy levels of very short-lived intermediate quantum states (or virtual states) of the molecule. Such virtual states were only previously accessible using ultra-fast (femtosecond) laser systems. However, with the use of a single-frequency continuous wave laser to produce SPDC photons, and QEMASS program, these short-lived molecular states can now be studied using much simpler laser systems. QE-MASS can also show the dependence of the Fourier spectrum on the tuning range of the entanglement time of any externally introduced optical-path delay time. QE-MASS can be extended to any molecule for which an appropriate spectroscopic database is available. It is a means of performing an a priori parametric analysis of entangled photon spectroscopy for development and implementation of emerging quantum-spectroscopic sensing techniques. QE-MASS is currently implemented using the Mathcad software package.

Nguyen, Quang-Viet↗

NASA NTRS2003

Mathematical Investigation of Gamma Ray and Neutron Absorption Grid Patterns for Homeland Defense Related Fourier Imaging Systems

Terrorist suitcase nuclear devices typically using converted Soviet tactical nuclear warheads contain several kilograms of plutonium. This quantity of plutonium emits a significant number of gamma rays and neutrons as it undergoes radioactive decay. These gamma rays and neutrons normally penetrate ordinary matter to a significant distance. Unfortunately this penetrating quality of the radiation makes imaging with classical optics impractical. However, this radiation signature emitted by the nuclear source may be sufficient to be imaged from low-flying aerial platforms carrying Fourier imaging systems. The Fourier imaging system uses a pair of co-aligned absorption grids to measure a selected range of spatial frequencies from an object. These grids typically measure the spatial frequency in only one direction at a time. A grid pair that looks in all directions simultaneously would be an improvement over existing technology. A number of grid pairs governed by various parameters were investigated to solve this problem. By examining numerous configurations, it became apparent that an appropriate spiral pattern could be made to work. A set of equations was found to describe a grid pattern that produces straight fringes. Straight fringes represent a Fourier transform of a point source at infinity. An inverse Fourier transform of this fringe pattern would provide an accurate image (location and intensity) of a point source.

Boccio, Dona↗

NASA NTRS2001

Development of a Submillimeter-Wavelength Immersion Grating Spectrometer

The broad goal of this project was to develop a broadband, moderate-resolution spectrometer for submillimeter wavelengths. Our original approach was to build an immersion grating spectrometer, and as such, the first step was to identify the best material (lowest loss, highest index) for the grating medium, and to characterize its properties at the foreseen optical-bench operating temperature of 1.5 K. To this end, we put our initial efforts into upgrading an existing laboratory submillimeter Fourier transform spectrometer, which allowed us to carry out the requisite materials measurements. The associated cryogenic detector dewar was also redesigned and rebuilt to carry out this work. This dewar houses the 1.5 K detector and the filter wheel used in the materials characterization. Our goal was to have the beam propagate through the samples as uniformly as possible, so the optics were redesigned to allow for the samples to be traversed by a well-defined collimated beam. The optics redesign also placed the samples at an image of the aperture stop located within the FTS. After the rebuild, we moved into the testing phase.

Phillips, T. G.↗

DOE OSTI2021

Background-free dual-mode optical and 13 C magnetic resonance imaging in diamond particles

Multimodal imaging—the ability to acquire images of an object through more than one imaging mode simultaneously—has opened additional perspectives in areas ranging from astronomy to medicine. In this paper, we report progress toward combining optical and magnetic resonance (MR) imaging in such a “dual” imaging mode. They are attractive in combination because they offer complementary advantages of resolution and speed, especially in the context of imaging in scattering environments. Our approach relies on a specific material platform, microdiamond particles hosting nitrogen vacancy (NV) defect centers that fluoresce brightly under optical excitation and simultaneously “hyperpolarize” lattice C 13 nuclei, making them bright under MR imaging. We highlight advantages of dual-mode optical and MR imaging in allowing background-free particle imaging and describe regimes in which either mode can enhance the other. Leveraging the fact that the two imaging modes proceed in Fourier-reciprocal domains (real and k-space), we propose a sampling protocol that accelerates image reconstruction in sparse-imaging scenarios. Our work suggests interesting possibilities for the simultaneous optical and low-field MR imaging of targeted diamond nanoparticles.

36 MATERIALS SCIENCE↗

NASA NTRS2004

Absolute Measurement of Tilts via Fourier Analysis of Interferograms

The Fourier method of interferogram analysis requires the introduction of a constant tilt into the inteferogram to serve as a 'carrier signal' for information on the figure of the surface under test. This tilt is usually removed in the first steps of analysis and ignored thereafter. However, in the problem of aligning optical components and systems, knowledge of part orientation is crucial to proper instrument performance. This paper outlines an algorithm which uses the normally ignored carrier signal in Fourier analysis to compute an absolute tilt (orientation) of the test surface. We also provide a brief outline of how this technique, incorporated in a rotating Twyman-Green interferometer, can be used in alignment and metrology of optical systems.

Toland, Ronald W.↗

NASA NTRS2004

Absolute Measurement of Tilts via Fourier Analysis of Interferograms

The Fourier method of interferogram analysis requires the introduction of a constant tilt into the interferogram to serve as a carrier signal for information on the figure of the surface under test. This tilt is usually removed in the first steps of analysis and ignored thereafter. However, in the problem of aligning optical components and systems, knowledge of part orientation is crucial to proper instrument performance. This paper outlines an algorithm which uses the normally ignored carrier signal in Fourier analysis to compute an absolute tilt (orientation) of the test surface. We also provide a brief outline of how this technique, incorporated in a rotating Twyman-Green interferometer, can be used in alignment and metrology of optical systems.

Toland, Ronald W.↗

DOE OSTI2026

Stochastic equilibrium Raman spectroscopy (STERS)

In this manuscript, we propose a new method for cavity- and surface-enhanced Raman spectroscopy (SERS) with improved temporal resolution in the measurement of stochastic Raman spectral fluctuations. Our approach combines Fourier spectroscopy and photon correlation to decouple the integration time from the temporal resolution. Using statistical optics Monte Carlo simulations, we establish the relationship between time resolution and Raman signal strength, revealing that typical Raman spectral fluctuations, commensurate with molecular conformational dynamics, can theoretically be resolved on micro- to millisecond timescales. The method can further extract average single-molecule dynamics from small sub-ensembles, thereby potentially mitigating challenges in achieving strictly single-molecule isolation on SERS substrates.

Cobb-Bruno, Colburn [University of California, Ber↗

NASA NTRS1973

Experimental and data analysis techniques for deducing collision-induced forces from photographic histories of engine rotor fragment impact/interaction with a containment ring

An analysis method termed TEJ-JET is described whereby measured transient elastic and inelastic deformations of an engine-rotor fragment-impacted structural ring are analyzed to deduce the transient external forces experienced by that ring as a result of fragment impact and interaction with the ring. Although the theoretical feasibility of the TEJ-JET concept was established, its practical feasibility when utilizing experimental measurements of limited precision and accuracy remains to be established. The experimental equipment and the techniques (high-speed motion photography) employed to measure the transient deformations of fragment-impacted rings are described. Sources of error and data uncertainties are identified. Techniques employed to reduce data reading uncertainties and to correct the data for optical-distortion effects are discussed. These procedures, including spatial smoothing of the deformed ring shape by Fourier series and timewise smoothing by Gram polynomials, are applied illustratively to recent measurements involving the impact of a single T58 turbine rotor blade against an aluminum containment ring. Plausible predictions of the fragment-ring impact/interaction forces are obtained by one branch of this TEJ-JET method; however, a second branch of this method, which provides an independent estimate of these forces, remains to be evaluated.

Yeghiayan, R. P.↗

NASA NTRS1979

Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms

Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.

Ikhabisimov, D. K.↗

NASA NTRS1984

Surface fluctuation spectroscopy - A novel technique for characterizing liquid interfaces

Surface fluctuation spectroscopy is a dynamic light scattering technique which involves the detection of thermal fluctuations (capillary waves) that cover every liquid interface. The advantages of this technique over conventional mechanical methods are discussed. The signal resolution and precision are improved by using a grating heterodyne technique coupled with a digital correlator. Detailed calculations showed that, for the measured power spectrum (the Fourier transform of the correlation function) to take the Lorentzian shape, it is necessary that certain optical conditions be met. These conditions are demonstrated with experimental data collected for ethanol at the ambient temperature as a function of the wave number. Once the optical parameters are adjusted correctly, the experimental results show excellent agreement with the literature values. It is also demonstrated that, using microcomputer technology, the entire system can be automated.

Shih, L. B.↗

NASA NTRS1992

Retrieval of aerosol optical properties from multi-angle satellite imagery

Simulation multiangle imagery have been used to investigate the capabilities of a novel method for retrieval of atmospheric aerosol optical properties over land; this method employs spatial contrasts within the imagery and compares the spatial Fourier transforms of the multiangle images at zero and nonzero spatial frequencies. While requiring the definition of a relationship between the angular variation of the Fourier transform of the intrinsic surface angular reflectance at the zero and nonzero frequencies, the method assumes no a priori knowledge about aerosols or surface characteristics. Sensitivities to various aerosol properties are assessed.

Martonchik, John V.↗

DOE OSTI2025

Ultrabroadband THz conductivity of gated graphene in- and out-of-equilibrium

We employ ultrabroadband terahertz (THz) spectroscopy to expose the high-frequency transport properties of Dirac fermions in monolayer graphene. By controlling the carrier concentration via tunable electrical gating, both equilibrium and transient optical conductivities are obtained for a range of Fermi levels. The frequency-dependent equilibrium response is determined through a combination of time-domain THz and Fourier-transform infrared spectroscopy for energies up to the near-infrared, which also provides a measure of the gate-voltage dependent Fermi level. Transient changes in the real and imaginary parts of the graphene conductivity are electro-optically resolved for frequencies up to 15 THz after near-infrared femtosecond excitation, both at the charge-neutral point and for higher electrostatic-doping levels. Modeling of the THz response provides insight into changes of the carrier spectral weights and scattering rates, and reveals an additional broad-frequency ($$\approx$$ 8 THz) component to the photo-induced response, which we attribute to the zero-momentum mode of quantum-critical transport observed here in large-area CVD graphene.

Coslovich, G↗