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A formula is derived that describes the size of the solid angle within which must be the normal to a flat specular reflector, if such a reflector is to redirect light from a small but finite extended source to a small but finite extended detector. The formula assumes the rules of geometrical optics and does not account for the effects of diffraction.
Some of the useful formulas and methods for determining antenna beam solid angle are presented. The applicability of these formulas in evaluating radiometric systems performance is illustrated.
Electric switch can be actuated /closed/ by a force applied from any direction within a hemispheric envelope. The switch is comprised of a flexible, electrically conductive reed holding a conductive contact disc, mounted concentrically within a conductive tube.
The design and performance of a new light trap for a spaceborne electron spectrometer are described. The light trap has a measured photon-rejection ratio of 2 x 10 exp -11, allowing only one in 5 x 10 exp 10 incident photons to reach the sensitive area of the instrument. This rejection is more than sufficient because the ambient UV in earth orbit requires a rejection no better than 10 exp -8 to maintain the photon interference to less than 10 count/s. The light trap uses triple reflections to keep most of the light passing through the entrance slit away from the sensitive area of the spectrometer. It is shown that the average reflectance of all the internal surfaces must be less than 0.006, which is consistent with the data on the black coating applied to all surfaces. The analysis makes it possible to compare the photon contributions of each of the internal reflecting areas and to estimate the effective scattering width of the metallic electrode edge.
The unsteady response of an axial flow fan rotor to steady, circumferential inflow velocity and stagnation pressure distortions is assessed by two different methods. These are: (1) investigation of the unsteady normal force and pitching moment on a chordwise element of a rotor blade; and (2) investigation of the variation of the stagnation pressure distortion between the inlet and exit of the rotor. Experimental measurements of these unsteady characteristics are presented as a function of the geometry of the rotor -- stagger angle, solidity and steady angle of incidence -- for sinusoidally varying circumferential distortions with different numbers of distortion cycles. These measurements are compared with several theoretical analyses. While these comparisons indicate some of the deficiencies which exist in the theories, the existence of an unsteady cascade effect and the ability of the theories to adequately predict the trend of the unsteady response due to variations in reduced frequency, rotor stagger angle, solidity and mean incidence angle is clearly demonstrated.
Relationship between dynamic contact angle and velocity of liquid front along solid surface
An expression for the flux into a retarding potential analyzer (RPA) is derived which takes into account the instrumental effect of a dependence on energy of the solid angle of the acceptance cone. A second instrumental effect of a limited bandpass is briefly discussed. Using the (LIMS) instrument on SCATHA, it is shown that temperatures and densities derived without considering the effect of the solid angle dependence on energy will be too low, dramatically so for E(t) E(1), where E(1) is the e folding distance of the solid angle dependence and E(t) is the thermal energy of the plasma. For E(t) E(1), there is effectively no impact on the derived temperatures and densities if the solid angle effect is ignored.
The second small astronomy satellite (SAS-2) carried a high energy gamma ray telescope into an equitorial orbit with a 2 D inclination, an apogee of 610 km, and a perigee of 440 km. The energy threshold of the instrument was about 30 MeV, the energy of the gamma rays could be measured up to about 200 MeV, and the integral intensity above 200 MeV could also be measured. Summary tables of the gamma ray data are presented in two energy bands, 35-100 MeV and 100 MeV. The sky was divided into 144 solid angle elements, and, in each solid angle element for which data exist, the number of gamma rays observed is given and also the exposure factor. Information is provided to permit conversion of these data into approximate intensities.
This slide presentation reviews the radiometric performance model for Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). This model allows for an estimation of the signal throughput and noise properties of AVIRIS for the components. This understanding can point to areas for improvements of the components.. The signal to noise ratio properties may be estimated. An accurate radiometric performance model is essential for the use of existing instruments and the design of new instruments. Included in the presentation is a design view and a picture of the AVIRIS instrument. There is discussion of the signal, the signal area solid angle product, aspects of area solid angle time, the idealized radiometer photon calculation and noise both instrument read and photon counting noise. Graphs of signal throughput efficiency, input radiance, photons at the detector, signal e-, noise e- and the signal to noise ratio are presented.
The wave-normal emissivity and the ray emissivity formulas for an electron moving along a helical path in a magnetoactive medium are presented. Simplified formulas for the case of an isotropic plasma are also given. Because of the helical motion of the electron, a difference exists between the radiated power per unit solid angle and the received power per unit solid angle. The relation between these two quantities in a magnetoactive medium is shown. Results are compared with those obtained by others, and the sources of discrepancies are pointed out.
Cosmology and other scientific results from the WMAP mission require an accurate knowledge of the beam patterns in flight. While the degree of beam knowledge for the WMAP one-year and three-year results was unprecedented for a CMB experiment, we have significantly improved the beam determination as part of the five-year data release. Physical optics fits are done on both the A and the B sides for the first time. The cutoff scale of the fitted distortions on the primary mirror is reduced by a factor of approximately 2 from previous analyses. These changes enable an improvement in the hybridization of Jupiter data with beam models, which is optimized with respect to error in the main beam solid angle. An increase in main-beam solid angle of approximately 1% is found for the V2 and W1-W4 differencing assemblies. Although the five-year results are statistically consistent with previous ones, the errors in the five-year beam transfer functions are reduced by a factor of approximately 2 as compared to the three-year analysis. We present radiometry of the planet Jupiter as a test of the beam consistency and as a calibration standard; for an individual differencing assembly. errors in the measured disk temperature are approximately 0.5%.
A three-component dual-beam laser-velocimeter system has been designed, fabricated, and implemented in the 7-by 10-Foot Wind Tunnel at NASA Ames Research Center. The instrument utilizes optical access from both sides and the top of the test section, and is configured for uncoupled orthogonal measurements of the three Cartesian coordinates of velocity. Bragg cell optics are used to provide fringe velocity bias. Modular system design provides great flexibility in the location of sending and receiving optics to adapt to specific experimental requirements. Near-focus Schmidt-Cassegrain optic modules may be positioned for collection of forward or backward scattered light over a large solid angle, and may be clustered to further increase collection solid angle. Multimode fiber optics transmit collected light to the photomultiplier tubes for processing. Counters are used to process the photomultiplier signals and transfer the processed data digitally via buffered interface controller to the host MS-DOS computer. Considerable data reduction and graphical display programming permit on-line control of data acquisition and evaluation of the incoming data. This paper describes this system in detail and presents sample data illustrating the system's capability.
The Mie scattering properties of a homogeneous, isotropic spherical particle, moving at a constant velocity and illuminated by two intersecting coherent plane waves having the same polarization direction, have been analyzed based upon an exact solution to Maxwell's equations. The solutions are in a form suitable for the calculation of the time varying scattered signal integrated across a detector aperture of variable size that is centered on either the forward or backward scattering direction. This problem is of importance in defining the scattered signal in a cross beam laser Doppler velocimeter (LDV). Results obtained from calculating the integrated scattered signal indicate a strong dependence upon the following physical parameters: particle size, index of refraction, cross beam angle, and collection solid angle.
We present the first results of a wide solid angle, moderately deep Chandra survey of the Lockman Hole North West Region. Our 9 ACIS-I fields cover an effective solid angle of 0.33 sq deg and reach a depth of 3 x 10(exp -16) erg/sq cm/s in the 0.4-2 keV band, and 3 x 10(exp -15) erg/sq cm/s in the 2-8 keV band. The best fit logN-logS for the entire field, the largest contiguous Chandra field yet observed, matches well onto that of the Chandra Deep Field North. This indicates that over 90% of the 2-8 keV X-ray background is resolved into point sources. We show that the full range of the 'cosmic variance' previously seen in different Chandra fields can be reproduced in a small region of the sky. The count-in-cells analysis shows that the 2-10 keV band sources have much larger angular correlation scale than that of the 0.4-2 keV band. We found the large difference is likely to be caused by a stronger spatial correlation in the hard band sources rather than the redshift effect.
It is proposed that a relation exists between the extent of interplanetary-magnetic-field sectors and observed variations in cosmic-ray intensity at earth. Changes that take place in the sector magnetic fields and solar polar fields during a sunspot cycle are described. It is argued that a geometrical effect arising from changes in sector-field and polar-field extent during sunspot cycles may be the principal cause of the 11-yr modulation of cosmic-ray intensity observed at earth. The fraction of the heliosphere occupied by sector fields is estimated as a function of time through an average sunspot cycle, the solid angle of the heliosphere occupied by the extended solar polar fields is plotted through the same cycle, and monthly averages of observed absolute intensities of primary cosmic rays with a rigidity greater than 0.5 GV are compared with the plot of polar-field extent. It is found that the average sunspot-cycle variation of the solid angle of the extended polar fields is rather similar to the observed variation in the flux of the cosmic rays considered.
In a weakly inhomogeneous plasma, the large-amplitude Alfven waves propagating parallel to the ambient magnetic field are shown to evolve into accelerated Alfven solitons. Nonlinear interaction of the accelerated Alfven solitons with the Langmuir waves results in the emission of coherent radiations. Analytical expression for the power radiated per unit solid angle from a soliton is derived for two inhomogeneity profiles, namely the linear profile and the parabolic profile. For the case of uniform plasmas, the emission occurs via a decay-type process or resonant modes. In the presence of inhomogeneity, nonresonant modes provide a new channel for the emission of radiation. The power radiated per unit solid angle is computed for the parameters relevant to Comet Halley's plasma environment. For the nonresonant modes it is found to be several orders of magnitude higher than that for the case of resonant modes.
NGC 4945 is one of the brightest Se.yfert galaxies on the sky at 100 keV, but is completely absorbed below 10 keV, implying an optical depth of the absorber to electron scattering of a few; its absorption column is probably the largest which still allows a direct view of the nucleus at hard X-ray energies. Our observations of it with the Rossi X-ray Timing Explorer (RXTE) satellite confirm the large absorption, which for a simple phenomenological fit using an absorber with Solar abundances implies a column of 4.5(sup 0.4, sub -0.4) x 10(exp 24) /sq cm. Using a a more realistic scenario (requiring Monte Carlo modeling of the scattering), we infer the optical depth to Thomson scattering of approximately 2.4. If such a scattering medium were to subtend a large solid angle from the nucleus, it should smear out any intrinsic hard X-ray variability on time scales shorter than the light travel time through it. The rapid (with a time scale of approximately a day) hard X-ray variability of NGC 4945 we observed with the RXTE implies that the bulk of the extreme absorption in this object does not originate in a parsec-size, geometrically thick molecular torus. Limits on the amount of scattered flux require that the optically thick material on parsec scales must be rather geometrically thin, subtending a half-angle < 10 deg. This is only marginally consistent with the recent determinations of the obscuring column in hard X-rays, where only a quarter of Seyfert 2s have columns which are optically thick, and presents a problem in accounting for the Cosmic X-ray Background primarily with AGN possessing the geometry as that inferred by us. The small solid angle of the obscuring material, together with the black hole mass (of approximately 1.4 x 10(exp 6) solar mass) from megamaser measurements. allows a robust determination of the source luminosity, which in turn implies that the source radiates at approximately 10% of the Eddington limit.