There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[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.

/pdf/the-shuttle-radar-topography-mission-4x49lt5xnj.pdf

The Shuttle Radar Topography Mission

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.

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.

/pdf/synthetic-aperture-radar-interferometry-28lm7jf0if.pdf

Synthetic aperture radar interferometry

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.

/pdf/radar-interferometry-and-its-application-to-changes-in-the-2xi2itqotn.pdf

Radar interferometry and its application to changes in the Earth's surface

Synthetic Aperture Radar (SAR) has been widely used for Earth remote sensing for more than 30 years. It provides high-resolution, day-and-night and weather-independent images for a multitude of applications ranging from geoscience and climate change research, environmental and Earth system monitoring, 2-D and 3-D mapping, change detection, 4-D mapping (space and time), security-related applications up to planetary exploration. With the advances in radar technology and geo/bio-physical parameter inversion modeling in the 90s, using data from several airborne and spaceborne systems, a paradigm shift occurred from the development driven by the technology push to the user demand pull. Today, more than 15 spaceborne SAR systems are being operated for innumerous applications. This paper provides first a tutorial about the SAR principles and theory, followed by an overview of established techniques like polarimetry, interferometry and differential interferometry as well as of emerging techniques (e.g., polarimetric SAR interferometry, tomography and holographic tomography). Several application examples including the associated parameter inversion modeling are provided for each case. The paper also describes innovative technologies and concepts like digital beamforming, Multiple-Input Multiple-Output (MIMO) and bi- and multi-static configurations which are suitable means to fulfill the increasing user requirements. The paper concludes with a vision for SAR remote sensing.

/pdf/a-tutorial-on-synthetic-aperture-radar-1v8k9pqokm.pdf

A tutorial on synthetic aperture radar

The authors examine the role of polarimetry in synthetic aperture radar (SAR) interferometry. They first propose a general formulation for vector wave interferometry that includes conventional scalar interferometry as a special case. Then, they show how polarimetric basis transformations can be introduced into SAR interferometry and applied to form interferograms between all possible linear combinations of polarization states. This allows them to reveal the strong polarization dependency of the interferometric coherence. They then solve the coherence optimization problem involving maximization of interferometric coherence and formulate a new coherent decomposition for polarimetric SAR interferometry that allows the separation of the effective phase centers of different scattering mechanisms. A simplified stochastic scattering model for an elevated forest canopy is introduced to demonstrate the effectiveness of the proposed algorithms. In this way, they demonstrate the importance of wave polarization for the physical interpretation of SAR interferograms. They investigate the potential of polarimetric SAR interferometry using results from the evaluation of fully polarimetric interferometric shuttle imaging radar (SIR)-C/X-SAR data collected during October 8-9, 1994, over the SE Baikal Lake Selenga delta region of Buriatia, Southeast Siberia, Russia.

Polarimetric SAR interferometry

Examines the application of single-baseline polarimetric SAR interferometry to the remote sensing and measurement of structure over forested terrain. For this, a polarimetric coherent scattering model for vegetation cover suitable for the estimation of forest parameters from interferometric observables is introduced, discussed and validated. Based on this model, an inversion algorithm which allows the estimation of forest parameters such as tree height, average extinction, and underlying topography from single-baseline fully polarimetric interferometric data is addressed. The performance of the inversion algorithm is demonstrated using fully polarimetric single baseline experimental data acquired by DLR's E-SAR system at L-band.

/pdf/single-baseline-polarimetric-sar-interferometry-2qev4xmjqk.pdf

Single-baseline polarimetric SAR interferometry

In this paper, we examine the role of polarimetry in synthetic aperture radar (SAR) interferometry. We first propose a general formulation for vector wave interferometry that includes conventional scalar interferometry as a special case. Then, we show how polarimetric basis transformations can be introduced into SAR interferometry and applied to form interferograms between all possible linear combinations of polarization states. This allows us to reveal the strong polarization dependency of the interferometric coherence. We then solve the coherence optimization problem involving maximization of interferometric coherence and formulate a new coherent decomposition for polarimetric SAR interferometry that allows the separation of the effective phase centers of different scattering mechanisms. A simplified stochastic scattering model for an elevated forest canopy is introduced to demonstrate the effectiveness of the proposed algorithms. In this way, we demonstrate the importance of wave polarization for the physical interpretation of SAR interferograms. We investigate the potential of polarimetric SAR interferometry using results from the evaluation of fully polarimetric interferometric shuttle imaging radar (SIR)-C/X-SAR data collected during October 8-9, 1994, over the SE Baikal Lake Selenga delta region of Buriatia, Southeast Siberia, Russia.

The authors provide a new geometrical approach for the inversion of a two-layer coherent scattering model, widely used for the interpretation of polarimetric interferometric SAR data. It has been shown in several recent publications that, by using interferograms in multiple polarisation channels, estimation of vegetation height, underlying ground topography and mean extinction is possible. Furthermore, this can be achieved with a single frequency sensor without the need for a separate reference DEM, other a priori information or the use of data-specific regression formulas. The authors first review the details of this approach and then develop a three-stage inversion procedure to illustrate the steps involved in parameter estimation. They then consider several possible sources of error in the inversion. In particular, they concentrate on the effects of vertical tree structure and on the effects of temporal decorrelation on inversion accuracy. It is shown that the former leads to errors, mainly in the extinction estimation, while the latter does not change the model structure but reduces the available parameter set and increases the variance of the parameter estimates. Finally, the new algorithm is applied to simulated vector coherent SAR data for a random canopy.

Konstantinos Papathanassiou

Papers

A tutorial on synthetic aperture radar

Polarimetric SAR interferometry

Single-baseline polarimetric SAR interferometry

Polarimetric SAR interferometry

Three-stage inversion process for polarimetric SAR interferometry