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The Fourier-Kelvin Stellar Interferometer Mission Concept

The Fourier-Kelvin Stellar Interferometer (FKSI) is a mission concept for an imaging interferometer for the mid-infrared spectral region (5-30 microns). FKSI is conceived as a scientific and technological precursor to TPF as well as Space Infrared Interferometric Telescope (SPIRIT), Submillimeter Probe Evolution of Cosmic Structure (SPECS), and Single Aperture for Infrared Observatory (SAFIR). It will also be a high angular resolution system complementary to Next Generation Space Telescope (NGST). The scientific emphasis of the mission is on the evolution of protostellar systems, from just after the collapse of the precursor molecular cloud core, through the formation of the disk surrounding the protostar, the formation of planets in the disk, and eventual dispersal of the disk material. FKSI will also search for brown dwarfs and Jupiter mass and smaller planets, and could also play a very powerful role in the investigation of the structure of active galactic nuclei and extra-galactic star formation. We are in the process of studying alternative interferometer architectures and beam combination techniques, and evaluating the relevant science and technology tradeoffs. Some of the technical challenges include the development of the cryocooler systems necessary for the telescopes and focal plane array, light and stiff but well-damped truss systems to support the telescopes, and lightweight and coolable optical telescopes. The goal of the design study is to determine if a mid-infrared interferometry mission can be performed within the cost and schedule requirements of a Discovery class mission. At the present time we envision the FKSI as comprised of five one meter diameter telescopes arranged along a truss structure in a linear non-redundant array, cooled to 35 K. A maximum baseline of 20 meters gives a nominal resolution of 26 mas at 5 microns. Using a Fizeau beam combination technique, a simple focal plane camera could be used to obtain both Fourier and spectral data simultaneously for a given orientation of the array. The spacecraft will be rotated to give sufficient Fourier data to reconstruct complex images of a broad range of astrophysical sources.

Danchi, W. C.↗

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.

Smith, Jeffrey, S.↗

Repeat-Orbit Interferometric Precision Measurement of Mercury Obliquity

Repeat-orbit or time-delayed interferometry has been widely used for SAR (Synthetic Aperture Radar)-based observations of such terrestrial phenomena as flow of glaciers and post-seismic displacements from radar on Earth-orbiting satellites and spacecraft. Repeat-orbit interferometry has also obtained fringes while investigating the measurement of topography of the Moon from Arecibo radar observations. Because of the unique spin-orbit resonance of Mercury, the locus of the sub-radar point on Mercury crosses over itself many times per year. Moreover, the locus of the sub-radar track repeats these crossings from year to year over many years. Given the proper geometry, these subradar point crossings offer the opportunity for interplanetary repeat-orbit interferometry via Earth-based radar observations. The ephemerides of Mercury and Earth, and the orientation of the Earth, are all known to sufficiently high-precision with respect to 'inertial space' to enable this kind of interferometry. This capability would merely be a curiosity, since Earth-based radar lacks the signal-to-noise to measure planetary-scale topography, except that the technique can be used to measure Mercury's obliquity (and possibly the forced libration in longitude). Combining very accurate measurements of the obliquity and the forced libration in longitude with Mercury-orbiter-based measurements of the low-order and degree Mercury gravity field can place constraints on the size and state of Mercury's fluid core. Additional information is contained in the original extended abstract.

Slade, M. A.↗

Radar Observations of Near Earth Asteroids 6489 Golevka and 4197 (1982 TA)

Radar observations of two near-Earth asteroids were performed using a bi-static radar technique with Kashima 34-m antenna and Usuda 64-m antenna as receiving stations and Goldstone 70-m antenna as a transmitting station. The asteroid 6489 Golevka was observed on June 15, 1995 when its distance from the Earth became 0.048 AU and the radar echo from the asteroid was detected from the data observed with Kashima 34-m antenna. The success of the trans-continental bistatic radar observations became the first detection of a radar echo from a solar system object beyond Moon in Japan. The asteroid 4197 (1982 TA) was observed on October 24, 1996 when its distance to the Earth became 0.086 AU. The radar echo signal from the asteroid was detected from both of the data observed at Kashima and at Usuda. The received signal was coherently sampled and recorded at both stations. By using these data, interferometric data analysis was examined.

Koyama, Yasuhiro↗

Formation Flying Design and Applications in Weak Stability Boundary Regions

Weak Stability regions serve as superior locations for interferometric scientific investigations. These regions are often selected to minimize environmental disturbances and maximize observing efficiency. Design of formations in these regions are becoming ever more challenging as more complex missions are envisioned. The development of algorithms to enable the capability for formation design must be further enabled to incorporate better understanding of WSB solution space. This development will improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple formation missions in WSB regions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes both algorithm and software development. The Constellation-X, Maxim, and Stellar Imager missions are examples of the use of improved numerical methods for attaining constrained formation geometries and controlling their dynamical evolution. This paper presents a survey of formation missions in the WSB regions and a brief description of the formation design using numerical and dynamical techniques.

Folta, David↗

Performance evaluation of the JPL TOPSAR system: An across-track interferometric SAR system for topographic mapping

An across-track interferometric (XTI) SAR has the capability of determining the three dimensional target location from the recorded radar echos thus providing high spatial resolution both horizontally and vertically. The output of an XTI SAR will typically include both a radar backscatter map and a digital elevation model (DEM). The accuracy of the derived DEM is determined by factors such as data acquisition geometry, signal-to-noise ratio, knowledge of platform position and attitude as well as the accuracy of the processing system. In the summer of 1992 the authors acquired TOPSAR data over the Ft. Irwin area in California, a desert area with significant relief (height standard deviation 150 m). Very accurate DEM's have been derived for this area by the Topographic Engineering Center (TEC) using digital correlation methods on 1:20,000 scale digitized photographs. Corner reflectors were deployed in the area, and their locations were determined to cm accuracies by the Defense Mapping Agency (DMA) using differential GPS techniques. DEM's generated from the acquired radar data have been rotated and translated to overlay the reference DEM's provided by TEC. A detailed description of the errors and their characteristics will be given. The standard deviations of the radar data sets we acquired measured over a 5.6 by 7 km area were 1.9 and 2.3 m. The corresponding numbers for flat areas were 1.1 and 2.0 m and for mountain areas 3.3 and 2.2 m.

Madsen, Soren N.↗

Radiometric correction of atmospheric path length fluctuations in interferometric experiments

To support very long baseline interferometric experiments, a system has been developed for estimating atmospheric water vapor path delay. The system consists of dual microwave radiometers, one operating at 20.7 GHz and the other at 31.4 GHz. The measured atmospheric brightness temperatures at these two frequencies yield the estimate of the precipitable water present in both vapor and droplets. To determine the accuracy of the system, a series of observations were undertaken, comparing the outputs of two water vapor radiometers with the phase variation observed with two connected elements of the very large array (VLA). The results show that: (1) water vapor fluctuations dominate the residual VLA phase and (2) the microwave radiometers can measure and correct these effects. The rms phase error after correction is typically 15 deg at a wavelength of 6 cm, corresponding to an uncertainty in the path delay of 0.25 cm. The residual uncertainty is consistent with the stability of the microwave radiometer but is still considerably larger than the stability of the VLA. The technique is less successful under conditions of heavy cloud.

Resch, G. M.↗

Measurement and Mitigation of the Ionosphere in L-Band Interferometric SAR Data

Satellite-based repeat-pass Interferometric Synthetic Aperture Radar (InSAR) provides a synoptic high spatial resolution perspective of Earth's changing surface, permitting one to view large areas quickly and efficiently. By measuring relative phase change from one observation to the next on a pixel-by-pixel basis, maps of deformation and change can be derived. Variability of the atmosphere and the ionosphere leads to phase/time delays that are present in the data that can mask many of the subtle deformation signatures of interest, so methods for mitigation of these effects are important. Many of these effects have been observed in existing ALOS PALSAR data, and studies are underway to characterize and mitigate the ionosphere using these data. Since the ionosphere is a dispersive medium, it is possible in principle distinguish the ionospheric signatures from the non-dispersive effects of deformation and the atmosphere. In this paper, we describe a method for mapping the ionosphere in InSAR data based on a multi-frequency split-spectrum processing technique.

Rosen, Paul A.↗

Integrated Analysis of Interferometric SAR, Satellite Altimetry and Hydraulic Modeling to Quantify Louisiana Wetland Dynamics

Wetland loss in Louisiana has been accelerating due primarily to anthropogenic and nature processes, and is being advocated as a problem with national importance. Accurate measurement or modeling of wetland-wide water level changes, its varying extent, its storage and discharge changes resulting in part from sediment loads, erosion and subsidence are fundamental to assessment of hurricane-induced flood hazards and wetland ecology. Here, we use innovative method to integrate interferometric SAR (InSAR) and satellite radar altimetry for measuring absolute or geocentric water level changes and applied the methodology to remote areas of swamp forest in coastal Louisiana. Coherence analysis of InSAR pairs suggested that the HH polarization is preferred for this type of observation, and polarimetric analysis can help to identi:fy double-bonnce backscattering areas in the wetland. Envisat radar altimeter-measured 18- Hz (along-track sampling of 417 m) water level data processed with regional stackfile method have been used to provide vertical references for water bodies separated by levees. The high-resolution (approx.40 m) relative water changes measured from ALOS PALSAR L-band and Radarsat-l C-band InSAR are then integrated with Envisat radar altimetry to obtain absolute water level. The resulting water level time series were validated with in situ gauge observations within the swamp forest. Furthermore, we compare our water elevation changes with 2D flood modeling from LISFLOOD hydrodynamic model. Our study demonstrates that this new technique allows retrospective reconstruction and concurrent monitoring of water conditions and flow dynamics in wetlands, especially those lacking gauge networks.

Lee, Hyongki↗

Mapping of sea bottom topography

Under suitable conditions the bottom topography of shallow seas is visible in remote sensing radar imagery. Two experiments were performed to establish which remote sensing technique or combination yields optimal imaging of bottom topography and which hydro-meteorological conditions are favorable. A further goal is to gain experience with these techniques. Two experiments were performed over an area in the North Sea near the measuring platform Meetpost Noordwijk (MPN). The bottom topography in the test area is dominated by sand waves. The crests of the sand waves are perpendicular to the coast line and the dominating (tidal-)current direction. A 4x4 sq km wide section of the test area was studied in more detail. The first experiment was undertaken on 16 Aug. 1989. During the experiment the following remote sensing instruments were used: Landsat-Thematic Mapper, and NASA/JPL Airborne Imaging Radar (AIR). The hydro-meteorological conditions; current, wind, wave, and air and water temperature were monitored by MPN, a ship of Rijkswaterstaat (the OCTANS), and a pitch-and-roll WAVEC-buoy. The second experiment took place on 12 July 1992. During this experiment data were collected with the NASA/JPL polarimetric synthetic aperture radar (SAR), and a five-band helicopter-borne scatterometer. Again the hydro-meteorological conditions were monitored at MPN and the OCTANS. Furthermore, interferometric radar data were collected.

Calkoen, C. J.↗

Development of advanced seal verification

The purpose of this research is to develop a technique to monitor and insure seal integrity with a sensor that has no active elements to burn-out during a long duration activity, such as a leakage test or especially during a mission in space. The original concept proposed is that by implementing fiber optic sensors, changes in the integrity of a seal can be monitored in real time and at no time should the optical fiber sensor fail. The electrical components which provide optical excitation and detection through the fiber are not part of the seal; hence, if these electrical components fail, they can be easily changed without breaking the seal. The optical connections required for the concept to work does present a functional problem to work out. The utility of the optical fiber sensor for seal monitoring should be general enough that the degradation of a seal can be determined before catastrophic failure occurs and appropriate action taken. Two parallel efforts were performed in determining the feasibility of using optical fiber sensors for seal verification. In one study, research on interferometric measurements of the mechanical response of the optical fiber sensors to seal integrity was studied. In a second study, the implementation of the optical fiber to a typical vacuum chamber was implemented and feasibility studies on microbend experiments in the vacuum chamber were performed. Also, an attempt was made to quantify the amount of pressure actually being applied to the optical fiber using finite element analysis software by Algor.

Workman, Gary L.↗

Wideband Interferometric Sensing and Imaging Polarimetry

Wideband Interferometric Sensing and Imaging Polarimetry (WISIP) has become an important, indispensible tool in wide area military surveillance and global environmental monitoring of the terrestrial and planetary covers. It enables dynamic, real time optimal feature extraction of significant characteristics of desirable targets and/or target sections with simultaneous suppression of undesirable background clutter and propagation path speckle at hitherto unknown clarity and never before achieved quality. WISIP may be adopted to the detection, recognition, and identification (DRI) of any stationary, moving or vibrating targets or distributed scatterer segments versus arbitrary stationary, dynamical changing and/or moving geo-physical/ecological environments, provided the instantaneous 2x2 phasor and 4x4 power density matrices for forward propagation/backward scattering, respectively, can be measured with sufficient accuracy. For example, the DRI of stealthy, dynamically moving inhomogeneous volumetric scatter environments such as precipitation scatter, the ocean/sea/lake surface boundary layers, the littoral coastal surf zones, pack ice and snow or vegetative canopies, dry sands and soils, etc. can now be successfully realized. A comprehensive overview is presented on how these modern high resolution/precision, complete polarimetric co-registered signature sensing and imaging techniques, complemented by full integration of novel navigational electronic tools, such as DGPS, will advance electromagnetic vector wave sensing and imaging towards the limits of physical realization. Various examples utilizing the most recent image data take sets of airborne, space shuttle, and satellite imaging systems demonstrate the utility of WISIP.

Verdi, James Salvatore↗

Radiative transfer in planetary atmospheres

Rheoretical techniques and observations at millimeter wavelengths are combined to study the atmosphere of planets and comets, planetary and satellite regoliths, and planetary rings. Analysis of the very high quality data on the 18 cm OH line observed in recent comets continued. The high spectral resolution and high signal-to-noise make these lines ideal for study of the kinematics in cometary comae. A model of the collisional quenching of the inversion of the lambda doublet responsible for the OH radio emission has been developed by P. Schloerb. For conditions appropriate to Halley's Comet, collisional quenching should lead radio observers to systematically underestimate the OH parent production rate by a factor of approximately 3 relative to its actual value, which is very consistent with differences observed between radio and ultraviolet-derived production rates. Modeling is likewise continuing for the profiles observed in the lowest rotational transition of HCN in Comet Halley in order to better estimate the excitation and hence the abundance of HCN, as well as the kinematics of parent molecules in the coma. A collaborative program to combine data from the 14 m antenna with interferometric data abtained at the Hat Creek Radio Observatory is allowing aperture synthesis mapping of Venus in the CO J=1-0 line.

Irvine, William M.↗

Digital cartography of Io

A high resolution controlled mosaic of the hemisphere of Io centered on longitude 310 degrees is produced. Digital cartographic techniques were employed. Approximately 80 Voyager 1 clear and blue filter frames were utilized. This mosaic was merged with low-resolution color images. This dataset is compared to the geologic map of this region. Passage of the Voyager spacecraft through the Io plasma torus during acquisition of the highest resolution images exposed the vidicon detectors to ionized radiation, resulting in dark-current buildup on the vidicon. Because the vidicon is scanned from top to bottom, more charge accumulated toward the bottom of the frames, and the additive error increases from top to bottom as a ramp function. This ramp function was removed by using a model. Photometric normalizations were applied using the Minnaert function. An attempt to use Hapke's photometric function revealed that this function does not adequately describe Io's limb darkening at emission angles greater than 80 degrees. In contrast, the Minnaert function accurately describes the limb darkening up to emission angles of about 89 degrees. The improved set of discrete camera angles derived from this effort will be used in conjunction with the space telemetry pointing history file (the IPPS file), corrected on 4 or 12 second intervals to derive a revised time history for the pointing of the Infrared Interferometric Spectrometer (IRIS). For IRIS observations acquired between camera shutterings, the IPPS file can be corrected by linear interpolation, provided that the spacecraft motions were continuous. Image areas corresponding to the fields of view of IRIS spectra acquired between camera shutterings will be extracted from the mosaic to place the IRIS observations and hotspot models into geologic context.

Mcewen, Alfred S.↗

A Solar System Survey of Forced Librations in Longitude

Physical librations in longitude are forced periodic variations of a body's rotation rate. If the torque producing the librations can be calculated, then observations of the phase and amplitude of librations can provide information on mass distribution, and effective strength of the body. In the near future prospects for observing physical librations look quite promising. Radio interferometric observations of Venus and Mercury may yield sufficiently accurate rotational observations that librations there may be visible. Range measurements from Earth to networks of landed instrument packages on Mars are likely to yield librational data there as well. We compute expected libration amplitudes from physical and orbital parameters of a set of planets and satellites partially motivated by a desire to identify candidates for future observations. Solar system bodies occupy one of three general rotation states: non-resonant states, resonant states, and the synchronous resonant state. Analytical treatments of forced librations were initially motivated by the Moon. Lunar librations were predicted by Newton, first detected telescopically by Bessel, and definitively resolved through lunar laser ranging which has led to quite thorough analysis of of librations for the synchronous case. The synchronous resonant state is commonly observed among satellites. The only known body to exist in a non-synchronous resonance is Mercury which exists in a 3:2 resonance, completing three rotations for every two revolutions about the sun. The analysis of Goldreich and Peale has lead to improved understanding of the general case of half integer resonance states. The dynamics of forced librations in non-resonant rotators has received less attention. While there are few cases in which non-resonant forced librations have been observed, Earth is an important exception, and current observing techniques may have the capacity to detect them on Venus. A comprehensive observing program spanning a range of solar system bodies can address an array of geophysical issues involving interior mass distribution of planets, satellites, and asteroids. Calculations of expected librations can supply amplitude estimates helpful in identifying the likelihood of detecting librations observationally. We present a survey of expected libration amplitudes for a subset of solar system bodies, identifying those bodies with amplitudes likely to be detectable, and commenting on spin state, and radial structure implications.

Comstock, R. L.↗

High Resolution Imaging of Circumstellar Disks at Millimeter Wavelengths

Our program uses the techniques of millimeter interferometry to make high resolution observations of dust continuum emission to study the structure of protoplanetary disks and debris disks around nearby stars. Observations of dust emission at these wavelengths are advantageous because the dust emission is generally optically thin and directly proportional to mass, and contrast with stellar photospheres is not a problem. We are using of several observational facilities, including (1) the Very Large Array (VLA) of the National Radio Astronomy Observatories, (2) the Plateau de Bure Interferometer (PdBI) of the Institut de RadioAstronomie Millimetrique, and (3) the Submillimeter Array (SMA), now under construction by the Smithsonian Astrophysical Observatory and Academia Sinica (Taiwan). In the past year, we have accomplished the following (more details below): (1) We continued work on our 'low resolution' VLA survey of disks in Herbig Ae star and binary systems, primarily to identify candidates for higher resolution follow-up. We have submitted a paper for publication on the detailed analysis of the structure of the disk around CQ Tauri; (2) We completed analysis of our PdBI observations of the debris disk around Vega, and we presented these results at (1) the 199th AAS meeting in Washington, DC, and (2) a symposium in memory of Fred Gillett on Debris Disks and the Formation of Planets, in Tucson, AZ; (3) We continue commissioning observations with the SMA, which include the first ever interferometric images in the 850 micron wavelength band, in preparation for eventually imaging debris disks.

Wilner, David J.↗

Self-Referencing Hartmann Test for Large-Aperture Telescopes

A method is proposed for end-to-end, full aperture testing of large-aperture telescopes using an innovative variation of a Hartmann mask. This technique is practical for telescopes with primary mirrors tens of meters in diameter and of any design. Furthermore, it is applicable to the entire optical band (near IR, visible, ultraviolet), relatively insensitive to environmental perturbations, and is suitable for ambient laboratory as well as thermal-vacuum environments. The only restriction is that the telescope optical axis must be parallel to the local gravity vector during testing. The standard Hartmann test utilizes an array of pencil beams that are cut out of a well-corrected wavefront using a mask. The pencil beam array is expanded to fill the full aperture of the telescope. The detector plane of the telescope is translated back and forth along the optical axis in the vicinity of the nominal focal plane, and the centroid of each pencil beam image is recorded. Standard analytical techniques are then used to reconstruct the telescope wavefront from the centroid data. The expansion of the array of pencil beams is usually accomplished by double passing the beams through the telescope under test. However, this requires a well-corrected, autocollimation flat, the diameter or which is approximately equal to that of the telescope aperture. Thus, the standard Hartmann method does not scale well because of the difficulty and expense of building and mounting a well-corrected, large aperture flat. The innovation in the testing method proposed here is to replace the large aperture, well-corrected, monolithic autocollimation flat with an array of small-aperture mirrors. In addition to eliminating the need for a large optic, the surface figure requirement for the small mirrors is relaxed compared to that required of the large autocollimation flat. The key point that allows this method to work is that the small mirrors need to operate as a monolithic flat only with regard to tip/tilt and not piston because in collimated space piston has no effect on the image centroids. The problem of aligning the small mirrors in tip/tilt requires a two-part solution. First, each mirror is suspended from a two-axis gimbal. The orientation of the gimbal is maintained by gravity. Second, the mirror is aligned such that the mirror normal is parallel to gravity vector. This is accomplished interferometrically in a test fixture. Of course, the test fixture itself needs to be calibrated with respect to gravity.

Korechoff, Robert P.↗

Imaging Radar in the Mojave Desert-Death Valley Region

The Mojave Desert-Death Valley region has had a long history as a test bed for remote sensing techniques. Along with visible-near infrared and thermal IR sensors, imaging radars have flown and orbited over the area since the 1970's, yielding new insights into the geologic applications of these technologies. More recently, radar interferometry has been used to derive digital topographic maps of the area, supplementing the USGS 7.5' digital quadrangles currently available for nearly the entire area. As for their shorter-wavelength brethren, imaging radars were tested early in their civilian history in the Mojave Desert-Death Valley region because it contains a variety of surface types in a small area without the confounding effects of vegetation. The earliest imaging radars to be flown over the region included military tests of short-wavelength (3 cm) X-band sensors. Later, the Jet Propulsion Laboratory began its development of imaging radars with an airborne sensor, followed by the Seasat orbital radar in 1978. These systems were L-band (25 cm). Following Seasat, JPL embarked upon a series of Space Shuttle Imaging Radars: SIRA (1981), SIR-B (1984), and SIR-C (1994). The most recent in the series was the most capable radar sensor flown in space and acquired large numbers of data swaths in a variety of test areas around the world. The Mojave Desert-Death Valley region was one of those test areas, and was covered very well with 3 wavelengths, multiple polarizations, and at multiple angles. At the same time, the JPL aircraft radar program continued improving and collecting data over the Mojave Desert Death Valley region. Now called AIRSAR, the system includes 3 bands (P-band, 67 cm; L-band, 25 cm; C-band, 5 cm). Each band can collect all possible polarizations in a mode called polarimetry. In addition, AIRSAR can be operated in the TOPSAR mode wherein 2 antennas collect data interferometrically, yielding a digital elevation model (DEM). Both L-band and C-band can be operated in this way, with horizontal resolution of about 5 m and vertical errors less than 2 m. The findings and developments of these earlier investigations are discussed.

Farr, Tom G.↗