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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Sampling and Reconstruction of the Pupil and Electric Field for Phase Retrieval

This technology is based on sampling considerations for a band-limited function, which has application to optical estimation generally, and to phase retrieval specifically. The analysis begins with the observation that the Fourier transform of an optical aperture function (pupil) can be implemented with minimal aliasing for Q values down to Q = 1. The sampling ratio, Q, is defined as the ratio of the sampling frequency to the band-limited cut-off frequency. The analytical results are given using a 1-d aperture function, and with the electric field defined by the band-limited sinc(x) function. Perfect reconstruction of the Fourier transform (electric field) is derived using the Whittaker-Shannon sampling theorem for 1<Q<2. The Fourier transform is constructed by periodic extension, i.e., by spacing copies of the transform in a definite way, recognizing that no aliasing occurs for values of the sampling ratio such that 1<Q<2, which can be used to advantage in the application of phase retrieval estimation. A method was developed for propagating the electro magnetic field with no aliasing, which has been extended to 2-d optical apertures.

Dean, Bruce↗
NASA NTRS2010

A Final Approach Trajectory Model for Current Operations

Predicting accurate trajectories with limited intent information is a challenge faced by air traffic management decision support tools in operation today. One such tool is the FAA's Terminal Proximity Alert system which is intended to assist controllers in maintaining safe separation of arrival aircraft during final approach. In an effort to improve the performance of such tools, two final approach trajectory models are proposed; one based on polynomial interpolation, the other on the Fourier transform. These models were tested against actual traffic data and used to study effects of the key final approach trajectory modeling parameters of wind, aircraft type, and weight class, on trajectory prediction accuracy. Using only the limited intent data available to today's ATM system, both the polynomial interpolation and Fourier transform models showed improved trajectory prediction accuracy over a baseline dead reckoning model. Analysis of actual arrival traffic showed that this improved trajectory prediction accuracy leads to improved inter-arrival separation prediction accuracy for longer look ahead times. The difference in mean inter-arrival separation prediction error between the Fourier transform and dead reckoning models was 0.2 nmi for a look ahead time of 120 sec, a 33 percent improvement, with a corresponding 32 percent improvement in standard deviation.

Gong, Chester↗
NASA NTRS2012

Broad-Bandwidth FPGA-Based Digital Polyphase Spectrometer

With present concern for ecological sustainability ever increasing, it is desirable to model the composition of Earth s upper atmosphere accurately with regards to certain helpful and harmful chemicals, such as greenhouse gases and ozone. The microwave limb sounder (MLS) is an instrument designed to map the global day-to-day concentrations of key atmospheric constituents continuously. One important component in MLS is the spectrometer, which processes the raw data provided by the receivers into frequency-domain information that cannot only be transmitted more efficiently, but also processed directly once received. The present-generation spectrometer is fully analog. The goal is to include a fully digital spectrometer in the next-generation sensor. In a digital spectrometer, incoming analog data must be converted into a digital format, processed through a Fourier transform, and finally accumulated to reduce the impact of input noise. While the final design will be placed on an application specific integrated circuit (ASIC), the building of these chips is prohibitively expensive. To that end, this design was constructed on a field-programmable gate array (FPGA). A family of state-of-the-art digital Fourier transform spectrometers has been developed, with a combination of high bandwidth and fine resolution. Analog signals consisting of radiation emitted by constituents in planetary atmospheres or galactic sources are downconverted and subsequently digitized by a pair of interleaved analog-to-digital converters (ADCs). This 6-Gsps (gigasample per second) digital representation of the analog signal is then processed through an FPGA-based streaming fast Fourier transform (FFT). Digital spectrometers have many advantages over previously used analog spectrometers, especially in terms of accuracy and resolution, both of which are particularly important for the type of scientific questions to be addressed with next-generation radiometers.

Jamot, Robert F.↗
NASA NTRS1991

A two-dimensional time domain near zone to far zone transformation

In a previous paper, a time domain transformation useful for extrapolating 3-D near zone finite difference time domain (FDTD) results to the far zone was presented. In this paper, the corresponding 2-D transform is outlined. While the 3-D transformation produced a physically observable far zone time domain field, this is not convenient to do directly in 2-D, since a convolution would be required. However, a representative 2-D far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required it can be obtained by inverse Fourier transform of the final frequency domain result.

Luebbers, Raymond J.↗
NASA NTRS1991

A two-dimensional time domain near zone to far zone transformation

A time domain transformation useful for extrapolating three dimensional near zone finite difference time domain (FDTD) results to the far zone was presented. Here, the corresponding two dimensional transform is outlined. While the three dimensional transformation produced a physically observable far zone time domain field, this is not convenient to do directly in two dimensions, since a convolution would be required. However, a representative two dimensional far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required, it can be obtained by inverse Fourier transform of the final frequency domain result.

Luebbers, Raymond J.↗
DOE OSTI2026

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗
NASA NTRS1992

Efficient demultiplexing algorithm for noncontiguous carriers

A channel separation algorithm for the frequency division multiple access/time division multiplexing (FDMA/TDM) scheme is presented. It is shown that implementation using this algorithm can be more effective than the fast Fourier transform (FFT) algorithm when only a small number of carriers need to be selected from many, such as satellite Earth terminals. The algorithm is based on polyphase filtering followed by application of a generalized Walsh-Hadamard transform (GWHT). Comparison of the transform technique used in this algorithm with discrete Fourier transform (DFT) and FFT is given. Estimates of the computational rates and power requirements to implement this system are also given.

Thanawala, A. A.↗
NASA NTRS2006

Pattern-Recognition Processor Using Holographic Photopolymer

proposed joint-transform optical correlator (JTOC) would be capable of operating as a real-time pattern-recognition processor. The key correlation-filter reading/writing medium of this JTOC would be an updateable holographic photopolymer. The high-resolution, high-speed characteristics of this photopolymer would enable pattern-recognition processing to occur at a speed three orders of magnitude greater than that of state-of-the-art digital pattern-recognition processors. There are many potential applications in biometric personal identification (e.g., using images of fingerprints and faces) and nondestructive industrial inspection. In order to appreciate the advantages of the proposed JTOC, it is necessary to understand the principle of operation of a conventional JTOC. In a conventional JTOC (shown in the upper part of the figure), a collimated laser beam passes through two side-by-side spatial light modulators (SLMs). One SLM displays a real-time input image to be recognized. The other SLM displays a reference image from a digital memory. A Fourier-transform lens is placed at its focal distance from the SLM plane, and a charge-coupled device (CCD) image detector is placed at the back focal plane of the lens for use as a square-law recorder. Processing takes place in two stages. In the first stage, the CCD records the interference pattern between the Fourier transforms of the input and reference images, and the pattern is then digitized and saved in a buffer memory. In the second stage, the reference SLM is turned off and the interference pattern is fed back to the input SLM. The interference pattern thus becomes Fourier-transformed, yielding at the CCD an image representing the joint-transform correlation between the input and reference images. This image contains a sharp correlation peak when the input and reference images are matched. The drawbacks of a conventional JTOC are the following: The CCD has low spatial resolution and is not an ideal square-law detector for the purpose of holographic recording of interference fringes. A typical state-of-the-art CCD has a pixel-pitch limited resolution of about 100 lines/mm. In contrast, the holographic photopolymer to be used in the proposed JTOC offers a resolution > 2,000 lines/mm. In addition to being disadvantageous in itself, the low resolution of the CCD causes overlap of a DC term and the desired correlation term in the output image. This overlap severely limits the correlation signal-to-noise ratio. The two-stage nature of the process limits the achievable throughput rate. A further limit is imposed by the low frame rate (typical video rates) of low- and medium-cost commercial CCDs.

Chao, Tien-Hsin↗
NASA NTRS1979

Transform approach to electromagnetic scattering

In this paper, a comprehensive review of the Fourier transform technique as applied to the problem of high-frequency scattering is presented and the concepts of the spectral theory of diffraction (STD) are introduced. In contrast to the more commonly employed ray-optical method for high-frequency scattering, the STD approach interprets the scattered field as the spectrum, or the Fourier transform of the induced current on the scatterer. Such an interpretation offers several important advantages: uniform nature of representation, capacity to improve and extend the ray-optical formulas in a systematic manner, and convenient accuracy tests for the results. Methods for combining integral equation methods with the Galerkin procedure and asymptotic techniques in the transform domain are described, and representative examples illustrating the application of the spectral approach are included.

Mittra, R.↗
NASA NTRS1976

Computation of scalar far-field patterns of large-aperture antennas

In computer programs used for evaluating the performance of high-gain antennas, efficient numerical methods for calculating the far-field patterns must be used since the majority of computer time and storage requirements may be attributed to this phase of the program. The numerical method most frequently used is the Fast Fourier Transform (FFT), which computes the far field as the Fourier transform of the field distribution in the antenna aperture. A new numerical method that in many applications is superior to the FFT in terms of reducing computer time and storage requirements is described.

Omalley, T. A.↗
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 NTRS1973

Optical data processing using paraboloidal mirror segments

An optical data processing system using paraboloidal reflecting surfaces is disclosed. In the preferred embodiment the paraboloidal reflecting surfaces are segments of a paraboloidal mirror. A source of coherent light is in the focal plane of the first paraboloidal mirror segment which collimates the beam and reflects it toward a second paraboloidal mirror surface. The information to be analyzed, on a transparency for example, is placed in the collimated beam. The beam is reflected from the second paraboloidal mirror segment and focused on a Fourier transform plane. A photon detector could be placed in the Fourier transform plane or suitable spatial filters, with the filtered beam then being reflected from a third paraboloidal mirror segment to be focused on a reconstruction plane.

Husain-Abidi, A. S.↗
NASA NTRS2002

An Investigation into the Potential Application of Wavelets to Modal Testing and Analysis

The analysis of transient data of the type found in vibrating mechanical systems has been greatly improved through the use of modern techniques such as Fourier analysis. This is especially true when considered in conjunction with the development of the so-called Fast Fourier Transform algorithm by Cooley and the tremendous strides in computational power of the last several decades. The usefulness of the discrete Fourier Transform is its ability to transform sampled data from the "time-domain" to the "frequency domain," thereby allowing the analyst to decompose a signal into its frequency content. More recent developments have led to the wavelet transform. The strength of wavelet analysis is its ability to maintain both time and frequency information, thus making it an attractive candidate for the analysis of non-stationary signals. This report is an overview of wavelet theory and the potential use of the wavelet transform as an alternative to Fourier analysis in modal identification.

A. Fort Gwinn, Jr.↗
NASA NTRS1975

Simulation of multicorrelated random processes using the FFT algorithm

A technique for the digital simulation of multicorrelated Gaussian random processes is described. This technique is based upon generating discrete frequency functions which correspond to the Fourier transform of the desired random processes, and then using the fast Fourier transform (FFT) algorithm to obtain the actual random processes. The main advantage of this method of simulation over other methods is computation time; it appears to be more than an order of magnitude faster than present methods of simulation. One of the main uses of multicorrelated simulated random processes is in solving nonlinear random vibration problems by numerical integration of the governing differential equations. The response of a nonlinear string to a distributed noise input is presented as an example.

Wittig, L. E.↗
NASA NTRS1983

The extreme nearfield of an acoustic diffraction grating

An expression for the transmitted sound field near (within a fraction of a wavelength) an array of slits is derived under the assumption that the normal component of the particle velocity is the same, in the slits, as if no grating were present and zero everywhere else in the plane of the grating. The expression is in the form of an inverse Fourier transform and can be evaluated quickly using a standard fast-Fourier-transform (FFT) algorithm. Using this technique, the sound pressure on the axis of symmetry normal to the grating was evaluated for a plane-wave incident at various angles with respect to the normal to the grating, and the results were found to provide an excellent qualitative (and to a significant degree quantitative) description of some experimental measurements. Extensions of the method to oscillating pistons of arbitrary (but planar) configuration in a rigid baffle are indicated.

Ochs, R. L., Jr.↗
NASA NTRS2013

On Using Intensity Interferometry for Feature Identification and Imaging of Remote Objects

We derive an approximation to the intensity covariance function of two scanning pinhole detectors, facing a distant source (e.g., a star) being occluded partially by an absorptive object (e.g., a planet). We focus on using this technique to identify or image an object that is in the line-of-sight between a well-characterized source and the detectors. We derive the observed perturbation to the intensity covariance map due to the object, showing that under some reasonable approximations it is proportional to the real part of the Fourier transform of the source's photon-flux density times the Fourier transform of the object's intensity absorption. We highlight the key parameters impacting its visibility and discuss the requirements for estimating object-related parameters, e.g., its size, velocity or shape. We consider an application of this result to determining the orbit inclination of an exoplanet orbiting a distant star. Finally, motivated by the intrinsically weak nature of the signature, we study its signal-to-noise ratio and determine the impact of system parameters.

quantum optics↗
NASA NTRS1992

Advanced satellite communication system

The objective of this research program was to develop an innovative advanced satellite receiver/demodulator utilizing surface acoustic wave (SAW) chirp transform processor and coherent BPSK demodulation. The algorithm of this SAW chirp Fourier transformer is of the Convolve - Multiply - Convolve (CMC) type, utilizing off-the-shelf reflective array compressor (RAC) chirp filters. This satellite receiver, if fully developed, was intended to be used as an on-board multichannel communications repeater. The Advanced Communications Receiver consists of four units: (1) CMC processor, (2) single sideband modulator, (3) demodulator, and (4) chirp waveform generator and individual channel processors. The input signal is composed of multiple user transmission frequencies operating independently from remotely located ground terminals. This signal is Fourier transformed by the CMC Processor into a unique time slot for each user frequency. The CMC processor is driven by a waveform generator through a single sideband (SSB) modulator. The output of the coherent demodulator is composed of positive and negative pulses, which are the envelopes of the chirp transform processor output. These pulses correspond to the data symbols. Following the demodulator, a logic circuit reconstructs the pulses into data, which are subsequently differentially decoded to form the transmitted data. The coherent demodulation and detection of BPSK signals derived from a CMC chirp transform processor were experimentally demonstrated and bit error rate (BER) testing was performed. To assess the feasibility of such advanced receiver, the results were compared with the theoretical analysis and plotted for an average BER as a function of signal-to-noise ratio. Another goal of this SBIR program was the development of a commercial product. The commercial product developed was an arbitrary waveform generator. The successful sales have begun with the delivery of the first arbitrary waveform generator.

Staples, Edward J.↗