Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “harmonic analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,027 records · Page 57

Gusev Meridiani will look different : radar scattering properties of the Mars Exploration Rover landing sites

Analysis of all existing radar data for the two Mars Exploration Rover (MER) landing sites at Meridiani Planum and Gusev Crater suggest that their meter-scale morphological appearance will be noticeably different than previous Mars landing sites; their "human-scale", decimeter- to meter-scal roughness is not the same as for previous Mars landing sites. We make this prediction based on the comparison of the MER landing sites.

Harmon, J. K.↗

A Study of Preliminary Design Methods for Low Noise Fans

Engineers need theory and computer codes to help them design quiet and efficient fans. A fast method to identify low-noise stator vane counts that might minimize tone noise for axial ducted fans has been developed. The analysis begins with a preliminary aerodynamic fan design. Duct acoustic and rotor-stator interaction theories are combined to predict the set of cut-on circumferential modes that are expected to be generated and propagate through the fan duct. By predicting the number of cut-on circumferential modes for each vane count, a set of low-noise vane counts for a given rotor and duct design can be identified. This method was used to design the stator set for NASA’s spacecraft cabin ventilation fan, in order to minimize tone noise generated by rotor-stator interaction at the first three blade passing frequency harmonics. This method was also applied to three other research fans that NASA uses for aeroacoustics research for comparison. This technique can be used to include acoustic design criteria early in the design of an axial fan and provide valuable information to guide the final design of quiet fans.

Fan↗

Analysis of simulated measurements of earth emitted radiation using geometric shape factors, and some results from analysis of ESSA 7 and Nimbus 6 data

In the reported study, simulated measurements of earth radiation with wide field-of-view (WFOV) radiometers are reduced to earth fluxes through geometric shape factors. Estimates of emitted flux for global and zonal scales and for regions smaller than the detector field-of-view are compared to fluxes derived directly from a model. Geometric shape factors are used to estimate global, zonal, and regional averages of earth-emitted flux from measurements with WFOV detectors on the ESSA 7 satellite and the Nimbus 6 satellite. Zonal and global averages of emitted flux for each of the 3-month periods of ESSA 7 data are shown in a graph. Another graph shows zonal and global averages of emitted flux for August 1975 obtained with the aid of Nimbus 6. The data are compared to values reported by Green and Smith (1977) who used a spherical harmonic solution.

Weaver, W. L.↗

Development of software to improve AC power quality on large spacecraft

To insure the reliability of a 20 kHz, alternating current (AC) power system on spacecraft, it is essential to analyze its behavior under many adverse operating conditions. Some of these conditions include overloads, short circuits, switching surges, and harmonic distortions. Harmonic distortions can become a serious problem. It can cause malfunctions in equipment that the power system is supplying, and, during distortions such as voltage resonance, it can cause equipment and insulation failures due to the extreme peak voltages. To address the harmonic distortion issue, work was begun under the 1990 NASA-ASEE Summer Faculty Fellowship Program. Software, originally developed by EPRI, called HARMFLO, a power flow program capable of analyzing harmonic conditions on three phase, balanced, 60 Hz AC power systems, was modified to analyze single phase, 20 kHz, AC power systems. Since almost all of the equipment used on spacecraft power systems is electrically different from equipment used on terrestrial power systems, it was also necessary to develop mathematical models for the equipment to be used on the spacecraft. The modelling was also started under the same fellowship work period. Details of the modifications and models completed during the 1990 NASA-ASEE Summer Faculty Fellowship Program can be found in a project report. As a continuation of the work to develop a complete package necessary for the full analysis of spacecraft AC power system behavior, deployment work has continued through NASA Grant NAG3-1254. This report details the work covered by the above mentioned grant.

Kraft, L. Alan↗

White Dwarf Pulsars

Work on NAG5-3288 ("White Dwarf Pulsars") has been fully integrated with the identically titled project NAG5-4734. The final report below is the same, since the data analysis and interpretative work are integrated, as are the resulting (previous and in-pipeline) publications. The proposal was designed to study pulse and orbital modulations in candidate DQ Herculis stars. Data on 5 stars were obtained. The best results were obtained on YY Draconis, which exhibited a strongly pulsed hard X-ray flux, and even suggested a transition between one-pole and two-pole emission during the course of the observation. This result is being readied for inclusion in a comprehensive study of YY Draconis. A strong pulsation appeared to be present also in H0857-242, but with a period of - 50 minutes, confusion with the first harmonic of the satellite's orbital frequency is possible. So that result is uncertain and is "on ice". A negative result was obtained on 4UO608-49 (V347 Pup), suggesting either that the X-ray identification is incorrect, or that the source is very transient. Finally, data was obtained on V1432 Aql and WZ Sge, respectively the slowest and fastest of these stars. Combined with the ASCA data, the high-energy data demonstrates the latter to contain a white dwarf rotating with P = 27.87 s (Patterson et al. 1998, PASP, 110, 403). Optical photometry contemporaneous with the X-ray data was obtained of V1432 Aql, in order to study the variations in the eclipse waveform. As anticipated, the width and centroid of the eclipse appeared to vary with the 50-day "supercycle".

Patterson, Joseph↗

A spectral filter for ESMR's sidelobe errors

Fourier analysis was used to remove periodic errors from a series of NIMBUS-5 electronically scanned microwave radiometer brightness temperatures. The observations were all taken from the midnight orbits over fixed sites in the Australian grasslands. The angular dependence of the data indicates calibration errors consisted of broad sidelobes and some miscalibration as a function of beam position. Even though an angular recalibration curve cannot be derived from the available data, the systematic errors can be removed with a spectral filter. The 7 day cycle in the drift of the orbit of NIMBUS-5, coupled to the look-angle biases, produces an error pattern with peaks in its power spectrum at the weekly harmonics. About plus or minus 4 K of error is removed by simply blocking the variations near two- and three-cycles-per-week.

Chesters, D.↗

Monitoring the Stable Pulsar PSR B1509-5B

The monitoring of this pulsar is still on-going, and hopefully will be for years to come. It has proved to be possible to fit the timing ephemeris for PSR B1509-59 for the entire monitoring period to date (five and a half years) with a single quintic polynomial. In order to establish its significance, we need at least one more year of monitoring data (for which we have proposed), but if this result is confirmed, it appears that two significant results may emerge: 1) well-determined values for the first and second braking indices; the first is well-established, but the second still needs a longer time base for a significant value 2) there seems to be a periodic variation in the pulse arrival times that can be fit with harmonic sinusoids with periods of approximately 790 and 395 days; if this result holds up on a longer time base it would be very exciting. Note that we are in position now to generate a timing ephemeris on the basis of the x-ray data that is more accurate than the radio ephemeris. In the meantime we have also determined a position for the pulsar that is more accurate than the ones derived from radio and Chandra observations. These results were reported at the 2000 HEAD meeting in Honolulu, HI. Travel was partly out of this grant. The remainder was applied toward the acquisition of a laptop computer that allows independent and fast analysis of all monitoring observations.

Rots, Arnold H.↗

An Analysis of the Flapwise Bending Frequencies and Mode Shapes of Rotor Blades Having Two Flapping Hinges to Reduce Vibration Levels

This paper presents the analysis of the flapwise natural bending frequencies and mode shapes of rotor blades with two flapping hinges located at arbitrary blade radii. The equations of motion are derived for a blade of variable mass and stiffness distribution. Solutions to the equations (natural frequencies and mode shapes) are presented for a typical blade of constant cross section having a wide range of hinge locations. The results show that the natural frequencies of the blades can be changed appreciably by varying the locations of the blade hinges, and that with two properly located flapping hinges, blade designs are possible which eliminate or greatly reduce conditions of resonance between the blade natural frequencies and the frequencies of the harmonic air loads. The results also show that ratios of natural frequency to rotor speed below a value of 6.0 are essentially constant for variations in rotor speed consistent with helicopter and VTOL applications.

Brooks, George W.↗

Empirical Tests of the Predicted Footprint for Uncontrolled Satellite Reentry Hazards

A number of statistical tools have been developed over the years for assessing the risk of reentering object to human populations. These tools make use of the characteristics (e.g., mass, material, shape, size) of debris that are predicted by aerothermal models to survive reentry. The statistical tools use this information to compute the probability that one or more of the surviving debris might hit a person on the ground and cause one or more casualties. The statistical portion of the analysis relies on a number of assumptions about how the debris footprint and the human population are distributed in latitude and longitude, and how to use that information to arrive at realistic risk numbers. Because this information is used in making policy and engineering decisions, it is important that these assumptions be tested using empirical data. This study uses the latest database of known uncontrolled reentry locations measured by the United States Department of Defense. The predicted ground footprint distributions of these objects are based on the theory that their orbits behave basically like simple Kepler orbits. However, there are a number of factors in the final stages of reentry - including the effects of gravitational harmonics, the effects of the Earth s equatorial bulge on the atmosphere, and the rotation of the Earth and atmosphere - that could cause them to diverge from simple Kepler orbit behavior and possibly change the probability of reentering over a given location. In this paper, the measured latitude and longitude distributions of these objects are directly compared with the predicted distributions, providing a fundamental empirical test of the model assumptions.

Matney, Mark↗

Statistical Issues for Uncontrolled Reentry Hazards Empirical Tests of the Predicted Footprint for Uncontrolled Satellite Reentry Hazards

A number of statistical tools have been developed over the years for assessing the risk of reentering objects to human populations. These tools make use of the characteristics (e.g., mass, material, shape, size) of debris that are predicted by aerothermal models to survive reentry. The statistical tools use this information to compute the probability that one or more of the surviving debris might hit a person on the ground and cause one or more casualties. The statistical portion of the analysis relies on a number of assumptions about how the debris footprint and the human population are distributed in latitude and longitude, and how to use that information to arrive at realistic risk numbers. Because this information is used in making policy and engineering decisions, it is important that these assumptions be tested using empirical data. This study uses the latest database of known uncontrolled reentry locations measured by the United States Department of Defense. The predicted ground footprint distributions of these objects are based on the theory that their orbits behave basically like simple Kepler orbits. However, there are a number of factors in the final stages of reentry - including the effects of gravitational harmonics, the effects of the Earth s equatorial bulge on the atmosphere, and the rotation of the Earth and atmosphere - that could cause them to diverge from simple Kepler orbit behavior and possibly change the probability of reentering over a given location. In this paper, the measured latitude and longitude distributions of these objects are directly compared with the predicted distributions, providing a fundamental empirical test of the model assumptions.

Matney, Mark↗

Test Methodology Development for Experimental Structural Assessment of ASC Planar Spring Material for Long-Term Durability

A vibration-based testing methodology has been developed that will assess fatigue behavior of the metallic material of construction for the Advanced Stirling Convertor displacer (planar) spring component. To minimize the testing duration, the test setup is designed for base-excitation of a multiplespecimen arrangement, driven in a high-frequency resonant mode; this allows completion of fatigue testing in an accelerated period. A high performance electro-dynamic exciter (shaker) is used to generate harmonic oscillation of cantilever beam specimens, which are clasped on the shaker armature with specially-designed clamp fixtures. The shaker operates in closed-loop control with dynamic specimen response feedback provided by a scanning laser vibrometer. A test coordinator function synchronizes the shaker controller and the laser vibrometer to complete the closed-loop scheme. The test coordinator also monitors structural health of the test specimens throughout the test period, recognizing any change in specimen dynamic behavior. As this may be due to fatigue crack initiation, the test coordinator terminates test progression and then acquires test data in an orderly manner. Design of the specimen and fixture geometry was completed by finite element analysis such that peak stress does not occur at the clamping fixture attachment points. Experimental stress evaluation was conducted to verify the specimen stress predictions. A successful application of the experimental methodology was demonstrated by validation tests with carbon steel specimens subjected to fully-reversed bending stress; high-cycle fatigue failures were induced in such specimens using higher-than-prototypical stresses

fatigue testing machines↗

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocity and attenuation of ultrasonic waves in two-phase media are determined for cases of distributed spheres and localized damage. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with spherical inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results or moduli, velocity and/or attenuation as functions of concentration of inclusion material, or porosity, are graphically displayed.

Fu, L. S.↗

Ultrasonic wave propagation in two-phase media - Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocity and attenuation of ultrasonic waves in two-phase media are determined for cases of distributed spheres and localized damage. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with spherical inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results or moduli, velocity and/or attenuation as functions of concentration of inclusion material, or porosity, are graphically displayed.

Fu, L. S.↗

Meta-Analysis of Electron Cyclotron Resonance Absorption Features Detected in High-Mass X-Ray Binaries

Using recent compilations of detailed X-ray observations and spectral models of exceptional quality, we record the electron cyclotron resonance absorption (ECRA) features that have been detected in 45 pulsating high-mass X-ray binaries (HMXBs) and ultraluminous X-ray (ULX) sources harboring neutron stars, although seven of these detections are still questionable and another 21 are single and/or not independently confirmed. From the comprehensive catalogs of Jaisawal & Naik and Staubert et al. and from several additional recent observations, we produce two lists of HMXB ECRA sources: a list of 17 sources in which multiple ECRA lines or single very low-energy lines are seen, in which we can reasonably assume that the lowest energy reveals the fundamental cyclotron level for each source; and a "contaminated" list of 38 sources including the 21 detections of single ECRA lines that may (not) be higher-level harmonics. Both lists confirm a previous result that we have obtained independently by modeling the propeller lines of Magellanic HMXB pulsars: the surface dipolar magnetic fields B * of HMXB neutron stars are segregated around five distinct values with B * = 0.28 ± 0.08, 0.55 ± 0.11, 1.3 ± 0.37, 3.0 ± 0.68 and 7.9 ± 3.1, in units of TG. However, an explanation of this phenomenon is currently lacking. We have found no correlation between these B * values and the corresponding observed spin periods, spin period derivatives, orbital periods, maximum X-ray luminosities, neutron star masses or companion star masses.

Christodoulou, Dimitris M.↗

A 200 GHz tripler using a single barrier varactor

The GaAs Schottky varactor diode is the nonlinear device most commonly used for submillimeter wave harmonic generation. Output power adequate to serve as a local oscillator source for SIS tunnel junctions has been demonstrated with whisker-contacted GaAs Schottky varactor multipliers in waveguide mounts up to about 800 GHz. In this paper, we present results for a tripler to 200 GHz using a new multiplier device, the single barrier varactor (SBV). This new varactor has potential advantages such as stronger nonlinearities or special symmetry, which make it attractive for submillimeter wave frequency multiplication. The performance of a tripler using a SBV over a output frequency range from 186 to 207 GHz has been measured in a crossed waveguide mount. The theoretical performance of the device has been calculated using large signal analysis. A comparison of theoretical and measured results and a discussion of various losses in the mount and the varactor have also been presented.

Choudhury, Debabani↗

A 200 GHz tripler using single barrier varactor

The GaAs Schottky varactor diode is the nonlinear device most commonly used for submillimeter wave harmonic generation. Output power adequate to serve as a local oscillator source for SIS tunnel junctions has been demonstrated with whisker-contacted GaAs Schottky varactor multipliers in waveguide mounts up to about 800 GHz. In this paper, we present results for a tripler to 200 GHz using a new multiplier device, the single barrier varactor (SBV). This new varactor has a potential advantages such as stronger nonlinearities or special symmetry, which make it attractive for submillimeter wave frequency multiplication. The performance of a tripler using a SBV over a output frequency range from 186 to 207 GHz has been measured in a crossed waveguide mount. The theoretical performance of the device has been calculated using large signal analysis. A comparison of theoretical and measured results and a discussion of various losses in the mount and the varactor have also been presented.

Choudhury, Debabani↗

Water Across Synthetic Aperture Radar Data (WASARD): SAR Water Body Classification for the Open Data Cube

The detection of inland water bodies from Synthetic Aperture Radar (SAR) data provides a great advantage over water detection with optical data, since SAR imaging is not impeded by cloud cover. Traditional methods of detecting water from SAR data involves using thresholding methods that can be labor intensive and imprecise. This paper describes Water Across Synthetic Aperture Radar Data (WASARD): a method of water detection from SAR data which automates and simplifies the thresholding process using machine learning on training data created from Geoscience Australia’s WOFS algorithm. Of the machine learning models tested, the Linear Support Vector Machine was determined to be optimal, with the option of training using solely the VH polarization or a combination of the VH and VV polarizations. WASARD was able to identify water in the target area with a correlation of 97% with WOFS. Sentinel-1, Open Data Cube, Earth Observations, Machine Learning, Water Detection 1. INTRODUCTION Water classification is an important function of Earth imaging satellites, as accurate remote classification of land and water can assist in land use analysis, flood prediction, climate change research, as well as a variety of agricultural applications [2]. The ability to identify bodies of water remotely via satellite is immensely cheaper than contracting surveys of the areas in question, meaning that an application that can accurately use satellite data towards this function can make valuable information available to nations which would not be able to afford it otherwise. Highly reliable applications for the remote detection of water currently exist for use with optical satellite data such as that provided by LANDSAT. One such application, Geoscience Australia’s Water Observations from Space (WOFS) has already been ported for use with the Open Data Cube [6]. However, water detection using optical data from Landsat is constrained by its relatively long revisit cycle of 16 days [5], and water detection using any optical data is constrained in that it lacks the ability to make accurate classifications through cloud cover [2]. The alternative solution which solves these problems is water detection using SAR data, which images the Earth using cloud-penetrating microwaves. Because of its advantages over optical data, much research has been done into water detection using SAR data. Traditionally, this has been done using the thresholding method, which involves picking a polarization band and labeling all pixels for which this band’s value is below a certain threshold as containing water. The thresholding method works since water tends to return a much lower backscatter value to the satellite than land [1]. However, this method can be flawed since estimating the proper threshold is often imprecise, complicated, and labor intensive for the end user. Thresholding also tends to use data from only one SAR polarization, when a combination of polarizations can provide insight into whether water is present. [2] In order to alleviate these problems, this paper presents an application for the Open Data Cube to detect water from SAR data using support vector machine (SVM) classification. 2. PLATFORM WASARD is an application for the Open Data Cube, a mechanism which provides a simple yet efficient means of ingesting, storing, and retrieving remote sensing data. Data can be ingested and made analysis ready according to whatever specifications the researcher chooses, and easily resampled to artificially alter a scene’s resolution. Currently WASARD supports water detection on scenes from ESA’s Sentinel-1 and JAXA’s ALOS. When testing WASARD, Sentinel-1 was most commonly used due to its relatively high spatial resolution and its rapid 6 day revisit cycle [5]. With minor alterations to the application's code, however, it could support data from other satellites. 3. METHODOLOGY Using supervised classification, WASARD compares SAR data to a dataset pre-classified by WOFS in order to train an SVM classifier. This classifier is then used to detect water in other SAR scenes outside the training set. Accuracy was measured according to the following metrics:  Precision: a measure of what percentage of the points WASARD labels as water are truly water  Recall: a measure of what percentage of the total water cover WASARD was able to identify.  F1 Score: a harmonic average of the precision and recall scores Both precision and recall are calculated at the end of the training phase, when the trained classifier is compared to a testing dataset. Because the WOFS algorithm’s classifications are used as the truth values when training a WASARD classifier, when precision and recall are mentioned in this paper, they are always with respect to the values produced by WOFS on a similar scene of Landsat data, which themselves have a classification accuracy of 97% [6]. Visual representations of water identified by WASARD in this paper were produced using the function wasard_plot(), which is included in WASARD. 3.1 Algorithm Selection The machine learning model used by WASARD is the Linear Support Vector Machine (SVM). This model uses a supervised learning algorithm to develop a classifier, meaning it creates a vector which can be multiplied by the vector formed by the relevant data bands to determine whether a pixel in a SAR scene contains water. This classifier is trained by comparing data points from selected bands in a SAR scene to their respective labels, which in this case are “water” or “not water” as given by the WOFS algorithm. The SVM was selected over the Random Forest model, which outperformed the SVM in training speed, but had a greater classification time and lower accuracy, and the Multilayer Perceptron Artificial Neural Network, which had a slightly higher average accuracy than the SVM, but much greater training and classification times. Figure 1: Visual representation of the SVM Classifier. Each white point represents a pixel in a SAR scene. In Figure 1, the diagonal line separating pixels determined to be water from those determined not to be water represents the actual classification vector produced by the SVM. It is worth noting that once the model has been trained, classification of pixels is done in a similar manner as in the thresholding method. This is especially true if only one band was used to train the model. 3.1 Feature Selection Sentinel-1 collects data from two bands: the Vertical/Vertical polarization (VV) and the Vertical/Horizontal polarization (VH). When 100 SVM classifiers were created for each polarization individually, and for the combination of the two, the following results were achieved: Figure 2: Accuracy of classifiers trained using different polarization bands. Precision and Recall were measured with respect to the values produced by WOFS. Figure 2 demonstrates that using both the VV and VH bands trades slightly lower recall for significantly greater precision when compared with the VH band alone, and that using the VV band alone is inferior in both metrics. WASARD therefore defaults to using both the VV and VH bands, and includes the option to use solely the VH band. The VV polarization’s lower precision compared to the VH polarization is in contrast to results from previous research and may merit further analysis [4]. 3.2 Training a Classifier The steps in training a classifier with WASARD are 1. Selecting two scenes (one SAR, one optical) with the same spatial extents, and acquired close to each other in time, with a preference that the scenes are taken on the same day. 2. Using the WOFS algorithm to produce an array of the detected water in the scene of optical data, to be used as the labels during supervised learning 3. Data points from the selected bands from the SAR acquisition are bundled together into an array with the corresponding labels gathered from WOFS. A random sample with an equal number of points labeled “Water” and “Not Water” is selected to be partitioned into a training and a testing dataset 4. Using Scikit-Learn’s LinearSVC object, the training dataset is used to produce a classifier, which is then tested against the testing dataset to determine its precision and recall The result is a wasard_classifier object, which has the following attributes: 1. f1, recall, and precision: 3 metrics used to determine the classifier’s accuracy 2. Coefficient: Vector which the SVM uses to make its predictions. The classifier detects water when the dot product of the coefficient and the vector formed by the SAR bands is positive 3. Save(): allows a user to save a classifier to the disk in order to use it without retraining 4. wasard_classify(): Classifies an entire xarray of SAR data using the SVM classifier All of the above steps are performed automatically when the user creates a wasard_classifier object. 3.3 Classifying a Dataset Once the classifier has been created, it can be used to detect water in an xarray of SAR data using wasard_classify(). By taking the dot product of the classifier’s coefficients and the vector formed by the selected bands of SAR data, an array of predictions is constructed. A classifier can effectively be used on the same spatial extents as the ones where it was trained, or on any area with a similar landscape. While

Kreiser, Zachary↗

Harmonized Landsat/Sentinel-2 Products for Land Monitoring

The Harmonized Landsat-8 and Sentinel-2 (HLS) project is a NASA initiative aiming to produce a seamless, harmonized surface reflectance record from the Operational Land Imager (OLI) and Multi-Spectral Instrument (MSI) aboard Landsat-8 and Sentinel-2 remote sensing satellites, respectively. The HLS products are based on a set of algorithms to obtain seamless products from both sensors (OLI and MSI): atmospheric correction, cloud and cloud-shadow masking, geographic co-registration and common gridding, bidirectional reflectance distribution function normalization and bandpass adjustment. As of version 1.3, the HLS v1.3 data set covers 9.12 million km2 and spans from first Landsat-8 data (2013) to present. HLS products provide near-daily surface reflectance information with a common geometric framework, and are suitable for a variety of agricultural and vegetation monitoring tasks, including analysis of crop type, condition, and phenology.

Masek, Jeffrey↗