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.

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Synthetic aperture radar interferometry

Synthetic aperture radar interferometry (InSAR) from Earth-orbiting spacecraft provides a new tool to map global topography and deformation of the Earth's surface. Radar images taken from slightly different viewing directions allow the construction of digital elevation models of meter-scale accuracy. These data sets aid in the analysis and interpretation of tectonic and volcanic landscapes. If the Earth's surface deformed between two radar image acquisitions, a map of the surface dis- placement with tens-of-meters resolution and subcentimeter accuracy can be con- structed. This review gives a basic overview of InSAR for Earth scientists and presents a selection of geologic applications that demonstrate the unique capabilities of InSAR for mapping the topography and deformation of the Earth.

/pdf/synthetic-aperture-radar-interferometry-to-measure-earth-s-1nugx1vz24.pdf

Synthetic aperture radar interferometry to measure earth's surface topography and its deformation

Phase shifting algorithms for fringe projection profilometry: A review

Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review

Interferometric radar techniques often necessitate two-dimensional (2-D) phase unwrapping, defined here as the estimation of unambiguous phase data from a 2-D array known only modulo 2pi rad. We develop a maximum a posteriori probability (MAP) estimation approach for this problem, and we derive an algorithm that approximately maximizes the conditional probability of its phase-unwrapped solution given observable quantities such as wrapped phase, image intensity, and interferogram coherence. Examining topographic and differential interferometry separately, we derive simple, working models for the joint statistics of the estimated and the observed signals. We use generalized, nonlinear cost functions to reflect these probability relationships, and we employ nonlinear network-flow techniques to approximate MAP solutions. We apply our algorithm both to a topographic interferogram exhibiting rough terrain and layover and to a differential interferogram measuring the deformation from a large earthquake. The MAP solutions are complete and are more accurate than those of other tested algorithms.

Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization

The advent of interferometric synthetic aperature radar for geophysical studies has resulted in the need for accurate, efficient methods of two-dimensional phase unwrapping. Inference of the lost integral number of cycles in phase measurements is critical for three-pass surface deformation studies as well as topographic mapping and can result in an order of magnitude increase in sensitivity for two-pass deformation analysis. While phase unwrapping algorithms have proliferated over the past ten years, two main approaches are currently in use. Each is most useful only for certain restricted applications. All these algorithms begin with the measured gradient of the phase field, which is subsequently integrated to recover the unwrapped phases. The earliest approaches in interferometric applications incorporated residue identification and cuts to limit the possible integration paths, while a second class using least-squares techniques was developed in the early 1990’s. We compare the approaches and find that the residue-cut algorithms are quite accurate but do not produce estimates in regions of moderate phase noise. The least-squares methods yield complete coverage but at the cost of distortion in the recovered phase field. A new synthesis approach, combining the cuts from the first class with a least-squares solution, offers greater spatial coverage with less distortion in many instances.

/pdf/phase-unwrapping-algorithms-for-radar-interferometry-residue-3f28hi8fyk.pdf

Phase unwrapping algorithms for radar interferometry: residue-cut, least-squares, and synthesis algorithms

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Phase unwrapping algorithms for radar interferometry: residue-cut, least-squares, and synthesis algorithms