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NASA NTRS1985

Infrared spectroscopic studies of the effect of elevated temperature on the association of pyroglutamic acid with clay and other minerals

Fourier transform i.r. measurements of L-pyroglutamic acid dispersed in a matrix of a clay, silica or alumina have been obtained at various temperatures between 25 and 220 degrees C. The i.r. spectrum of L-pyroglutamic acid varies in a manner dependent upon the matrix material and shows considerable change as the temperature of the mixtures is increased. The differences in the spectrum at elevated temperatures are explained in terms of a chemical reaction between hydroxyl groups in the matrix and the carboxylic acid. The i.r. spectra of trimethylsilyl derivatives of L-pyroglutamic acid and aluminum pyroglutamate were also measured to assist the understanding of spectra and interpretation of the spectral changes dependent upon increasing temperature.

Aluminum Oxide/analysis/chemistry↗

NASA NTRS2014

A Frequency Analysis Approach for Categorizing Air Traffic Behavior

A method of analyzing National Air Space (NAS) air traffic that uses the Discrete Fourier Transform (DFT) is presented. The DFT is used to transform time domain traffic count data into the frequency domain where the sources of traffic in air spaces can be identified and characterized more easily. It is shown in simulation that individual traffic flows within Air Route Traffic Control Centers can be distinguished by their periodicity in the DFT plot. Next, three Traffic Management Initiatives (playbook rerouting, metered flows, and Ground Delay Programs) are implemented in simulations and their signature effects on the traffic are identified using the DFT. Finally, historical flight data is studied and the DFT is applied to sector traffic count data. It is found that in many cases, variations in traffic due to rerouting and convective weather disturbances are better highlighted in the frequency domain than in the original time domain data. Initial results of the DFT show it has potential as a tool for measuring and/or predicting NAS behavior for daily tactical planning and control purposes.

fourier transform↗

NASA NTRS2006

TES Level 1 Algorithms: Interferogram Processing, Geolocation, Radiometric, and Spectral Calibration

The Tropospheric Emission Spectrometer (TES) on the Earth Observing System (EOS) Aura satellite measures the infrared radiance emitted by the Earth's surface and atmosphere using Fourier transform spectrometry. The measured interferograms are converted into geolocated, calibrated radiance spectra by the L1 (Level 1) processing, and are the inputs to L2 (Level 2) retrievals of atmospheric parameters, such as vertical profiles of trace gas abundance. We describe the algorithmic components of TES Level 1 processing, giving examples of the intermediate results and diagnostics that are necessary for creating TES L1 products. An assessment of noise-equivalent spectral radiance levels and current systematic errors is provided. As an initial validation of our spectral radiances, TES data are compared to the Atmospheric Infrared Sounder (AIRS) (on EOS Aqua), after accounting for spectral resolution differences by applying the AIRS spectral response function to the TES spectra. For the TES L1 nadir data products currently available, the agreement with AIRS is 1 K or better.

infrared remote sensing↗

NASA NTRS2001

Spectroscopic characterization of collagen cross-links in bone

Collagen is the most abundant protein of the organic matrix in mineralizing tissues. One of its most critical properties is its cross-linking pattern. The intermolecular cross-linking provides the fibrillar matrices with mechanical properties such as tensile strength and viscoelasticity. In this study, Fourier transform infrared (FTIR) spectroscopy and FTIR imaging (FTIRI) analyses were performed in a series of biochemically characterized samples including purified collagen cross-linked peptides, demineralized bovine bone collagen from animals of different ages, collagen from vitamin B6-deficient chick homogenized bone and their age- and sex-matched controls, and histologically stained thin sections from normal human iliac crest biopsy specimens. One region of the FTIR spectrum of particular interest (the amide I spectral region) was resolved into its underlying components. Of these components, the relative percent area ratio of two subbands at approximately 1660 cm(-1) and approximately 1690 cm(-1) was related to collagen cross-links that are abundant in mineralized tissues (i.e., pyridinoline [Pyr] and dehydrodihydroxylysinonorleucine [deH-DHLNL]). This study shows that it is feasible to monitor Pyr and DHLNL collagen cross-links spatial distribution in mineralized tissues. The spectroscopic parameter established in this study may be used in FTIRI analyses, thus enabling the calculation of relative Pyr/DHLNL amounts in thin (approximately 5 microm) calcified tissue sections with a spatial resolution of approximately 7 microm.

Non-NASA Center↗

NASA NTRS1994

Alpha-helical hydrophobic polypeptides form proton-selective channels in lipid bilayers

Proton translocation is important in membrane-mediated processes such as ATP-dependent proton pumps, ATP synthesis, bacteriorhodopsin, and cytochrome oxidase function. The fundamental mechanism, however, is poorly understood. To test the theoretical possibility that bundles of hydrophobic alpha-helices could provide a low energy pathway for ion translocation through the lipid bilayer, polyamino acids were incorporated into extruded liposomes and planar lipid membranes, and proton translocation was measured. Liposomes with incorporated long-chain poly-L-alanine or poly-L-leucine were found to have proton permeability coefficients 5 to 7 times greater than control liposomes, whereas short-chain polyamino acids had relatively little effect. Potassium permeability was not increased markedly by any of the polyamino acids tested. Analytical thin layer chromatography measurements of lipid content and a fluorescamine assay for amino acids showed that there were approximately 135 polyleucine or 65 polyalanine molecules associated with each liposome. Fourier transform infrared spectroscopy indicated that a major fraction of the long-chain hydrophobic peptides existed in an alpha-helical conformation. Single-channel recording in both 0.1 N HCl and 0.1 M KCl was also used to determine whether proton-conducting channels formed in planar lipid membranes (phosphatidylcholine/phosphatidylethanolamine, 1:1). Poly-L-leucine and poly-L-alanine in HCl caused a 10- to 30-fold increase in frequency of conductive events compared to that seen in KCl or by the other polyamino acids in either solution. This finding correlates well with the liposome observations in which these two polyamino acids caused the largest increase in membrane proton permeability but had little effect on potassium permeability. Poly-L-leucine was considerably more conductive than poly-L-alanine due primarily to larger event amplitudes and, to a lesser extent, a higher event frequency. Poly-L-leucine caused two populations of conductive events, one in the 0.1-0.5 pA range, and one in the 1.0-5.0 pA range, whereas nearly all events caused by poly-L-alanine were in the 0.1-0.5 pA range at an applied voltage of +60 mV. The channel-like activity appeared to switch between conductive and nonconductive states, with most open-times in the range of 50-200 ms. We conclude that hydrophobic polyamino acids produce proton-conducting defects in lipid bilayers that may be used to model functional proton channels in biological membranes.

NASA Discipline Exobiology↗

NASA NTRS1975

On the Laplace transform for distributions

A new characterization of the Laplace transform for Schwartz distributions is developed, using sequences of linear transformations on the space of distributions. The standard theorems on analyticity, uniqueness and invertibility of the transform are proved, using the new characterization as the definition of the Laplace transform. It is shown that this sequential definition is equivalent to Schwartz's extension of the ordinary Laplace transform to distributions which he obtained from the Fourier transform.

Price, D. B.↗

NASA NTRS1985

A separable two-dimensional discrete Hartley transform

Bracewell has proposed the Discrete Hartley Transform (DHT) as a substitute for the Discrete Fourier Transform (DFT), particularly as a means of convolution. Here, it is shown that the most natural extension of the DHT to two dimensions fails to be separate in the two dimensions, and is therefore inefficient. An alternative separable form is considered, corresponding convolution theorem is derived. That the DHT is unlikely to provide faster convolution than the DFT is also discussed.

Watson, A. B.↗

NASA NTRS1986

Separable two-dimensional discrete Hartley transform

Watson, Andrew B.↗

NASA NTRS1977

Computer control of a far infrared interferometer

A simple interface has been designed for the automatic control and data collection from a Grubb Parsons Mark III cube interferometer. A computer is used to automatically step the movable mirror on the interferometer. Data may be directly input into the computer for immediate transformation or stored for later analysis via a fast Fourier transformation. The interface is based on a commercial analog-to-digital converter having a parallel-to-serial data converter. The device can also display ASCII characters sent from the computer in parallel binary code. The system is applicable to recording interferograms having long time durations and to measuring multiple interferograms for statistical averaging.

Breecher, J.↗

NASA NTRS1992

Error analysis of optical correlators

With the growing interest in using binary phase only filters (BPOF) in optical correlators that are implemented on magnetooptic spatial light modulators, an understanding of the effect of errors in system alignment and optical components is critical in obtaining optimal system performance. We present simulations of optical correlator performance degradation in the presence of eight errors. We break these eight errors into three groups: 1) alignment errors, 2) errors due to a combination of component imperfections and alignment errors, and 3) errors which result solely from non-ideal components. Under the first group, we simulate errors in the distance from the object to the first principle plane of the transform lens, the distance from the second principle plane of the transform lens to the filter plane, and rotational misalignment of the input mask with the filter mask. Next we consider errors which result from a combination of alignment and component imperfections. These include errors in the transform lens, the phase compensation lens, and the inverse Fourier transform lens. Lastly we have the component errors resulting from the choice of spatial light modulator. These include contrast error and phase errors caused by the non-uniform flatness of the masks. The effects of each individual error are discussed, and the result of combining all eight errors under assumptions of reasonable tolerances and system parameters is also presented. Conclusions are drawn as to which tolerances are most critical for optimal system performance.

Ma, Paul W.↗

NASA NTRS1976

Effects of multiple scattering on light pulses reflected by turbid atmospheres

Multiple scattering contributions to lidar returns from turbid atmospheres are derived by means of an analytical theory. It is assumed that scattering takes place mainly at small angles except for one event that scatters the light backward. The phase functions are approximated by the sum of Gaussian functions of the scattering angle in both the forward and backward directions. The three-dimensional radiative transfer equation is transformed to a one-dimensional problem by means of Fourier transforms. Neumann solutions to the transformed equation of radiative transfer are then found. A number of examples are presented for cloud, fog and haze models. The results are found to be in satisfactory agreement with results obtained from the Monte Carlo analysis of Kunkel (1974) and the theory of light pulses doubly scattered by turbid atmospheres which was developed by Eloranta (1972).

Weinman, J. A.↗

NASA NTRS1985

Secondary pattern computation of an offset reflector antenna

Reflector antennas are widely used in communications satellite systems because they provide high gain at low cost. In analyzing reflector antennas the computation of the secondary pattern is the main concern. A computer program for calculating the secondary pattern of an offset reflector has been developed and implemented at the NASA Lewis Research Center. The theoretical foundation for this program is based on the use of geometrical optics to describe the fields from the feed to the reflector surface and to the aperture plane. The resulting aperture field distribution is then transformed to the far-field zone by the fast Fourier transform algorithm. Comparing this technique with other well-known techniques (the geometrical theory of diffraction, physical optics (Jacobi-Bessel), etc.) shows good agreement for large (diameter of 100 lambda or greater) reflector antennas.

Acosta, R. J.↗

NASA NTRS1976

Balloon-borne transform spectroscopy

The design and construction of a high-resolution far-infrared Fourier-transform spectrometer for use on the Smithsonian balloon-borne one-meter telescope is described. The instrument will operate at a resolution of about 0.1 kayser in the region from 25 to 150 microns. It will be used to obtain spectra of Jupiter, Venus, Orion, and other H II and molecular cloud regions, as well as the terrestrial stratosphere.

Traub, W. A.↗

NASA NTRS1999

A Critical Examination of Wind-Wave Spectral Functional Form

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.

Huang, Norden E.↗

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 NTRS1976

The fast decoding of Reed-Solomon codes using number theoretic transforms

It is shown that Reed-Solomon (RS) codes can be encoded and decoded by using a fast Fourier transform (FFT) algorithm over finite fields. The arithmetic utilized to perform these transforms requires only integer additions, circular shifts and a minimum number of integer multiplications. The computing time of this transform encoder-decoder for RS codes is less than the time of the standard method for RS codes. More generally, the field GF(q) is also considered, where q is a prime of the form K x 2 to the nth power + 1 and K and n are integers. GF(q) can be used to decode very long RS codes by an efficient FFT algorithm with an improvement in the number of symbols. It is shown that a radix-8 FFT algorithm over GF(q squared) can be utilized to encode and decode very long RS codes with a large number of symbols. For eight symbols in GF(q squared), this transform over GF(q squared) can be made simpler than any other known number theoretic transform with a similar capability. Of special interest is the decoding of a 16-tuple RS code with four errors.

Reed, I. S.↗

NASA NTRS1997

Frictionless Contact of Multilayered Composite Half Planes Containing Layers With Complex Eigenvalues

A previously developed local-global stiffness matrix methodology for the response of a composite half plane, arbitrarily layered with isotropic, orthotropic or monoclinic plies, to indentation by a rigid parabolic punch is further extended to accommodate the presence of layers with complex eigenvalues (e.g., honeycomb or piezoelectric layers). First, a generalized plane deformation solution for the displacement field in an orthotropic layer or half plane characterized by complex eigenvalues is obtained using Fourier transforms. A local stiffness matrix in the transform domain is subsequently constructed for this class of layers and half planes, which is then assembled into a global stiffness matrix for the entire multilayered half plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary condition on the top surface of the half plane indented by a rigid punch results in an integral equation for the unknown pressure in the contact region. The integral possesses a divergent kernel which is decomposed into Cauchy-type and regular parts using the asymptotic properties of the local stiffness matrix and a relationship between Fourier and finite Hilbert transform of the contact pressure. The solution of the resulting singular integral equation is obtained using a collocation technique based on the properties of orthogonal polynomials developed by Erdogan and Gupta. Examples are presented that illustrate the important influence of low transverse properties of layers with complex eigenvalues, such as those exhibited by honeycomb, on the load versus contact length response and contact pressure distributions for half planes containing typical composite materials.

Zhang, Wang↗

NASA NTRS1974

An extension of the Laplace transform to Schwartz distributions

A characterization of the Laplace transform is developed which extends the transform to the Schwartz distributions. The class of distributions includes the impulse functions and other singular functions which occur as solutions to ordinary and partial differential equations. The standard theorems on analyticity, uniqueness, and invertibility of the transform are proved by using the characterization as the definition of the Laplace transform. The definition uses sequences of linear transformations on the space of distributions which extends the Laplace transform to another class of generalized functions, the Mikusinski operators. It is shown that the sequential definition of the transform is equivalent to Schwartz' extension of the ordinary Laplace transform to distributions but, in contrast to Schwartz' definition, does not use the distributional Fourier transform. Several theorems concerning the particular linear transformations used to define the Laplace transforms are proved. All the results proved in one dimension are extended to the n-dimensional case, but proofs are presented only for those situations that require methods different from their one-dimensional analogs.

Price, D. R.↗