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Venus' spectroscopic phase variation - Implications of the Mariner 10 photographs
The recent ultraviolet photographs of Venus by Mariner 10 have shown an irregular cloud structure. There is an apparent tendency for clearing along a wide equatorial band more or less centered on the subsolar point. This synoptic picture is in marked contrast to the uniform cloud cover conventionally used in model calculations of the variation with phase of CO2 absorption bands. To illustrate the consequences of subsolar weakening of CO2 absorption, a mathematically simple (but realistically naive) model is used. Two conclusions are reached: (1) efforts to distinguish between single- and double-layer models for the clouds from spectroscopic data alone are not merely ambiguous (as argued earlier by Chamberlain and Smith); with present data they are hopeless; (2) the decrease in the CO2 absorption close to full phase, as reported by Young et al., could result entirely from an equatorial darkening that is relatively inconsequential at the crescent phase and increasingly predominant for fuller phases.
Whole earth telescope observations of the white dwarf G29-38 - Phase variations of the 615 second period
An extensive set of high-speed photometric observations obtained with the Whole Earth Telescope network is used to show that the complex light curve of the ZZ Zeti (DAV) star G29-38 is dominated by a single, constant amplitude period of 615 s during the time span of these observations. The pulse arrival times for this period exhibit a systematic variation in phase readily explained by light-travel time effects produced by reflex orbital motion about an unseen companion. The best-fit model to the observations indicates a highly eccentric orbit, a period of 109 + or - 13 days and a minimum mass of 0.5 solar mass for the companion.
Thermal Phase Variations of WASP-12b: Defying Predictions
We report Warm Spitzer full-orbit phase observations of WASP-12b at 3.6 and 4.5 micrometers. This extremely inflated hot Jupiter is thought to be overflowing its Roche lobe, undergoing mass loss and accretion onto its host star, and has been claimed to have a C/O ratio in excess of unity. We are able to measure the transit depths, eclipse depths, thermal and ellipsoidal phase variations at both wavelengths. The large-amplitude phase variations, combined with the planet's previously measured dayside spectral energy distribution, are indicative of non-zero Bond albedo and very poor day-night heat redistribution. The transit depths in the mid-infrared-(R(sub p)/R(sub ∗))(sup 2) = 0.0123(3) and 0.0111(3) at 3.6 and 4.5 micrometers, respectively-indicate that the atmospheric opacity is greater at 3.6 than at 4.5 micrometers, in disagreement with model predictions, irrespective of C/O ratio. The secondary eclipse depths are consistent with previous studies: F(sub day)/F(sub ∗) = 0.0038(4) and 0.0039(3) at 3.6 and 4.5 micrometers, respectively. We do not detect ellipsoidal variations at 3.6 micrometers, but our parameter uncertainties-estimated via prayer-bead Monte Carlo-keep this non-detection consistent with model predictions. At 4.5 micrometers, on the other hand, we detect ellipsoidal variations that are much stronger than predicted. If interpreted as a geometric effect due to the planet's elongated shape, these variations imply a 3:2 ratio for the planet's longest:shortest axes and a relatively bright day-night terminator. If we instead presume that the 4.5 micrometer ellipsoidal variations are due to uncorrected systematic noise and we fix the amplitude of the variations to zero, the best-fit 4.5 micrometer transit depth becomes commensurate with the 3.6 micrometer depth, within the uncertainties. The relative transit depths are then consistent with a solar composition and short scale height at the terminator. Assuming zero ellipsoidal variations also yields a much deeper 4.5 micrometer eclipse depth, consistent with a solar composition and modest temperature inversion. We suggest future observations that could distinguish between these two scenarios.
Comments on "Venus' spectroscopic phase variation: Implications of the Mariner 10 photographs
From a misinterpretation of Mariner 10 pictures, Chamberlain (1974) constructed a model in which he used horizontal variations in the Venus atmosphere to explain the phase-variation of CO2 absorption at small phase angles. Published observations of spatial variations in CO2 absorption on Venus show that they are too small to explain the phase effect. The question of uniqueness that is, if more than one model can explain the phase-effect observations is discussed. Before this question can be answered, a realistic model that does account for the data must be constructed. No such calculations exist.
Separate reference beam holographic interferometry and its application to the measurement of small phase variations in sub-fringe systems
Application of separate reference beam holographic interferometry for measurement of small phase variations in sub-fringe systems
Estimating Transmitted-Signal Phase Variations for Uplink Array Antennas
A method of estimating phase drifts of microwave signals distributed to, and transmitted by, antennas in an array involves the use of the signals themselves as phase references. The method was conceived as part of the solution of the problem of maintaining precise phase calibration required for proper operation of an array of Deep Space Network (DSN) antennas on Earth used for communicating with distant spacecraft at frequencies between 7 and 8 GHz. The method could also be applied to purely terrestrial phased-array radar and other radio antenna array systems. In the DSN application, the electrical lengths (effective signal-propagation path lengths) of the various branches of the system for distributing the transmitted signals to the antennas are not precisely known, and they vary with time. The variations are attributable mostly to thermal expansion and contraction of fiber-optic and electrical signal cables and to a variety of causes associated with aging of signal-handling components. The variations are large enough to introduce large phase drifts at the signal frequency. It is necessary to measure and correct for these phase drifts in order to maintain phase calibration of the antennas. A prior method of measuring phase drifts involves the use of reference-frequency signals separate from the transmitted signals. A major impediment to accurate measurement of phase drifts over time by the prior method is the fact that although DSN reference-frequency sources separate from the transmitting signal sources are stable and accurate enough for most DSN purposes, they are not stable enough for use in maintaining phase calibrations, as required, to within a few degrees over times as long as days or possibly even weeks. By eliminating reliance on the reference-frequency subsystem, the present method overcomes this impediment. In a DSN array to which the present method applies (see figure), the microwave signals to be transmitted are generated by exciters in a signal-processing center, then distributed to the antennas via optical fibers. At each antenna, the signals are used to drive a microwave power-amplifier train, the output of which is coupled to the antenna for transmission. A small fraction of the power-amplifier-train output is sent back to the signal-processing center along another optical fiber that is part of the same fiber-optic cable used to distribute the transmitted signal to the antenna. In the signal-processing center, the signal thus returned from each antenna is detected and its phase is compared with the phase of the signal sampled directly from the corresponding exciter. It is known, from other measurements, that the signal-propagation path length from the power-amplifier-train output port to the phase center of each antenna is sufficiently stable and, hence, that sampling the signal at the power-amplifier-train output port suffices for the purpose of characterizing the phase drift of the transmitted signal at the phase center of the antenna
Measurement of the GPS Transmitting Antenna Phase Variations
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Venus - On the phase variation of CO2 line profiles
The shapes of Venus' CO2 profiles are found to vary with solar phase angle. High-resolution spectra of the P16 and P14 lines in the 8689- and 7820-A bands, respectively, are presented for phase angles ranging from 6 to 158 deg. The scattering mean free path at 80 mbar, approximately the effective pressure, is 1.7 km. Use of the van de Hulst (1974) similarity relations with simple parametric scattering models is inadequate to separate effects due to the scattering phase function from those due to inhomogeneities in depth when one attempts to determine the atmospheric structure by fitting a family of such models over a wide range of phase angles.
Observations of the phase variation of Venus CO2 equivalent widths
Equivalent widths determined from photoelectric scans of Venus CO2 absorption lines measured at phase angles of 5.1 to 170 deg are presented. The data-reduction procedure is described in detail, and phase curves are plotted for three model atmospheres in which CO2 is homogeneously mixed with Mie-scattering particles or inhomogeneously mixed with Henyey-Greenstein particles. All three data sets are found to indicate that the equivalent-width maximum occurs at a phase angle much lower than 100 deg. It is concluded that two scattering layers are not required on Venus to explain the shape of the observed phase curve and that the mixing ratio of scattering particles to CO2 increases with depth at high altitudes.
The radial phase variation of reversed-shear and toroidicity-induced Alfvén eigenmodes in DIII-D
The eigenfunction of an instability contains information about energy flow in the wave. Here, the amplitude and phase of electron cyclotron emission radiometer data from hundreds of DIII-D reversed shear Alfvén eigenmodes (RSAE) and toroidicity-induced Alfvén eigenmodes (TAE) are analyzed along the outboard horizontal midplane. The radial phase profile can be flat, linearly rising or falling, convex or concave; in other words, a wide variety of shapes is observed. For a particular mode, often the radial phase profile remains approximately constant as the mode evolves in time but sometimes it changes rapidly. Many TAEs and some RSAEs have phase profiles that are rather flat where the mode amplitude is largest but rise steadily by ~2π at large major radius. Rapid phase changes are observed when the frequencies of an RSAE and TAE overlap and the modes couple. The phase profile depends weakly on the fast-ion gradient that would appear in the absence of wave-induced transport. Linear and quadratic fits to the phase profiles, together with many plasma parameters, are assembled into RSAE and TAE databases. In both cases, large variability is observed. For RSAEs, the strongest phase dependencies are on electron temperature T e , RSAE mode frequency, and the density of carbon impurities. For TAEs, the strongest dependencies are on beam power and major radius of the mode. In general, the average RSAE radial phase profile is essentially flat but the TAE profile has non-zero slope and curvature.
Saturn's rings - Azimuthal variations, phase curves, and radial profiles in four colors
Four-color photographic photometry, at effective wavelengths of 5900, 5350, 4150, and 3560 A, obtained during the 1977, 1978, and 1979 Saturn apparitions, were analyzed to determine the ring brightness as a function of wavelength, solar phase angle, ring particle orbital phase (the azimuthal effect), declination of the earth relative to the ring plane (tilt effect), and radial distance from Saturn. Data were obtained using the International Planetary Patrol network when the ring tilt angle B was approximately 16.5, 11.5, and 6 deg, respectively. From the approximately 40,000 original images, 364 were scanned and digitized, along with corresponding calibration exposures. The smearing correction technique used achieved better signal-to-noise by utilizing such constraints as the known width of Cassini's Division on the major axis. The most important observational results were summarized, and included the following: the azimuthal brightness variations for the brighter portion of ring A increased as the ring tilt decreased from B = 26 deg to less than 16 deg, reaching the order of + or 20% with respect to the ansae; they are not detectable for ring B or the outer portion of ring A.
Atomic-Scale Mapping and Quantification of Local Ruddlesden–Popper Phase Variations
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Lidar Observations of Predawn Thermosphere‐Ionosphere Na (TINa) Layers Over Boulder (40.13°N, 105.24°W): Annual Phase Variations and Correlation With Sunrise and Tidal Winds
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Global Pc5 Pulsations From the Polar Cap to the Equator: Wave Characteristics, Phase Variations, Disturbance Current System, and Signal Transmission
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A variational phase-field framework for thermal softening and dynamic ductile fracture
A variational phase field model for dynamic ductile fracture is presented. Here, the model is designed for elasto-viscoplastic materials subjected to rapid deformations in which the effects of heat generation and material softening are dominant. The variational framework allows for the consistent inclusion of plastic dissipation in the heat equation as well as thermal softening. It employs a coalescence function to degrade fracture energy during regimes of high plastic flow. A variationally consistent form of the Johnson–Cook model is developed for use with the framework. Results from various benchmark problems in dynamic ductile fracture are presented to demonstrate capabilities. In particular, the ability of the model to regularize shear band formation and subsequent damage evolution in two- and three-dimensional problems is demonstrated. Importantly, these phenomena are naturally captured through the underlying physics without the need for phenomenological criteria such as stability thresholds for the onset of shear band formation.
Variable Sampling Mapping
The performance of an optical system (for example, a telescope) is limited by the misalignments and manufacturing imperfections of the optical elements in the system. The impact of these misalignments and imperfections can be quantified by the phase variations imparted on light traveling through the system. Phase retrieval is a methodology for determining these variations. Phase retrieval uses images taken with the optical system and using a light source of known shape and characteristics. Unlike interferometric methods, which require an optical reference for comparison, and unlike Shack-Hartmann wavefront sensors that require special optical hardware at the optical system's exit pupil, phase retrieval is an in situ, image-based method for determining the phase variations of light at the system s exit pupil. Phase retrieval can be used both as an optical metrology tool (during fabrication of optical surfaces and assembly of optical systems) and as a sensor used in active, closed-loop control of an optical system, to optimize performance. One class of phase-retrieval algorithms is the iterative transform algorithm (ITA). ITAs estimate the phase variations by iteratively enforcing known constraints in the exit pupil and at the detector, determined from modeled or measured data. The Variable Sampling Mapping (VSM) technique is a new method for enforcing these constraints in ITAs. VSM is an open framework for addressing a wide range of issues that have previously been considered detrimental to high-accuracy phase retrieval, including undersampled images, broadband illumination, images taken at or near best focus, chromatic aberrations, jitter or vibration of the optical system or detector, and dead or noisy detector pixels. The VSM is a model-to-data mapping procedure. In VSM, fully sampled electric fields at multiple wavelengths are modeled inside the phase-retrieval algorithm, and then these fields are mapped to intensities on the light detector, using the properties of the detector and optical system, for comparison with measured data. Ultimately, this model-to-data mapping procedure enables a more robust and accurate way of incorporating the exit-pupil and image detector constraints, which are fundamental to the general class of ITA phase retrieval algorithms.
Impact of longitudinal phase-matching variations on three-wave nonlinear interactions
A general study of three-wave nonlinear mixing in the presence of longitudinal variations in phase-matching conditions is presented. The efficiency of second-harmonic generation and optical parametric amplification is quantified using a normalized set of equations and a polynomial description of the wave-vector mismatch as a function of the longitudinal coordinate. These modeling results are used to estimate the impact of spatial variations in wave-vector mismatch experimentally obtained for five partially deuterated potassium dihydrogen phosphate crystals. The longitudinal inhomogeneities in the properties of crystals of similar quality are not expected to have a significant impact on their use for second-harmonic generation and optical parametric amplification, but the efficiency of nonlinear processes in crystals with larger variations could decrease.