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An Analytical Calibration Approach for the Polarimetric Airborne C Band Radiometer

Passive microwave remote sensing is sensitive to the quantity and distribution of water in soil and vegetation. During summer 2000, the Microwave Geophysics Group a t the University of Michigan conducted the seventh Radiobrighness Energy Balance Experiment (REBEX-7) over a corn canopy in Michigan. Long time series of brightness temperatures, soil moisture and micrometeorology on the plot were taken. This paper addresses the calibration of the NASA GSFC polarimetric airborne C band microwave radiometer (ACMR) that participated in REBEX-7. These passive polarimeters are typically calibrated using an end-to-end approach based upon a standard artificial target or a well-known geophysical target. Analyzing the major internal functional subsystems offers a different perspective. The primary goal of this approach is to provide a transfer function that not only describes the system in its entire5 but also accounts for the contributions of each subsystem toward the final modified Stokes parameters. This approach does not assume that the radiometric system is linear as it does not take polarization isolation for granted, and it also serves as a realistic instrument simulator, a useful tool for future designs. The ACMR architecture can be partitioned into functional subsystems. The characteristics of each subsystem was extensively measured and the estimated parameters were imported into the overall dosed form system model. Inversion of the model yields a calibration for the modeled Stokes parameters with uncertainties of 0.2 K for the V and H polarizations and 2.4 K for the 3rd and 4th parameters. Application to the full Stokes parameters over a senescent cornfield is presented.

Pham, Hanh

Polarimetric measurements of sea surface brightness temperatures using an aircraft K-band radiometer

This paper presents the first experimental evidence that the polarimetric brightness temperatures of sea surfaces are sensitive to ocean wind direction in the incidence angle range of 30 to 50 degrees. Our experimental data were collected by a K-band (19.35 GHz) polarimetric wind radiometer (WINDRAD) mounted on the NASA DC-8 aircraft. A set of aircraft radiometer flights was successfully completed in November 1993. We performed circle flights over National Data Buoy Center (NDBC) moored buoys deployed off the northern California coast, which provided ocean wind measurements. The first WINDRAD flight was made on November 4, 1993. There was clear weather with a wind speed of 12 m/s at 330 degrees around the Pt. Arena buoy. We circled the buoy at three incidence angles, and all data when plotted as functions of azimuth angles show clear modulations of several Kelvin. At 40 degrees incidence angle, there is a 5 Kelvin peak-to-peak signal in the second Stokes parameter Q and the third Stokes parameter U. The Q data maximum is in the upwind direction and U has a 45 degrees phase shift in azimuth as predicted by theory. There is also an up/downwind asymmetry of 2 Kelvin in the Q data, and 1 Kelvin in the U data. At 50 degrees incidence angle, the collected data show very similar wind direction signatures to the SSM/I model function. Additional flights were made on other days under cloudy conditions. Data taken at a wind speed of 8 m/s show that at 40 degrees incidence Q and U have a smaller azimuthal modulation of 3 Kelvin, probably due to the lower wind speed. Additionally, the simultaneously recorded video images of sea surfaces suggested that Q and U data were less sensitive to unpolarized geophysical variations, such as clouds and whitecaps, while the T(v) and T(h) increased by a few Kelvin when the radiometer beam crossed over clouds, or there was a sudden increase of whitecaps in the radiometer footprint. The results of our aircraft flights indicate that passive polarimetric radiometry has a strong potential for global ocean wind speed and direction measurements from space.

Yueh, Simon H.

Models of polarized infrared emission from bipolar nebulae

Many stars with circumstellar dust shells show a high degree of linear polarization (Sato et al. 1985). We are developing a model which assumes that the polarization arises from scattering by circumstellar dust. Our model assumes a geometry in which the star is surrounded by an optically thin spherical dust shell and embedded within an optically thick disk. This geometry is consistent with that proposed for objects with bipolar molecular outflow. This is important because many bipolar flow objects have also been observed to be highly polarized. The high degree of linear polarization is produced because the disk differentially attenuates the light from the star. The light incident from the point source is attenuated by a factor of exp(-tau/cos theta) where theta is the angle between a ray from the point source to the scatterer and a ray normal to the disk; tau is the optical depth at the wavelength of interest. Hence, the light scattered from the regions directly above and below the disk give the largest contribution to the total flux. The scattering angle for light from these regions is near 90 deg., so the light is strongly polarized and, in the Rayleigh scattering regime, is polarized parallel to the disk. The Stokes parameters for the scattered light from each particle in the shell are calculated by using the scattering matrix elements generated by a Mie scattering program. After the Stokes parameters for each particle are computed they are summed to give the Stokes parameters for the entire shell. Two graphs are presented which show the intensity and polarization spectrum generated by our model using the optical constants for astronomical silicates as defined by Draine and Lee (1984).

Burns, M. S.

A theoretical and numerical study of polarimetric scattering and emission from random rough surfaces with anisotropic directional spectrum

In this paper, theoretical and numerical results of the polarimetric scattering and emission from random rough surfaces with anisotropic directional spectrum are presented for the remote sensing of ocean and soil surfaces. The polarimetric scattered field for rough dielectric surfaces is derived to the second order by the small perturbation method (SPM). It is found that the second-order scattered field is coherent in nature, and its coefficients for different polarizations present the lowest-order corrections to the Fresnel reflection coefficients of the surfaces. In addition, the cross-polarized (HV and VH) components of the coherent fields are reciprocal and not zero for surfaces with anisotropic directional spectrum when the azimuth angle of the incident direction is not aligned with the symmetry directions of surfaces. In order to verify the energy conservation condition of the theoretical results, which is important if the theory is to be applied to the passive polarimetry of rough surfaces, a Monte Carlo simulation is performed to numerically calculate the polarimetric reflectivities of one-dimensional random rough surfaces which are generated with a prescribed power-law spectrum in the spectral domain and transformed to the spatial domain by the FFT. The surfaces simulated by this approach are periodic with the period corresponding to the low-wavenumber cutoff. To calculate the scattering from periodic dielectric surfaces, the authors present a new numerical technique which applies the Floquet theorem to reduce the problem to one period and does not require the evaluation of one-dimensional periodic Green's function used in the conventional method of moment formulation. Once the scattering coefficients are obtained, the polarimetric Stokes vectors for the emission from the random surfaces are then calculated according to the Kirchhoff's law and are illustrated as functions of relative azimuth observation and row directions. The second-order SPM is also reduced to this one-dimensional case, and theoretical results for all four Stokes parameters are in excellent agreement with the numerical results obtained from the Monte Carlo simulation. Moreover, the second order coherent fields are found to be necessary for the theoretical evaluation of the third and fourth Stokes parameters. Without that, the reflectivities of random rough surfaces are significantly over-estimated, and the signs of the third and the fourth Stokes parameters are found to be incorrect, if calculated by using the first-order incoherent fields alone.

Yueh, S. H.

The Primordial Inflation Polarization Explorer (PIPER)

The Primordial Inflation Polarization Explorer (PIPER) is it balloon-borne instrument designed to search for the faint signature of inflation in the polarized component of the cosmic microwave background (C-N-113). Each flight will be configured for a single frequency, but in order to aid in the removal of the polarized foreground signal due to Galactic dust, the filters will be changed between flights. In this way, the CMB polarization at a total of four different frequencies (200, 270, 350, and 600 GHz) will be, measured on large angular scales. PIPER consists of a pair of cryogenic telescopes, one for measuring each of Stokes Q and U in the instrument frame. Each telescope receives both linear orthogonal polarizations in two 32 x 40 element planar arrays that utilize Transition-Edge Sensors (TES). The first element in each telescope is a variable-delay polarization modulator (VPM) that fully modulates the linear Stokes parameter to which the telescope is sensitive. There are several advantages to this architecture. First, by modulating at the front of the optics, instrumental polarization is unmodulated and is therefore cleanly separated from source polarization. Second, by implementing this system with the appropriate symmetry, systematic effects can be further mitigated. In the PIPER design, many of the. systematics are manifest in the unmeasured linear Stokes parameter for each telescope and this can be separated from the desired signal. Finally, the modulation cycle never mixes the Q and U linear Stokes parameters, and thus residuals in the modulation do not twist the observed polarization vector. This is advantageous because measuring the angle of linear polarization is critical for separating the inflationary signal from other polarized components.

Chuss, David T.

Polarization of synchrotron radiation from relativistic Schwarzschild circular geodesics.

The pattern of geodesic synchrotron radiation emitted by a charge in an orbit close to the circular photon orbit at 3M around a nonrotating black hole of mass M is studied. The analysis is carried out using Stokes parameters, which completely characterize the state of the wave. The linear polarization, as observed at infinity, is total in the orbital plane and not smaller than 90% at the half-width of the beam. At the poles, pure circular polarization would be observed. In the region between the orbit plane and the poles the polarization shows features not present in ordinary synchrotron radiation. In our model, parameters more sensitive to deviations from the orbital plane are the Stokes parameter s (sub 2) and the tilt angle of the polarization ellipse.

Breuer, R. A.

Phase-Controlled Polarization Modulators

We report technology development of millimeter/submillimeter polarization modulators that operate by introducing a a variable, controlled phase delay between two orthogonal polarization states. The variable-delay polarization modulator (VPM) operates via the introduction of a variable phase delay between two linear orthogonal polarization states, resulting in a variable mapping of a single linear polarization into a combination of that Stokes parameter and circular (Stokes V) polarization. Characterization of a prototype VPM is presented at 350 and 3000 microns. We also describe a modulator in which a variable phase delay is introduced between right- and left- circular polarization states. In this architecture, linear polarization is fully modulated. Each of these devices consists of a polarization diplexer parallel to and in front of a movable mirror. Modulation involves sub-wavelength translations of the mirror that change the magnitude of the phase delay.

Chuss, D. T.

MCM Polarimetric Radiometers for Planar Arrays

A polarimetric radiometer that operates at a frequency of 40 GHz has been designed and built as a prototype of multiple identical units that could be arranged in a planar array for scientific measurements. Such an array is planned for use in studying the cosmic microwave background (CMB). All of the subsystems and components of this polarimetric radiometer are integrated into a single multi-chip module (MCM) of substantially planar geometry. In comparison with traditional designs of polarimetric radiometers, the MCM design is expected to greatly reduce the cost per unit in an array of many such units. The design of the unit is dictated partly by a requirement, in the planned CMB application, to measure the Stokes parameters I, Q, and U of the CMB radiation with high sensitivity. (A complete definition of the Stokes parameters would exceed the scope of this article. In necessarily oversimplified terms, I is a measure of total intensity of radiation, while Q and U are measures of the relationships between the horizontally and vertically polarized components of radiation.) Because the sensitivity of a single polarimeter cannot be increased significantly, the only way to satisfy the high-sensitivity requirement is to make a large array of polarimeters that operate in parallel. The MCM includes contact pins that can be plugged into receptacles on a standard printed-circuit board (PCB). All of the required microwave functionality is implemented within the MCM; any required supporting non-microwave ("back-end") electronic functionality, including the provision of DC bias and control signals, can be implemented by standard PCB techniques. On the way from a microwave antenna to the MCM, the incoming microwave signal passes through an orthomode transducer (OMT), which splits the radiation into an h + i(nu) beam and an h - i(nu) beam (where, using complex-number notation, h denotes the horizontal component, nu denotes the vertical component, and +/-i denotes a +/-90deg phase shift). Each of these beams enters the MCM through one of two WR-22 waveguide input terminals in the lid of the MCM. The h + i(nu0 and h - i(nu) signals are amplified, then fed to a phase-discriminator hybrid designed specifically to fit the predominantly planar character of the MCM geometry and to enable determination of Q and U. The phase-discriminator hybrid generates four outputs, which are detected and used to calculate I, Q, and U.

Kangaslahti, Pekka

Time and polarization dependent double scattering calculations of lidar returns from water clouds

We describe and present results of a double scattering lidar model which we use to calculate lidar returns from water clouds. The model is used in conjunction with the Phillips Laboratory's (Geophysics Directorate) low altitude Nd:YAG lidar system to determine microphysical properties of water clouds. The model determines the Stokes parameters of the backscattered lidar radiation, from media composed of spherical particles, as a function of time. The Stokes parameters of the radiation of the lidar return are determined, at each time, by considering all radiation which has traveled the same path length from transmitter to receiver while making two successive single scatters. Each single scatter is considered a Mie scatter. We have also developed a Mie scattering program for use with the double scattering model. Each single scatter takes into account the polarization of the incident and scattered radiation. Inputs to the double scattering mode include the receiver area and field of view, the receiver integration time, the extinction coefficient as a function of distance into the cloud, the particle size distribution (assumed independent of position), and the complex index of refraction of the spherical particles.

Garner, R. C.

Effects of the Antenna Aperture on Remote Sensing of Sea Surface Salinity at L-Band

Remote sensing of sea surface salinity with sufficient accuracy to meet the needs of global oceanography is a challenging task. The global variability of the salinity signal in the open ocean is only a few Kelvin even at L-band and an accuracy on the order of 0.1K is desired to study the influence of salinity on ocean circulation and energy exchange with the atmosphere. On the other hand, resolution is not an issue for understanding the dynamics of the open ocean where scales of hundreds of km are not uncommon. This permits remote sensing with large antenna footprints and spatial averaging to reduce noise. However, antennas with large footprints introduce other problems. For example, the angle of incidence and hence the brightness temperature varies over the footprint. Similarly, the polarization of brightness temperature relative to the antenna ports changes. Studies have been conducted using antenna patterns representative of the antenna that will be flown on the Aquarius mission to examine these effects. Aquarius is a pushbroom style radiometer with three beams looking across track away from the sun. The beams are at incidences angles (at the spacecraft) of about 26.5, 34 and 40 degrees each with a half-power beam width of about 5.8 degrees. It is shown that the measured brightness temperature is biased relative to the value at boresight because of changes across the field of view. The bias can be as much as 4K and positive or negative depending on polarization. Polarization mixing because of the variations of the local plane of incidence across the footprint also occur and can result in biased polarimetric measurements. A bias in the third Stokes parameter of as much as 0.4K is possible. Such effects may affect algorithms that use the third Stokes parameter to correct for Faraday rotation. Another issue associated with the antenna is sun glint. This is an issue determined by surface roughness and antenna sidelobes. Examples will be given for the random component (glint) for the case of the Aquarius antenna beams. Fortunately, the Aquarius beams mostly look to the dark side of the day-night termination, but during some portions of the year they will see sun-lighted ocean. In this case, glint could be an issue for the inner-most beam.

Dinnat, Emmanuel P.

A comparison of vector magnetograms from the Marshall Space Flight Center and Mees Solar Observatory

The paper compares completely independent vector magnetic field measurements from two very different polarimetric instruments. The Marshall Space Flight Center's (MSFC's) imaging vector magnetograph is based on a birefringent filter, routinely measuring all four Stokes parameters integrated over the filter bandpass (1/8 A) which is tunable across the Fe I 5250 line in 10 mA steps. The Haleakala Stokes Polarimeter of the Mees Solar Observatory (MSO) is based on a spectrometer, routinely measuring all four Stokes parameters of the Fe I 6302.5 line simultaneously and then spatially scanning to build up a vector magnetogram. Active region magnetic field data were obtained with both the MSFC and MSO systems on five days during June 1985. After interpolating the MSFC vector fields onto the more coarse spatial grid of MSO, a point-by-point comparison of the two vector fields is made for data obtained on two of these days (June 8 and 9). From this comparison it is concluded that the spatially-averaged line-of-sight components agree quite well, and that although the MSO spatial grid is coarser, the quality of the MSO image is better than that of the MSFC data because of better seeing conditions.

Ronan, R. S.

Determination of Atmospheric Aerosol Characteristics from the Polarization of Scattered Radiation

Aerosols affect the polarization of radiation in scattering, hence measured polarization can be used to infer the nature of the particles. Size distribution, particle shape, real and absorption parts of the complex refractive index affect the scattering. From Lorenz-Mie calculations of the 4-Stokes parameters as a function of scattering angle for various wavelengths the following polarization parameters were plotted: total intensity, intensity of polarization in plane of observation, intensity perpendicular to the plane of observation, polarization ratio, polarization (using all 4-Stokes parameters), plane of the polarization ellipse and its ellipticity. A six-component log-Gaussian size distribution model was used to study the effects of the nature of the polarization due to variations in the size distribution and complex refractive index. Though a rigorous inversion from measurements of scattering to detailed specification of aerosol characteristics is not possible, considerable information about the nature of the aerosols can be obtained. Only single scattering from aerosols was used in this paper. Also, the background due to Rayleigh gas scattering, the reduction of effects as a result of multiple scattering and polarization effects of possible ground background (airborne platforms) were not included.

Harris, F. S., Jr.

Optical Properties of Ice Particles in Young Contrails

The single-scattering properties of four types of ice crystals (pure ice crystals, ice crystals with an internal mixture of ice and black carbon, ice crystals coated with black carbon, and soot coated with ice) in young contrails are investigated at wavelengths 0.65 and 2.13 micrometers using Mie codes from coated spheres. The four types of ice crystals have distinct differences in their single-scattering properties because of the embedded black carbon. The bulk scattering properties of young contrails consisting of the four types of ice crystals are further investigated by averaging their single-scattering properties over a typical ice particle size distribution found in young contrails. The effect of the radiative properties of the four types of ice particles on the Stokes parameters I, Q, U, and V is also investigated for different viewing zenith angles and relative azimuth angles with a solar zenith angle of 30 degrees using a vector radiative transfer model based on the adding-doubling technique. The Stokes parameters at a wavelength of 0.65 micrometers show pronounced differences for the four types of ice crystals. Those at a wavelength of 2.13 micrometers show similar variations with the viewing zenith angle and relative azimuth angle, but their values are noticeably different.

Hong, Gang

Diagnostics of Magnetohydrodynamic Modes in the Interstellar Medium through Synchrotron Polarization Statistics

One of the biggest challenges in understanding magnetohydrodynamic (MHD) turbulence is identifying the plasma mode components from observational data. Previous studies on synchrotron polarization from the interstellar medium (ISM) suggest that the dominant MHD modes can be identified via statistics of Stokes parameters, which would be crucial for studying various ISM processes such as the scattering and acceleration of cosmic rays, star formation, and dynamo. In this paper, we present a numerical study of the synchrotron polarization analysis (SPA) method through systematic investigation of the statistical properties of the Stokes parameters. We derive the theoretical basis for our method from the fundamental statistics of MHD turbulence, recognizing that the projection of the MHD modes allows us to identify the modes dominating the energy fraction from synchrotron observations. Based on the discovery, we revise the SPA method using synthetic synchrotron polarization observations obtained from 3D ideal MHD simulations with a wide range of plasma parameters and driving mechanisms, and present a modified recipe for mode identification. We propose a classification criterion based on a new SPA+ fitting procedure, which allows us to distinguish between Alfvén mode and compressible/slow mode dominated turbulence. We further propose a new method to identify fast modes by analyzing the asymmetry of the SPA+ signature and establish a new asymmetry parameter to detect the presence of fast mode turbulence. Additionally, we confirm through numerical tests that the identification of the compressible and fast modes is not affected by Faraday rotation in both the emitting plasma and the foreground.

97 MATHEMATICS AND COMPUTING

Horizontal Wavenumber Spectra of Winds, Temperature and Trace Gases During the Pacific Exploratory Missions: Gravity Waves, Quasi-Two-Dimensional Turbulence, and Vortical Modes - 2

We examine the horizontal wavenumber spectra of horizontal velocity and potential temperature collected by aircraft above the Pacific Ocean to determine whether gravity waves, quasi-two-dimensional (Q-2-D) turbulence, or vortical modes dominate atmospheric fluctuations at scale sizes of 1-100 km and altitudes of 2-12 km. We conclude from the study of Doppler-shifting effects that Q-2-D turbulence and/or vortical modes are more prevalent than gravity waves over the ocean, except in the equatorial zone. The results are consistent with recent numerical simulations of Q-2-D turbulence, which show that the characteristic inverse cascade of energy is greatly facilitated by the presence of background rotation. Furthermore, a Stokes-parameter analysis reveals the general paucity of coherent wavelike motions, although specific cases of gravity-wave propagation are observed. Finally, a case study of a long flight segment displays a k(sup -3) horizontal velocity variance spectrum at scales longer than about 100 km. A Stokes-parameter analysis indicates that these large-scale fluctuations were likely due to vortical modes rather than inertio-gravity waves.

Cho, John Y. N.

Polarized views of the earth from orbital altitude

By means of a pair of boresighted and synchronized cameras fitted with orthogonally oriented polarizing filters and carried aboard the Space Shuttle, a large number of polarized images of the earth's surface have been obtained from orbital altitude. Selected pairs of images, both in color and in black and white, have been digitized and computer processed to yield analogous images in each of the three Stokes parameters necessary for characterizing the state of linear polarization of the emergent light. Many of the images show surface properties more distinctly in degree and plane of polarization than in simple intensity alone. However, the maximum information content as well as noise suppression and minimization of atmospheric interference, is achieved by proper combinations of the Stokes parameters. It is believed that these are the first, and certainly the most extensive, set of polarized images of the earth ever obtained from space.

Coulson, Kinsell L.

Thermal emission of nonspherical particles

The thermal emission of nonspherical particles is studied by applying the fluctuation dissipation theorem to calculate the Stokes' vector source terms in radiative transfer theory. Generally, all the four Stokes' parameters in the source term are nonzero and are proportional to the absorption coefficient in the backward direction. The measurements of active and passive remote sensing are related by showing that within the framework of radiative transfer theory, the emissivity of vertically and horizontally polarized waves can be expressed in terms of the bistatic scattering coefficients in the usual manner. In addition, the emissions of the third and fourth Stokes' parameters are also expressed in terms of bistatic scattering coefficients.

Tsang, L.

Contribution functions for Zeeman-split lines, and line formation in photospheric faculae

The transfer of polarized light in an inhomogeneous stellar atmosphere, and the formation of magnetically sensitive spectral lines, are discussed. A new method for the solution of the transfer equations is proposed. The method gives a natural definition of the contribution functions for Stokes' parameters, i.e., functions describing the contributions from different parts along the line-of-sight (LOS). The formalism includes all magneto-optical effects, and allows for an arbitrary variation of magnetic field, velocity field, temperature, density, etc., along the LOS. The formation of FeI lambda 5250.2 in photospheric faculae is described. A potential-field model of a facular element is presented, and spectra profiles and contribution functions are computed for the Stokes parameters I, Q, and V.

Vanballegooijen, A. A.