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NASA NTRS1982

Estimating planetary terrain slopes from range measurements using a two dimensional spline smoothing technique

A new scanning scheme is presented for implementation for terrain slope estimation on a Martian exploratory rover. The rover will be equipped with a laser rangefinder as a principal sensing device for distance in its navigational equipment. A scan of the horizontal terrain from 5-50 m is indicated, and calculations are devised for quantifying the range errors. A constant incremental pointing angle is ruled out and a set of three pointing angles for different sub-areas of scan are defined. A two-dimensional smoothing algorithm is described for estimating slopes. The resultant scanning scheme involves the use of the characteristic curves derived from the relationships between the incremental elevation angle and the horizontal data spacing and the slope error index. A simulation was run and wavy terrain was produced from noise corrupted range measurements.

Kim, C. S.↗

NASA NTRS1985

Determining The Slope Error Of A Parabolic Reflector

Approximate slope error determined with minimal test equipment. Test Setup for Determining Slope Error for Point-Focusing Dish includes pinhole camera at center of curvature and color-coded target mounted around pinhole. Floodlights illuminate target to minimize exposure time. New procedure provides good approximation of reflector slope error and is excellent tool for comparative analysis of reflectors used as solar collectors for microwave receivers.

Christ, G. R.↗

NASA NTRS1983

Flight-test of the glide-slope track and flare-control laws for an automatic landing system for a powered-lift STOL airplane

An automatic landing system was developed for the Augmentor Wing Jet STOL Research Airplane to establish the feasibility and examine the operating characteristics of a powered-lift STOL transport flying a steep, microwave landing system (MLS) glide slope to automatically land on a STOL port. The flight test results address the longitudinal aspects of automatic powered lift STOL airplane operation including glide slope tracking on the backside of the power curve, flare, and touchdown. Three different autoland control laws were evaluated to demonstrate the tradeoff between control complexity and the resulting performance. The flight test and simulation methodology used in developing conventional jet transport systems was applied to the powered-lift STOL airplane. The results obtained suggest that an automatic landing system for a powered-lift STOL airplane operating into an MLS-equipped STOL port is feasible. However, the airplane must be provided with a means of rapidly regulation lift to satisfactorily provide the glide slope tracking and control of touchdown sink rate needed for automatic landings.

Watson, D. M.↗

NASA NTRS1984

A cockpit-display concept for executing a multiple glide-slope approach for wake-vortex avoidance

A piloted simulation study was undertaken to determine the feasibility of utilizing a forward-looking display to provide information that would enable aircraft to rredue their in-trail separation interval, and hence increase airport capacity, through the application of multiple glide-path approach techniques. The primary objective of this study was to determine whether information could be satisfactorily provided on a head-up display (HUD) format to permit the pilot to conduct a multiple glide-slope approach while maintaining a prespecified in-trail separation interval. The tests were conducted in a motion-base cockpit simulator configured as a current-generation transport aircraft and included dynamic effects of the vortices generated by the lead aircraft. The information provided on the HUD included typical aircraft guidance information and the current and past positions of the lead aircraft. Additionally, the displayed information provided self-separation cues that allowed the pilot to maintain separation on the lead aircraft. Performance data and pilot subjective ratings and comments were obtained during the tests. The results of this study indicate that multiple glide-slope approaches, procedurally designed for vortex avoidance, are possible while maintaining pilot work load and performance within operationally acceptable limits. In general, it would seem that multiple glide-slope approaches are possible even under reduced in-trail separation conditions if the pilot is provided with adequate situational information.

Abbott, T. S.↗

NASA NTRS1985

Location of noise sources using a phase-slope method

Two three-element microphone arrays have been used to predict the position of both pure-tone and broadband noise sources in an anechoic chamber under different ground impedance conditions. Source positions are predicted using the slope of phase-frequency plots between array elements. A phase-slope method for quantitatively assessing both the accuracy and precision of estimates of noise source location is introduced and illustrated. When the phase-slope method is used, there is higher accuracy and more precision in estimates of source location with a small ground impedance than with a large ground impedance. As would be expected, ground impedance effects are larger for low elevation angles than for high elevation angles.

Deloach, R.↗

NASA NTRS1986

The diverse soft X-ray slopes of QSOS

Einstein spectra are presented for 30 QSOs which indicate a large diversity in their soft X-ray slopes, unlike the uniform slopes found for AGN with higher X-ray energies. The slope is related to radio properties, X-ray luminosity, or possibly redshift, but these possibilities cannot be definitively distinguished.

Wilkes, Belinda↗

NASA NTRS1987

LogN-logS slope determination in imaging X-ray astronomy

The problem of estimating the slope of the number-counts relations for the specific case of imaging X-ray surveys is briefly discussed. Results have been obtained from extensive simulations of Einstein Observatory imaging X-ray data. It is concluded that the bias which affects the X-ray number-counts slope determination is much smaller than that which affects the radio number-counts slope.

Maccacaro, Tommaso↗

NASA NTRS1989

The dependence of the soft X ray spectral slope with radio property, luminosity, and redshift, for a large sample of AGN from the Einstein IPC data base

The dependence of the soft X-ray spectral slope on radio, optical and X-ray properties, and on redshift are reported for a large sample of Active Galactic Nuclei (AGN). The sample includes 317 optically and radio-selected AGN from a preliminary version of the Einstein Imaging Proportional Counter (IPC) quasar and AGN data base. The main results are: the difference in X-ray slope between radio-loud and radio-quiet AGN were confirmed for an independent and much larger sample of sources; a difference in X-ray slope between flat and steep radio spectrum AGN is observed only in high luminosity sub-sample; in flat radio spectrum AGNs there is an indication for a dependence of the X-ray spectral index on X-ray luminosity redshift and alpha sub 0x.

Brunner, H.↗

NASA NTRS1991

Asteroid absolute magnitudes and slope parameters

A new listing of absolute magnitudes (H) and slope parameters (G) has been created and published in the Minor Planet Circulars; this same listing will appear in the 1992 Ephemerides of Minor Planets. Unlike previous listings, the values of the current list were derived from fits of data at the V band. All observations were reduced in the same fashion using, where appropriate, a single basis default value of 0.15 for the slope parameter. Distances and phase angles were computed for each observation. The data for 113 asteroids was of sufficiently high quality to permit derivation of their H and G. These improved absolute magnitudes and slope parameters will be used to deduce the most reliable bias-corrected asteroid size-frequency distribution yet made.

Tedesco, Edward F.↗

NASA NTRS1993

Topographic slope from the SAR interferometric phase gradient

A new algorithm for the direct calculation of topographic slope maps from synthetic aperture radar (SAR) interferograms is presented. The algorithm derives slope maps without first requiring the creation of a digital elevational model (DEM) from the interferogram, thus obviating the need for high SNR in the interferogram and altitude calibration points for the scene. SAR data useful for interferometry has been collected by the Active Microwave Imager on board the ERS-1 satellite, when it was in a short period repeat orbit. Two passes of the radar sensor form a cross-track interferometric baseline. For a point target at some position (x,y,h), the interferometric phase difference phi is proportional to the difference in path lengths for the two sensor positions to the scatterer. Given the phase difference as measured in the complex interferogram and an accurate baseline geometry, the position of the scatterer, most significantly the height h, can be determined through triangulation. The interferometric phase measurement however is known only modulo 2-pi, and hence it is necessary to determine the correct multiple of 2-pi to add to the phase at each point to obtain an estimate of the actual phase with respect to an absolute datum. This phase unwrapping process is required for creating DEM's, and is difficult or impossible for regions of low SNR or SAR image layover. The new algorithm described here derives slope maps without requiring phase unwrapping.

Werner, Charles L.↗

NASA NTRS1995

Note on use of slope diffraction coefficients for aperture antennas on finite ground planes

The use of slope diffraction coefficients along with regular diffraction coefficients for calculating the radiation patterns of aperture antennas in a finite ground plane is investigated. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The expressions for the incident magnetic field in terms of the magnetic current in the aperture are given. The slope of the incident magnetic field is calculated and closed form expressions are presented.

Cockrell, C. R.↗

NASA NTRS2001

Diurnal and Seasonal Cold Lands Signatures in SSM/I-scale Microwave Radiometry of the North Slope of Alaska

In this paper, we explore scaling and data assimilation-related issues associated with utilizing passive microwave satellite observations of Cold Lands-in this case, the climatologically and ecologically sensitive arctic tundra. Our approach expands on our earlier work using a one-year dataset from the Radiobrightness Energy Balance Experiment-3 (REBEX-3). REBEX-3 featured a tower-based SSM/I (Special Sensor Microwave/Imager) simulator deployed on the North Slope of Alaska in 1994-95. Two findings are significant here. First, a comparison of tower and satellite signatures at 19 and 37 GHz strongly suggested that the North Slope is radiometrically homogeneous for spatial scales up to SSM/I footprints (approximately 25 km), an unusual and valuable characteristic for monitoring and retrieving land surface conditions. And second, at the plot scale, signatures of snow/no-snow and freeze/thaw transitions were identifiable for tussock tundra land cover, so that even snow-free frozen tundra could be unambiguously distinguished from tundra covered with dry snow, another unusual and valuable characteristic. We present results from analyzing satellite brightness signatures of selected North Slope pixels corresponding to instrumented sites along a transect from the Brooks Range to the Arctic Ocean. A custom EASE (Equal Area Scalable Earth)-Grid processor was used to extract SSMJI data for every orbit with observations of this region during the 1994-95 year. The resulting high temporal-resolution (4-8 points/day), gridded data were then analyzed for evidence of the same diurnal and seasonal signatures seen at the plot scale (through micrometeorological and/or brightness data). Differences between satellite and tower brightness observations are quantified for various conditions at the REBEX-3 site. Such differences from the less-frequent and/or larger-scale satellite observations represent a form of input 'noise' in data assimilation applications. For the other sites, the performance of snow/no-snow and freeze/thaw discriminators vs. ground truth represents an opportunity to gauge the homogeneity of other pixels.

Kim, Edward J.↗

NASA NTRS2004

ICESat Observations of Inland Surface Water Stage, Slope, and Extent: a New Method for Hydrologic Monitoring

River discharge and changes in lake, reservoir and wetland water storage are critical terms in the global surface water balance, yet they are poorly observed globally and the prospects for adequate observations from in-situ networks are poor (Alsdorf et al., 2003). The NASA-sponsored Surface Water Working Group has established a framework for advancing satellite observations of river discharge and water storage changes which focuses on obtaining measurements of water surface height (stage), slope, and extent. Satellite laser altimetry, which can achieve centimeter-level elevation precision for single, small laser footprints, provides a method to obtain these inland water parameters and contribute to global water balance monitoring. Since its launch in January, 2003 the Ice, Cloud, and land Elevation Satellite (ICESat), a NASA Earth Observing System mission, has achieved over 540 million laser pulse observations of ice sheet, ocean surface, land topography, and inland water elevations and cloud and aerosol height distributions. By recording the laser backscatter from 80 m diameter footprints spaced 175 m along track, ICESat acquires globally-distributed elevation profiles, using a 1064 nm laser altimeter channel, and cloud and aerosol profiles, using a 532 nm atmospheric lidar channel. The ICESat mission has demonstrated the following laser altimeter capabilities relevant to observations of inland water: (1) elevation measurements with a precision of 2 to 3 cm for flat surfaces, suitable for detecting river surface slopes along long river reaches or between multiple crossings of a meandering river channel, (2) from the laser backscatter waveform, detection of water surface elevations beneath vegetation canopies, suitable for measuring water stage in flooded forests, (3) single pulse absolute elevation accuracy of about 50 cm (1 sigma) for 1 degree sloped surfaces, with calibration work in progress indicating that a final accuracy of about 12 cm (1 sigma) will be achieved for clear atmosphere conditions, suitable for detection of stage changes through time, (4) ability to precisely point the spacecraft so as to position the laser profile on the Earth the surface with a cross-track accuracy of 50 m (1 sigma), enabling small water bodies and specific locations to be targeted and re-observed through time, (5) adequate signal levels from specular water surfaces up to 5 degrees off-nadir, enabling complete global access to any location on the Earth's surface from the ICESat repeat orbit by off-nadir pointing, and (6) day and night operation with successful laser ranging to the Earth's surface through thin to moderate cloud cover, enabling more frequent measurements than can be achieved by passive optical sensors. Here we illustrate these capabilities by showing ICESat observations through time for selected river and lake locations.

Harding, David J.↗

NASA NTRS2010

Slopes To Prevent Trapping of Bubbles in Microfluidic Channels

The idea of designing a microfluidic channel to slope upward along the direction of flow of the liquid in the channel has been conceived to help prevent trapping of gas bubbles in the channel. In the original application that gave rise to this idea, the microfluidic channels are parts of micro-capillary electrophoresis (microCE) devices undergoing development for use on Mars in detecting compounds indicative of life. It is necessary to prevent trapping of gas bubbles in these devices because uninterrupted liquid pathways are essential for sustaining the electrical conduction and flows that are essential for CE. The idea is also applicable to microfluidic devices that may be developed for similar terrestrial microCE biotechnological applications or other terrestrial applications in which trapping of bubbles in microfluidic channels cannot be tolerated. A typical microCE device in the original application includes, among other things, multiple layers of borosilicate float glass wafers. Microfluidic channels are formed in the wafers, typically by use of wet chemical etching. The figure presents a simplified cross section of part of such a device in which the CE channel is formed in the lowermost wafer (denoted the channel wafer) and, according to the present innovation, slopes upward into a via hole in another wafer (denoted the manifold wafer) lying immediately above the channel wafer. Another feature of the present innovation is that the via hole in the manifold wafer is made to taper to a wider opening at the top to further reduce the tendency to trap bubbles. At the time of reporting the information for this article, an effort to identify an optimum technique for forming the slope and the taper was in progress. Of the techniques considered thus far, the one considered to be most promising is precision milling by use of femtosecond laser pulses. Other similar techniques that may work equally well are precision milling using a focused ion beam, or a small diamond-tipped drill bit.

Greer, Harold E.↗

NASA NTRS2013

Mixed Linear/Square-Root Encoded Single-Slope Ramp Provides Low-Noise ADC with High Linearity for Focal Plane Arrays

Single-slope analog-to-digital converters (ADCs) are particularly useful for onchip digitization in focal plane arrays (FPAs) because of their inherent monotonicity, relative simplicity, and efficiency for column-parallel applications, but they are comparatively slow. Squareroot encoding can allow the number of code values to be reduced without loss of signal-to-noise ratio (SNR) by keeping the quantization noise just below the signal shot noise. This encoding can be implemented directly by using a quadratic ramp. The reduction in the number of code values can substantially increase the quantization speed. However, in an FPA, the fixed pattern noise (FPN) limits the use of small quantization steps at low signal levels. If the zero-point is adjusted so that the lowest column is onscale, the other columns, including those at the center of the distribution, will be pushed up the ramp where the quantization noise is higher. Additionally, the finite frequency response of the ramp buffer amplifier and the comparator distort the shape of the ramp, so that the effective ramp value at the time the comparator trips differs from the intended value, resulting in errors. Allowing increased settling time decreases the quantization speed, while increasing the bandwidth increases the noise. The FPN problem is solved by breaking the ramp into two portions, with some fraction of the available code values allocated to a linear ramp and the remainder to a quadratic ramp. To avoid large transients, both the value and the slope of the linear and quadratic portions should be equal where they join. The span of the linear portion must cover the minimum offset, but not necessarily the maximum, since the fraction of the pixels above the upper limit will still be correctly quantized, albeit with increased quantization noise. The required linear span, maximum signal and ratio of quantization noise to shot noise at high signal, along with the continuity requirement, determines the number of code values that must be allocated to each portion. The distortion problem is solved by using a lookup table to convert captured code values back to signal levels. The values in this table will be similar to the intended ramp value, but with a correction for the finite bandwidth effects. Continuous-time comparators are used, and their bandwidth is set below the step rate, which smoothes the ramp and reduces the noise. No settling time is needed, as would be the case for clocked comparators, but the low bandwidth enhances the distortion of the non-linear portion. This is corrected by use of a return lookup table, which differs from the one used to generate the ramp. The return lookup table is obtained by calibrating against a stepped precision DC reference. This results in a residual non-linearity well below the quantization noise. This method can also compensate for differential non-linearity (DNL) in the DAC used to generate the ramp. The use of a ramp with a combination of linear and quadratic portions for a single-slope ADC is novel. The number of steps is minimized by keeping the step size just below the photon shot noise. This in turn maximizes the speed of the conversion. High resolution is maintained by keeping small quantization steps at low signals, and noise is minimized by allowing the lowest analog bandwidth, all without increasing the quantization noise. A calibrated return lookup table allows the system to maintain excellent linearity.

Wrigley, Chris J.↗

NASA NTRS2020

Design and Testing of an Ultra-Light Weight Perching System for Sloped or Vertical Rough Surfaces on Mars

In this paper, we present the design, characterization, and functional demonstration of a perching system that enables a flying vehicle to land on rough sloped or vertical surfaces. Steep slopes are of particular scientific interest since they are often associated with geologically interesting features including sites of active modification (e.g. landslides/avalanches, slope streaks), exposed bedrock and/or ice, and as-yet unmodified young features (e.g. walls of fresh craters or polar pits that are actively expanding). However the steep nature of these sites makes access with traditional field robots difficult: ground vehicles are unable to traverse the steep terrain and aerial vehicles are limited by their flight time and an ability to operate near terrain. We propose to address these limitation by enabling the UAV to reliably perch on steep terrain to perform in situ measurements and collect samples. Perching also enables a solar powered UAV to traverse large terrain features such as the Valles Marineris that could not be covered in a single flight by repeatedly perching and recharging its batteries. The proposed perching system that is being developed consists of a microspine gripper, a compliant gripper to vehicle interface, and a flying vehicle equipped with an autonomy sensor suite. The system also includes perception and control algorithms that identify perching targets and execute the required perching maneuver. To date, the majority of the effort has focused on developing and characterizing the microspine gripper. The initial prototype weighs 100 g, is capable of securely grasping a range of natural surfaces, and successful grasps support loads of over 10 N. Refinement of the gripper, integrating and testing it on a UAV, measuring aerodynamic distrubances from wall effects, and developing the required perception and control algorithms is ongoing. This paper describes the overall architecture of our proposed system, the design of the gripper, and its performance during initial testing.

Backus, Spencer↗

NASA NTRS2024

An Interesting Correlation Between the Peak Slope and Peak Value of a Sunspot Cycle

The maximum slope of the sunspot number during the rising phase of a sunspot cycle has an excellent correlation with the maximum value of the sunspot number during that cycle. This is demonstrated using a Savitzky–Golay filter to both smooth and calculate the derivative of the sunspot-number data. Version 2 of the International Sunspot Number (S) is used to represent solar activity. The maximum of the slope during the rising phase of each cycle was correlated against the peaks of solar activity. Using three different correlation fits, the average predicted amplitude for Solar Cycle 25 is 130.7 ± 0.5, among the best correlations in solar predictions. A possible explanation for this correlation is given by the similar behavior of a shape function representing the time variation of the sunspot number. This universal function also provides the timing of the solar maximum by the time from the slope maximum to the peak in the function as late 2023 or early 2024. A Hilbert transform gives similar results, which are caused by the dominance of the 11-yr sunspot-cycle period in a Fourier fit of the sunspot number.

W. Dean Pesnell↗

DOE OSTI2025

Modeling gas, hydrates, and slope stability on the U.S. Atlantic margin during Pleistocene glacial cycles

Changes in temperature and sea level can cause dissociation of methane hydrates in shallow marine sediments, leading to seafloor destabilization. Along the U.S. Atlantic margin, there exists a well-documented history of slope failure and numerous recorded occurrences of gas seeps. Several studies have linked slope failure in the region to gas seepage and hydrate dissociation driven by glacial-interglacial transitions, but this linkage has not been quantitatively demonstrated. Along the shelf edge, in an area where shallow methane gas seeps have been identified, we modeled methane gas and hydrate formation using a one-dimensional fluid flow model. Methane gas formation was modeled over the last 120,000 years to simulate a glacial-interglacial cycle. Here, we ran this model at 16,044 individual locations in the region between 29° N – 45° N and 82° W – 66° W at a resolution of 1 x 1 arcminutes, focusing specifically on water depths between 200 and 1000 m that bracket the seafloor outcrop of the base of the hydrate stability zone. Using historic temperature and pressure records from the last 120,000 years, sediment properties in the area, and factor of safety calculations, we found that hydrate dissociation alone is unlikely to cause sediment failure in the region, implying that an additional driving force would be necessary for failure to occur.

Hydrate dissociation↗