Satellite radar interferometry: Two-dimensional phase unwrapping
TL;DR: In this paper, an approach to 'unwrapping' the 2 pi ambiguities in the two-dimensional data set is presented, where it is found that noise and geometrical radar layover corrupt measurements locally, and these local errors can propagate to form global phase errors that affect the entire image.
Abstract: Interferometric synthetic aperture radar observations provide a means for obtaining high-resolution digital topographic maps from measurements of amplitude and phase of two complex radar images. The phase of the radar echoes may only be measured modulo 2 pi; however, the whole phase at each point in the image is needed to obtain elevations. An approach to 'unwrapping' the 2 pi ambiguities in the two-dimensional data set is presented. It is found that noise and geometrical radar layover corrupt measurements locally, and these local errors can propagate to form global phase errors that affect the entire image. It is shown that the local errors, or residues, can be readily identified and avoided in the global phase estimation. A rectified digital topographic map derived from the unwrapped phase values is presented.
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TL;DR: The Shuttle Radar Topography Mission produced the most complete, highest-resolution digital elevation model of the Earth, using dual radar antennas to acquire interferometric radar data, processed to digital topographic data at 1 arc sec resolution.
Abstract: [1] The Shuttle Radar Topography Mission produced the most complete, highest-resolution digital elevation model of the Earth. The project was a joint endeavor of NASA, the National Geospatial-Intelligence Agency, and the German and Italian Space Agencies and flew in February 2000. It used dual radar antennas to acquire interferometric radar data, processed to digital topographic data at 1 arc sec resolution. Details of the development, flight operations, data processing, and products are provided for users of this revolutionary data set.
5,019 citations
Cites methods from "Satellite radar interferometry: Two..."
...This process is called phase unwrapping, and a number of algorithms have been invented to optimize the process [e.g., Goldstein et al., 1988 ]....
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01 Oct 2000
TL;DR: The most complete digital topographic map of Earth was made by the Shuttle Radar Topography Mission (SRTM) as discussed by the authors, which used a single-pass radar interferometer to produce a digital elevation model (DEM) of the Earth's land surface between about 60 deg north and 56 deg south latitude.
Abstract: On February 22, 2000 Space Shuttle Endeavour landed at Kennedy Space Center, completing the highly successful 11-day flight of the Shuttle Radar Topography Mission (SRTM). Onboard were over 300 high-density tapes containing data for the highest resolution, most complete digital topographic map of Earth ever made. SRTM is a cooperative project between NASA and the National Imagery and Mapping Agency (NIMA) of the U.S. Department of Defense. The mission was designed to use a single-pass radar interferometer to produce a digital elevation model (DEM) of the Earth's land surface between about 60 deg north and 56 deg south latitude. When completed, the DEM will have 30 m pixel spacing and about 15 m vertical accuracy. Two orthorectified image mosaics (one from the ascending passes with illumination from the southeast and one from descending passes with illumination from the southwest) will also be produced.
3,137 citations
01 Mar 2000
TL;DR: In this paper, the authors present a review of the techniques of interferometry, systems and limitations, and applications in a rapidly growing area of science and engineering, including cartography, geodesy, land cover characterization, and natural hazards.
Abstract: Synthetic aperture radar interferometry is an imaging technique for measuring the topography of a surface, its changes over time, and other changes in the detailed characteristic of the surface. By exploiting the phase of the coherent radar signal, interferometry has transformed radar remote sensing from a largely interpretive science to a quantitative tool, with applications in cartography, geodesy, land cover characterization, and natural hazards. This paper reviews the techniques of interferometry, systems and limitations, and applications in a rapidly growing area of science and engineering.
3,042 citations
Cites background or methods from "Satellite radar interferometry: Two..."
...This figure shows a profile of the terrain at constant azimuth, with the radar flight track into the page....
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...In interferometry, the complex phasor information of one image is multiplied by the complex conjugate phasor information of the second image to form an “interferogram,” effectively canceling the common backscatter phase in each resolution element, but leaving a phase term proportional to the…...
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TL;DR: In this paper, a review of the use of radar interferometry to measure changes in the Earth's surface has exploded in the early 1990s, and a practical summary explains the techniques for calculating and manipulating interferograms from various radar instruments, including the four satellites currently in orbit: ERS-1, ERS2, JERS-1 and RADARSAT.
Abstract: Geophysical applications of radar interferometry to measure changes in the Earth's surface have exploded in the early 1990s. This new geodetic technique calculates the interference pattern caused by the difference in phase between two images acquired by a spaceborne synthetic aperture radar at two distinct times. The resulting interferogram is a contour map of the change in distance between the ground and the radar instrument. These maps provide an unsurpassed spatial sampling density (∼100 pixels km−2), a competitive precision (∼1 cm), and a useful observation cadence (1 pass month−1). They record movements in the crust, perturbations in the atmosphere, dielectric modifications in the soil, and relief in the topography. They are also sensitive to technical effects, such as relative variations in the radar's trajectory or variations in its frequency standard. We describe how all these phenomena contribute to an interferogram. Then a practical summary explains the techniques for calculating and manipulating interferograms from various radar instruments, including the four satellites currently in orbit: ERS-1, ERS-2, JERS-1, and RADARSAT. The next chapter suggests some guidelines for interpreting an interferogram as a geophysical measurement: respecting the limits of the technique, assessing its uncertainty, recognizing artifacts, and discriminating different types of signal. We then review the geophysical applications published to date, most of which study deformation related to earthquakes, volcanoes, and glaciers using ERS-1 data. We also show examples of monitoring natural hazards and environmental alterations related to landslides, subsidence, and agriculture. In addition, we consider subtler geophysical signals such as postseismic relaxation, tidal loading of coastal areas, and interseismic strain accumulation. We conclude with our perspectives on the future of radar interferometry. The objective of the review is for the reader to develop the physical understanding necessary to calculate an interferogram and the geophysical intuition necessary to interpret it.
2,319 citations
Cites background from "Satellite radar interferometry: Two..."
...Several solutions have been proposed to avoid integrating errors [Ghiglia et al., 1987], such as detecting residuals where the integral along a closed path is not zero and avoiding them [Goldstein et al., 1988]....
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...Phase unwrapping is a very active field, as measured by the number of recent publications [Ghiglia et al., 1987; Goldstein et al., 1988; Ghiglia and Romero, 1994; Griffiths and Wilkinson, 1994; Lin et al., 1994; Pandit et al., 1994; Tarayre, 1994; Zebker et al., 1994b; Marroquin and Rivera, 1995; Song et al., 1995; Fornaro et al., 1996; Pritt, 1996; Ghiglia and Pritt, 1998]....
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..., 1987], such as detecting residuals where the integral along a closed path is not zero and avoiding them [Goldstein et al., 1988]....
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...…of creating ghost lines, etc. Phase unwrapping is a very active field, as measured by the number of recent publications [Ghiglia et al., 1987; Goldstein et al., 1988; Ghiglia and Romero, 1994; Griffiths and Wilkinson, 1994; Lin et al., 1994; Pandit et al., 1994; Tarayre, 1994; Zebker et al.,…...
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TL;DR: It is found that there is decorrelation increasing with time but that digital terrain model generation remains feasible and such a technique could provide a global digital terrain map.
Abstract: A radar interferometric technique for topographic mapping of surfaces, implemented utilizing a single synthetic aperture radar (SAR) system in a nearly repeating orbit, is discussed. The authors characterize the various sources contributing to the echo correlation statistics, and isolate the term which most closely describes surficial change. They then examine the application of this approach to topographic mapping of vegetated surfaces which may be expected to possess varying backscatter over time. It is found that there is decorrelation increasing with time but that digital terrain model generation remains feasible. The authors present such a map of a forested area in Oregon which also includes some nearly unvegetated lava flows. Such a technique could provide a global digital terrain map. >
2,167 citations
Cites methods from "Satellite radar interferometry: Two..."
...Topographic maps using this technique have been demonstrated by Goldstein et al. [ 8 ], Gabriel et al. [9], and Gabriel and Goldstein [3]....
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References
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01 May 1981
TL;DR: Specific conditions under which a sequence can be exactly reconstructed from phase are reviewed, both for one-dimensional and multi-dimensional sequences, and algorithms for both approximate and exact reconstruction of signals from phase information are presented.
Abstract: In the Fourier representation of signals, spectral magnitude and phase tend to play different roles and in some situations many of the important features of a signal are preserved if only the phase is retained. Furthermore, under a variety of conditions, such as when a signal is of finite length, phase information alone is sufficient to completely reconstruct a signal to within a scale factor. In this paper, we review and discuss these observations and results in a number of different contexts and applications. Specifically, the intelligibility of phase-only reconstruction for images, speech, and crystallographic structures are illustrated. Several approaches to justifying the relative importance of phase through statistical arguments are presented, along with a number of informal arguments suggesting reasons for the importance of phase. Specific conditions under which a sequence can be exactly reconstructed from phase are reviewed, both for one-dimensional and multi-dimensional sequences, and algorithms for both approximate and exact reconstruction of signals from phase information are presented. A number of applications of the observations and results in this paper are suggested.
1,850 citations
TL;DR: In this article, the authors reported the production of high-resolution topographic maps derived from interferometric synthetic aperture radar observations of the earth, which is related to the stereo technique in that the terrain is viewed at two different angles.
Abstract: The production of high-resolution topographic maps derived from interferometric synthetic aperture radar observations of the earth is reported. Topographic maps are typically determined from stereo-pair optical photographs. Vertical relief causes the same terrain to appear in a slightly different projection for differing look angles, and this shift in appearance is interpreted in terms of the height of the terrain. The radar interferometric approach is related to the stereo technique in that the terrain is viewed at two different angles; however, in this case, the angular separation of the antennas is extremely small, on the order of a milliradian or less, as compared to tens of degrees for the optical case. Thus, the geometrical distortion and subsequent rectification correction algorithms are much less severe in the reduction of interferometric data.
1,048 citations
01 Jun 1974
TL;DR: Radar used specifically for this purpose employs synthetic-aperture techniques to obtain fine resolution measurement in two dimensions and interferometry to obtain the third measurement.
Abstract: The production of topographic maps requires two kinds of information. First, the detail to be placed on the map sheet must be identified. Second, the positions of the various objects and features must be measured in three dimensions. Current airborne radar technology provides the means to satisfy both of these requirements in adverse weather and at any time, day or night. Radar used specifically for this purpose employs synthetic-aperture techniques to obtain fine resolution measurement in two dimensions and interferometry to obtain the third measurement.
661 citations
TL;DR: A new phase unwrapping algorithm is proposed that combines the information contained in both the phase derivative and the principal value of the phase into an adaptive numerical integration scheme.
Abstract: A new phase unwrapping algorithm is proposed that combines the information contained in both the phase derivative and the principal value of the phase into an adaptive numerical integration scheme. This new algorithm has proven itself to be very reliable and it can be easily incorporated in standard homomorphic signal processors.
465 citations
01 Jul 1972
TL;DR: In this article, radio interferometry is used for the measurement of the surface topography of the Moon without regard for unambiguously-identified features, for any lunar surface element that yields a recognizable radar echo.
Abstract: Radio interferometry is a new technique for the measurement of the surface topography of the Moon. Elevation data may be obtained directly without regard for unambiguously-identified features, for any lunar surface element that yields a recognizable radar echo. A program has been undertaken at the Haystack Observatory for the topographic mapping of the major part of the lunar Earthside hemisphere. Some results are presented for the Alphonsus-Arzachel region, showing evidence for a late lava flow of a viscosity and, hence, presumably a chemical composition, differing from that of near-by mare surfaces.
57 citations