X-SAR interferometry: first results

Repeat-pass interferometry data were acquired during the first and second SIR-C/X-SAR missions in April and October 1994. This paper presents the first results from X-SAR interferometry at four different sites. The temporal separations were one day and six months. At two sites the coherence requirements were met, resulting in high quality interferograms. A digital elevation model in ground range geometry has been derived. The limitations of the X-SAR interferometry are discussed     

X-SAR radiometric calibration and data quality

In April and October, 1994 the X-SAR was flown as part of the SIR-C/X-SAR space radar laboratory missions (SRL-1/2) on the Space Shuttle. Amongst other activities DLR is responsible for the calibration of all X-SAR data products and is running the German Processing and Archiving Facility (D-PAF). Calibration activities included three major parts. Before the first mission, the authors performed a detailed analysis of the overall system to localize the main error sources and developed algorithms and procedures to correct these errors. During the missions they concentrated their efforts on calibration campaigns at the Oberpfaffenhofen super test site. Post mission activities included the determination of the antenna pattern and the absolute calibration factor as well as detailed performance analyses. This paper describes the overall approach to radiometrically calibrate the X-SAR and provides information on system performance and data quality to users in the different application fields     

Phase statistics of interferograms with applications to synthetic aperture radar

Interferometric methods are well established in optics and radio astronomy. In recent years, interferometric concepts have been applied successfully to synthetic aperture radar (SAR) and have opened up new possibilities in the area of earth remote sensing. However interferometric SAR applications require thorough phase control through the imaging process. The phase accuracy of SAR images is affected by decorrelation effects between the individual surveys. We analyze quantitatively the influence of decorrelation on the phase statistics of SAR interferograms. In particular, phase aberrations as they occur in typical SAR processors are studied in detail. The dependence of the resulting phase bias and variance on processor parameters is presented in several diagrams.     

Doppler frequency estimation and the Cramer-Rao bound

Addresses the problem of Doppler frequency estimation in the presence of speckle and receiver noise. An ultimate accuracy bound for Doppler frequency estimation is derived from the Cramer-Rao inequality. It is shown that estimates based on the correlation of the signal power spectra with an arbitrary weighting function are approximately Gaussian-distributed. Their variance is derived in terms of the weighting function. It is shown that a special case of a correlation-based estimator is a maximum-likelihood estimator that reaches the Cramer-Rao bound. These general results are applied to the problem of Doppler centroid estimation from SAR (synthetic aperture radar) data     

Precision SAR processing using chirp scaling

A space-variant interpolation is required to compensate for the migration of signal energy through range resolution cells when processing synthetic aperture radar (SAR) data, using either the classical range/Doppler (R/D) algorithm or related frequency domain techniques. In general, interpolation requires significant computation time, and leads to loss of image quality, especially in the complex image. The new chirp scaling algorithm avoids interpolation, yet performs range cell migration correction accurately. The algorithm requires only complex multiplies and Fourier transforms to implement, is inherently phase preserving, and is suitable for wide-swath, large-beamwidth, and large-squint applications. This paper describes the chirp scaling algorithm, summarizes simulation results, presents imagery processed with the algorithm, and reviews quantitative measures of its performance. Based on quantitative comparison, the chirp scaling algorithm provides image quality equal to or better than the precision range/Doppler processor. Over the range of parameters tested, image quality results approach the theoretical limit, as defined by the system bandwidth     

Optimum look weighting for burst-mode and ScanSAR processing

Burst-mode and ScanSAR systems record only short pieces of Doppler histories; the energy contained in each echo ensemble and, hence, the intensity in the final burst image (look) depends on the scatterer's position relative to the time of the burst event according to the azimuth antenna pattern, an effect known as scalloping. Most systems employ a burst period short enough that adjacent looks overlap allowing for individual weighting of the looks before summation. The paper introduces a new class of look weighting functions for burst-mode and ScanSAR processing that correct for scalloping while simultaneously keeping the S/N ratio constant over azimuth and maximizing the equivalent number of looks. The achievable radiometric resolution and the sensitivity to Doppler centroid estimation errors are discussed. A 3-look example using ASAR parameters illustrates the proposed weighting functions     

Noise-induced slope distortion in 2-D phase unwrapping by linearestimators with application to SAR interferometry

This paper explains the underestimation of phase slope and the consequent distortion of the phase surface, observed in two-dimensional (2-D) phase unwrapping by linear estimators, like least squares methods applied to synthetic aperture radar (SAR) interferometry. These methods minimize the difference between the gradient of the unwrapped phase and the wrapped differences of the measured wrapped phase. Using the probability distributions of phase noise and phase differences for a given coherence, the probability of a phase gradient error giving rise to a nonconservative vector field is derived. It is shown that this phase gradient error has nonzero mean in the presence of phase slopes. Linear phase estimators cannot distinguish the mean phase gradient error from a true phase slope; hence, the unwrapped phase shows a slope bias. This bias is quantified as a function of coherence and the number of independent samples that are averaged. The theoretical results are confirmed by simulations     

Comments on "Geometric Deconvolution: A Meta-Algorithm for Limited View Computed Tomography"

A recent paper1 on improving computed tomography images suffering from artifacts due to a missing sector of projection angles is criticized. It is shown that the proposed deconvolution approach is not applicable, since the transfer function to be inverted is zero in the whole sector of interest.