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NASA NTRS1986

Virtual space and 2-dimensional effects in perspective displays

When interpreting three dimensional spatial relationships presented on a two dimensional display surface, the viewer is required to mentally reconstruct the original information. This reconstruction is influenced by both the perspective geometry of the displayed image and the viewer's eye position relative to the display. In a study which manipulated these variables, subjects judged the azimuth direction of a target object relative to a reference object fixed in the center of a perspective display. The results support a previously developed model which predicted that the azimuth judgement error would be a sinusoidal function of stimulus azimuth. The amplitude of this function was correctly predicted to be systematically modulated by both the perspective geometry of the image and the viewer's eye position relative to the screen. Interaction of the two components of the model, the virtual space effect and the 3D-to-2D projection effect, predicted the relative amplitudes of the sinusoidal azimuth error functions for the various conditions of the experiment. Mean azimuth judgements in some directions differed by as much as 25 degrees as a result of different combinations of eye position and image geometry. The results illustrate the need to consider the effects of perspective geometry when designing spatial information instruments, and show the model to be a reliable predictor of average performance.

Mcgreevy, M. W.↗

NASA NTRS1992

Seawifs Technical Report Series. Volume 2: Analysis of Orbit Selection for Seawifs: Ascending Versus Descending Node

Due to range safety considerations, the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) ocean color instrument may be required to be launched into a near-noon descending node, as opposed to the ascending node used by the predecessor sensor, the Coastal Zone Color Scanner (CZCS). The relative importance of ascending versus descending near-noon orbits was assessed here to determine if descending node will meet the scientific requirements of SeaWiFS. Analyses focused on ground coverage, local times of coverage, solar and viewing geometries (zenith and azimuth angles), and sun glint. Differences were found in the areas covered by individual orbits, but were not important when taken over a 16 day repeat time. Local time of coverage was also different: for ascending node orbits the Northern Hemisphere was observed in the morning and the Southern Hemisphere in the afternoon, while for descending node orbits the Northern Hemisphere was observed in the afternoon and the Southern in the morning. There were substantial differences in solar azimuth and spacecraft azimuth angles both at equinox and at the Northern Hemisphere summer solstice. Negligible differences in solar and spacecraft zenith angles, relative azimuth angles, and sun glint were obtained at the equinox. However, large differences were found in solar zenith angles, relative azimuths, and sun glint for the solstice. These differences appeared to compensate across the scan, however, an increase in sun glint in descending node over that in ascending node on the western part of the scan was compensated by a decrease on the eastern part of the scan. Thus, no advantage or disadvantage could be conferred upon either ascending node or descending node for noon orbits. Analyses were also performed for ascending and descending node orbits that deviated from a noon equator crossing time. For ascending node, afternoon orbits produced the lowest mean solar zenith angles in the Northern Hemisphere, and morning orbits produced the lowest angles for the Southern Hemisphere. For descending node, morning orbits produced the lowest mean solar zenith angles for the Northern Hemisphere; afternoon orbits produced the lowest angles for the Southern Hemisphere.

Hooker, Stanford B.↗

NASA NTRS1992

High resolution observations of the magnetic and velocity field of simple sunspots

We have observed the disk passage of relatively simple round sunspots using a narrowband filter and a large format CCD detector and have created magnetograms, Dopplergrams, and continuum images nearly simultaneously. In addition the spectral resolution of the filter allows the construction of 'spectra' for all points in the field of view. The mean inclination of the magnetic field increases from 45-50 deg to 70-75 deg across the penumbra and there is a fluctuation of the inclination angle about the mean of about 4 +/- 18 deg. The variation in inclination is large enough that substantial amounts of magnetic field are parallel to the solar surface from the mid to outer penumbra. The Evershed flow tends to occur in the regions where the magnetic field is horizontal. This suggests that the Evershed flow is confined to the regions of horizontal fields. We show that a simple sunspot model with azimuthal variations in inclination but no azimuthal variations of field strength is free from azimuthal Lorentz forces. The meridional component of the currents which arise from the azimuthal variation in inclination are parallel to the field lines. This suggests that a cylindrically symmetric magnetostatic sunspot model can be perturbed into one with azimuthal variations in inclination with some adjustment in the meridional force balance.

Title, Alan M.↗

NASA NTRS1999

Development of a Three-Dimensional PSE Code for Compressible Flows: Stability of Three-Dimensional Compressible Boundary Layers

A program is developed to investigate the linear stability of three-dimensional compressible boundary layer flows over bodies of revolutions. The problem is formulated as a two dimensional (2D) eigenvalue problem incorporating the meanflow variations in the normal and azimuthal directions. Normal mode solutions are sought in the whole plane rather than in a line normal to the wall as is done in the classical one dimensional (1D) stability theory. The stability characteristics of a supersonic boundary layer over a sharp cone with 50 half-angle at 2 degrees angle of attack is investigated. The 1D eigenvalue computations showed that the most amplified disturbances occur around x(sub 2) = 90 degrees and the azimuthal mode number for the most amplified disturbances range between m = -30 to -40. The frequencies of the most amplified waves are smaller in the middle region where the crossflow dominates the instability than the most amplified frequencies near the windward and leeward planes. The 2D eigenvalue computations showed that due to the variations in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the most amplified disturbances are shifted to 120 degrees compared to 90 degrees for the parallel theory. It is also observed that the nonparallel amplification rates are smaller than that is obtained from the parallel theory.

Balakumar, P.↗

NASA NTRS2011

Improved Systematic Pointing Error Model for the DSN Antennas

New pointing models have been developed for large reflector antennas whose construction is founded on elevation over azimuth mount. At JPL, the new models were applied to the Deep Space Network (DSN) 34-meter antenna s subnet for corrections of their systematic pointing errors; it achieved significant improvement in performance at Ka-band (32-GHz) and X-band (8.4-GHz). The new models provide pointing improvements relative to the traditional models by a factor of two to three, which translate to approximately 3-dB performance improvement at Ka-band. For radio science experiments where blind pointing performance is critical, the new innovation provides a new enabling technology. The model extends the traditional physical models with higher-order mathematical terms, thereby increasing the resolution of the model for a better fit to the underlying systematic imperfections that are the cause of antenna pointing errors. The philosophy of the traditional model was that all mathematical terms in the model must be traced to a physical phenomenon causing antenna pointing errors. The traditional physical terms are: antenna axis tilts, gravitational flexure, azimuth collimation, azimuth encoder fixed offset, azimuth and elevation skew, elevation encoder fixed offset, residual refraction, azimuth encoder scale error, and antenna pointing de-rotation terms for beam waveguide (BWG) antennas. Besides the addition of spherical harmonics terms, the new models differ from the traditional ones in that the coefficients for the cross-elevation and elevation corrections are completely independent and may be different, while in the traditional model, some of the terms are identical. In addition, the new software allows for all-sky or mission-specific model development, and can utilize the previously used model as an a priori estimate for the development of the updated models.

Rochblatt, David J.↗

NASA NTRS2011

Diagonal-Axes Stage for Pointing an Optical Communications Transceiver

Traditional azimuth-elevation ("az-el") stages are used to point a variety of devices ranging from large optical telescopes to tank guns. Such a stage typically has an elevation stage having a horizontal axis mounted on an azimuth stage with a vertical axis. Both stages are often motorized. Optical communications transceivers often require two-axis motorized control, as when the communications link is between a ground station and an aircraft or satellite. In such applications, the traditional azimuth-elevation stage has two important drawbacks: a gimbal lock exclusion zone at zenith and susceptibility to pointing errors caused by backlash. Az-el stages in which the azimuth stage cannot rotate a full 360deg have the additional drawback of an azimuth exclusion zone. The diagonal-axes stage described here mitigates or eliminates all of these problems. Instead of one vertical axis and one horizontal axis, a diagonal-axes stage has two horizontal axes, both oriented at 45 to the trajectory of the target. For example, a ground station located on the equator tracking a satellite with an equatorial orbit would have one axis parallel to northeast and southwest, and the other axis parallel to northwest and southeast. The diagonal-axes stage is considerably less vulnerable to backlash. If it is correctly oriented, its axes rotate in only one direction during an overhead pass by a satellite. As a result, the effects of backlash may be inherently eliminated. If the gravity-induced torque on either axis changes during the pass, then backlash may become important during the part of the pass where the gravity torque, instead of opposing the motion of the stage, pushes the stage in the direction of motion. This can result in the loss of gear-to-gear contact in one or more stages of the gear reduction mechanism. In this case, a preload spring used to eliminate backlash need only be sufficiently strong to overcome the gravity torque, i.e. it need not overcome friction in the gear train. The diagonal-axes stage is not backlash-free for arbitrary target trajectories such as an aircraft might execute. If properly oriented for any particular satellite, however, it is backlash-free for all passes of that satellite, which will trace out parallel paths on the sky, and for all passes of any other satellite that are perpendicular to the first. It will also be backlash-free for some fraction of other satellite trajectories.

Regehr, Martin W.↗

NASA NTRS2014

A Design of Experiments Investigation of Offset Streams for Supersonic Jet Noise Reduction

An experimental investigation into the noise characteristics of a dual-stream jet with four airfoils inserted in the fan nozzle was conducted. The intent of the airfoils was to deflect the fan stream relative to the core stream and, therefore, impact the development of the secondary potential core and noise radiated in the peak jet-noise direction. The experiments used a full-factorial Design of Experiments (DoE) approach to identify parameters and parameter interactions impacting noise radiation at two azimuthal microphone array locations, one of which represented a sideline viewing angle. The parameters studied included airfoil angle-of-attack, airfoil azimuthal location within the fan nozzle, and airfoil axial location relative to the fan-nozzle trailing edge. Jet conditions included subsonic and supersonic fan-stream Mach numbers. Heated jets conditions were simulated with a mixture of helium and air to replicate the exhaust velocity and density of the hot jets. The introduction of the airfoils was shown to impact noise radiated at polar angles in peak-jet noise direction and to have no impact on noise radiated at small and broadside polar angles and to have no impact on broadband-shock-associated noise. The DoE analysis showed the main effects impacting noise radiation at sideline-azimuthal-viewing angles included airfoil azimuthal angle for the airfoils on the lower side of the jet near the sideline array and airfoil trailing edge distance (with airfoils located at the nozzle trailing edge produced the lowest sound pressure levels). For an array located directly beneath the jet (and on the side of the jet from which the fan stream was deflected), the main effects impacting noise radiation included airfoil angle-of-attack and airfoil azimuthal angle for the airfoils located on the observation side of the jet as well and trailing edge distance. Interaction terms between multiple configuration parameters were shown to have significant impact on the radiated noise. The models were shown to adequately describe the sound-pressure levels obtained for a configuration in the center of the design space indicating the models can be used to navigate the design space.

Jet Noise↗

NASA NTRS2022

Nonlinear Evolution of Instabilities in a Laminar Separation Bubble at a Hypersonic Mach Number

The development of both convective stationary perturbation as well as global instabilities in the vicinity of a laminar separation bubble above an axisymmetric compression corner in a hypersonic flow is investigated using numerical simulations. The flow configuration of primary interest corresponds to the cone-cylinder-flare model used in experimental measurements in the Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue University. For a flare angle of 10 degrees and a unit Reynolds number of 11.5 x 10 6 m -1 , their surface flow visualizations identified the presence of streamwise elongated thermal streaks near the reattachment position and the dominant azimuthal spacing between the streaks was determined to be approximately 10 degrees (i.e., an azimuthal mode number of 36). Previous linear stability analyses predicted that the amplification characteristics of small amplitude, unsteady, convective instabilities within this flow were consistent with the surface pressure fluctuations measured in the experiment. However, their accompanying analysis of global instabilities had found the separation bubble to be weakly unstable at the 10 degrees flare angle, with the most unstable global mode corresponding to a stationary disturbance with an azimuthal wavenumber of m ≈ 5, which was well below the measured wavenumber of m = 36. Besides confirming the presence of the global instability at these flow conditions, the present numerical simulations quantify the details of the stationary equilibrium state associated with the supercritical bifurcation resulting from the nonlinear saturation of the unstable global mode. Although velocity perturbations associated with the saturated global mode are dominated by the fundamental spanwise wavelength associated with the linear global instability, the surface heat flux downstream of reattachment is dominated by m = 36 in agreement with experimental measurements. However, the shorter wavelength peak ( m = 36) in the azimuthal spectrum is not manifested as streaks with an azimuthal spacing of 10 degrees. An additional simulation of the combined evolution of both unsteady convective and global instabilities indicates that the nonlinear interactions between a broadband spectrum of oblique Mack’s first mode instabilities generate stationary vortex modes with a higher dominant wavenumber ( m = 60) as that observed in the experiments. Additional analyses are performed to predict the global mode behavior at other flare angles and how it differs from the convective centrifugal instability due to concave streamline curvature over the compression corner.

Hypersonic flow↗

NASA NTRS2022

Nonlinear Evolution of Instability in a Laminar Separation Bubble at Hypersonic Mach Number

High speed flow↗

DOE OSTI2020

Sub-Degree-Per-Hour MEMS Gyroscope for Measurement While Drilling at 300°C

The orientation module of MWD tool offers the critical drill bit orientation information, including azimuth, inclination and toolface in order to control the path of wellbore. Although high end navigation grade gyroscope can meet the accuracy requirement for azimuth finding, the requirements of cost, size and reliability under harsh environment have largely limited the deployment of gyroscopes in MWD tools. To overcome these constraints, GE Research has developed a low cost, MEMS based Multi-Ring Gyroscope (MRG) capable of azimuth-seeking in MWD applications at 300°C. The MRG prototype has been demonstrated to achieve angular random walk (ARW) better than 0.003 deg/rt(hr) and bias instability of 0.01 deg/hr, capable of meeting azimuth finding accuracy better than 0.25 deg. It has further been tested to remain fully operational at 300 °C.

15 GEOTHERMAL ENERGY↗

DOE OSTI2022

Performance of a MQXF Nb 3 Sn Quadrupole Magnet Under Different Stress Level

In a dipole or in a quadrupole accelerator magnet, the displacement of the coil turns induced by the electromagnetic forces can cause quenches limiting the magnet performance. For this reason, an azimuthal preload is applied to avoid azimuthal movements of the coil up to the required operational current. However, several tests showed that accelerator magnets can operate with a partial preload, i.e. that coil unloading during the ramp does not prevent reaching higher currents. This issue is particularly relevant for Nb 3 Sn magnets, where the loads applied to the Nb3Sn filaments can reach the degradation limits of critical current. In order to investigate the impact of coil preload on the quench performance, the MQXFS6 short model quadrupole for the High Luminosity Upgrade was tested under an azimuthal preload at 80% of the short sample current, reaching 93% of short sample current at 1.9 K. The preload was then released to 60%, still showing ability to operate in the range of 80-85% of short sample current as required by HL-LHC project. With this lower preload, the ability of going above 90% of short sample was lost, and a significant training appeared above 85%. When the preload was restored to the original 80% value, the magnet reached with few quenches 95% of short sample (13.4 T peak field). Magnetic measurements confirm the larger movement of the coil in the case with lower preload, and agree with finite element simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Relocating microseismicity from downhole monitoring of the Decatur CCS site using a modified double-difference algorithm

SUMMARY The injection of CO2 at the Decatur carbon capture and storage site has generated significant microseismic activity, which occurs in distinct spatial clusters up to approximately 2.2 km from the primary injection well. Accurate and precise event locations are vital for the characterization of the microseismicity to help understand the reservoir response to the CO2 injection, whilst enabling the identification of minor faults and fractures below the resolution of conventional active seismic imaging. However, microseismic monitoring of fluid injection sites, such as Decatur, is often performed using a network of borehole sensors often from a single well. While these downhole sensors have excellent detection capabilities, their poor azimuthal coverage limits the ability to precisely determine event locations. We have developed a modified double-difference relocation algorithm suitable for both 1-D and 3-D velocity models, and which incorporates differential back azimuth observations to allow the benefits of the original double-difference algorithm to be applicable to a downhole microseismic monitoring setting. Applying the modified double-difference algorithm to the microseismicity at Decatur, we have successfully relocated 4293 events. The relocation included over 59 million observations for 757 285 event pairs, split across seven geographic regions. Despite the majority of observations being recorded in only two boreholes, with an almost identical azimuthal coverage, the results have shown to be reliable with significantly reduced residuals and low uncertainties associated with the final locations. We have analysed the residuals in terms of their association with each geographic region, data type, station and individual events, to fully appreciate their influence in the inversion and the fit of the data to the final set of event locations. For each region, the relocated seismicity has become less diffuse with improved clustering, and with newly visible linear features often orientated in a NE–SW direction. These results show the potential improvements that can be made to microseismic event locations recorded by a borehole network with a limited and variable azimuthal distribution.

58 GEOSCIENCES↗

DOE OSTI2023

A Novel Design for Improving the Control on the Stainless-Steel Vessel Welding Process for Superconducting Magnets

Stainless steel vessels see widespread use in superconducting magnets for particle accelerator applications. Their function varies in different magnet designs: they always provide the necessary liquid helium containment, but in some cases are also used to provide azimuthal prestress and can also be welded to the magnet end plate to provide additional longitudinal stiffness. A magnet designed with the bladder and key technology does not rely on the structural role of the vessel. They are structurally supported using azimuthally prestressed aluminum shells, and the longitudinal constraint by rods. In this case, the magnet designer would generally like to minimize the interaction between the magnet and the stainless-steel vessel and to minimize the coil stress variation due to the vessel. The stress state in the vessel and in the coil is a function of the circumferential interference, defined as the vessel azimuthal length minus the magnet circumference. The vessel and the magnet azimuthal length machining tolerances are relatively large resulting in significant stress variations in the superconducting coils. Here in this paper we introduce an interference-control shim, which can significantly limit the stress variation of the coils for a given variation of the interference. The effectiveness of the interference-control shim is evaluated numerically on the MQXF, the low-β quadrupole for the High Luminosity LHC.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Determining fast-S and slow-S propagation directions with SV-P data produced by buried explosives and recorded with vertical geophones

We have evaluated the concept of practicing S-wave reflection seismology with legacy 3D seismic data generated by a P-wave source and recorded with only vertical geophones. This type of S-wave imaging is based on the principle that seismic P-wave sources not only produce a downgoing illuminating P wavefield, but they also simultaneously produce a downgoing illuminating SV wavefield that, in almost all cases, is suitable for S-wave reflection imaging. The S-mode used in this study is the SV-P, or converted-P, mode. This mode involves a downgoing illuminating SV wavefield and an upgoing reflected P-mode that is recorded by vertical geophones. In flat-layered stratigraphy, the lengths of the SV and P raypaths in SV-P imaging are identical to the lengths of the SV and P raypaths in P-SV imaging with P-sources and 3C geophones. P-SV imaging of deep rocks has been practiced for more than two decades; SV-P imaging is a new concept. SV-P data should provide the same options for investigating deep rocks as do P-SV data. We have determined one of the equivalences between SV-P data extracted from vertical-geophone data and P-SV data extracted from horizontal geophones: that both modes react to azimuth-dependent variations in the S velocity in anisotropic rocks. Azimuthal variations in the SV-P traveltime can be used to define the polarization direction of the fast-S-wave mode, which is also the azimuth of the maximum horizontal stress (SHmax). Our investigation demonstrates a noninvasive method for monitoring changes in the SHmax azimuth across a CO 2 storage reservoir, or any targeted porous rock, as fluids are cycled into, and then out of, that rock’s pore space.

Geochemistry & Geophysics↗

DOE OSTI2025

Simulating Isotropic Rayleigh Wave Horizontal to Vertical Ratios at Rock Valley

Elastic anisotropy in the subsurface can manifest from pre-existing structure or stress-induced cracking – both phenomena are of interest at the Rock Valley site in Nevada. The azimuthal dependence of Rayleigh wave ellipticity, also known as H/V, can reveal elastic anisotropy, but the effect of isotropic variability in H/V must first be accounted for. To that end, we simulate synthetic seismograms from a ring of sources in a fully 3-D isotropic velocity model that captures the geology at Rock Valley. We measure H/V from these waveforms and compare them with H/V predictions obtained using 1D models extracted at specific locations from the 3D model. We find that an average of the azimuthal H/V measurements from the 3-D simulations and 1-D predictions agree, but that the azimuthal variability of H/V is a large fraction of the mean value. These results estimate the noise character in azimuthal H/V so it can be factored out of future anisotropic simulations.

58 GEOSCIENCES↗

DOE OSTI2023

Leipzig University W-Band Cloud Radar, Gothic (Colorado), SAIL Campaign Second Winter (15.11.2022 - 05.06.2023)

The instrument is a polarimetric W-Band simultaneous transmission simultaneous reception (STSR) Doppler Cloud Radar manufactured by Radiometer Physics GmbH (RPG, instrument type RPG-FMCW-94-DP). It was deployed about 500m away from the ARM M1 facility in Gothic (CO) near the Ore House between Nov 15, 2022 and Jun 5, 2023 at an altitude of 2913 m. The Doppler cloud radar was mounted on a prototype of a cold temperature scanner manufactured by RPG. The dataset contains common radar variables like equivalent radar reflectivity factor, mean Doppler velocity, Doppler spectrum width as well as common polarimetric radar variables like differential phase shift (PhiDP), specific differential phase shift (KDP), correlation coefficient (RHV) and differential reflectivity (ZDR). Between Nov 15, 2022, and Feb 7, 2023 the radar was operated at 40° constant elevation and 151° azimuth (towards the KAZR at the AMF1). Between Feb 7 and Mar 15, 2023 the following scan cycle was repeated in 15min intervals: zenith pointing measurements, RHI scans from 0° to 90° and 90° to 0° elevation at 151° azimuth, constant elevation measurements at 40° elevation and 151° azimuth and PPI scans at 85° elevation for wind retrievals (one PPI per hour). Between Mar 15 18:18 UTC and Apr 8, 2023 11:04 UTC, the scanner was stuck at 72° elevation, which resulted in corrupted files for this period. For that period, the files containing data are uploaded but should be treated with care. Between Apr 8 and Apr 14, 2023 the scanning pattern described above was performed again. Afterwards, except for May 17 and May 18, 2023 where scanning patterns as described above were performed, measurements continued at 40° elevation and 151° azimuth until May 22, 2023 09:00 UTC. The scanning pattern was then started again, but without hourly PPI measurements until May 31, 2023. Between May 31 and Jun 5, 2023 solely zenith-pointing observations were performed. The data provided here are the RPG Level 1 (L1) files, Doppler spectra Level 0 (L0) files are available upon request.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1974

A wind-tunnel investigation of parameters affecting helicopter directional control at low speeds in ground effect

An investigation was conducted in the Langley full-scale tunnel to measure the performance of several helicopter tail-rotor/fin configurations with regard to directional control problems encountered at low speeds in ground effect. Tests were conducted at wind azimuths of 0 deg to 360 deg in increments of 30 deg and 60 deg and at wind speeds from 0 to 35 knots. The results indicate that at certain combinations of wind speed and wind azimuth, large increases in adverse fin force require correspondingly large increases in the tail-rotor thrust, collective pitch, and power required to maintain yaw trim. Changing the tail-rotor direction of rotation to top blade aft for either a pusher tail rotor (tail-rotor wake blowing away from fin) or a tractor tail rotor (tail-rotor wake blowing against fin) will alleviate this problem. For a pusher tail rotor at 180 deg wind azimuth, increases in the fin/tail-rotor gap were not found to have any significant influence on the overall vehicle directional control capability. Changing the tail rotor to a higher position was found to improve tail-rotor performance for a fin-off configuration at a wind azimuth of 180 deg. A V-tail configuration with a pusher tail rotor with top blade aft direction of rotation was found to be the best configuration with regard to overall directional control capability.

Yeager, W. T., Jr.↗

NASA NTRS1975

Radiative property investigation

Measurements of the bidirectional reflections of NASA paints Z-93 and S-13G were made for 0.5, 1.78, and 2.5 microns, source incidence angles of 0, 30, 60, and 75 deg, and four detector azimuth positions. The bidirectional reflectance distribution was found to be near Lambert for azimuth positions not to close to 180 deg from the source incident azimuth. The reflectance distribution at an azimuth of 180 deg from the source is close to Lambert for near normal source incidents angles, and becomes much larger than Lambert as the source incident angle approach grazing. The reflectance deviates from Lambert as the wavelength increases. Comparison of data for the paints shows Z-93 reflectance is much closer to Lambert than S-13G. When there is a peak in the reflectance distribution it occurred at the specular angle or an angle larger than the specular angle.

Scott, R. L., Jr.↗