SAR resolution in the presence of phase errors

The author analyzes the effects of phase errors on synthetic aperture radar (SAR). The theory is applied to the following question: how does the achievable resolution vary with the carrier frequency when optimum quadratic focus and/or optimum processing interval (synthetic aperture length) are used? Numerous related results are given, so that much of the material is tutorial. For phase errors corresponding to uncompensated motion, the best achievable RMS resolution with any phase error spectrum satisfies the derived equation. For motion-induced phase errors it is seen that resolution improves with increasing carrier frequency when the first term in the expression applies (e.g. for phase errors concentrated at low frequencies) and resolution is independent of carrier frequency when R δ/v/v is the smaller term (e.g. with broad band or high frequency phase errors)     

Resolution Limits with Propagation Phase Errors

Resolution limits and corresponding optimum linear apertures are determined in the presence of phase errors. Let ?(t) be the phase aberration at position t across the aperture; it is assumed that the random process ? has a power law structure function, E{[(?(t)-?(?)]2}= c|t-?|n. Beam tilting caused by the phase error is "removed" (for each sample of ?), then resolution formulas are developed. An approximate analysis is obtained in closed form and yields an optimum resolution proportional to c1/n for O < n < 2. The exact analysis is given for Gaussian ?, and again the optimum resolution is proportional to c1/n. In applications n= 5/3 is of interest, and in the Gaussian case the best obtainable equivalent rectangle resolution is ? ?)/2? (0.975)c3/5 radians with a corresponding optimum linear aperture of 14c-3/5. When long exposures are considered, imaging without removing beam tilting is of interest, and resolution is degraded by a factor of about 2.5 for a linear aperture. Alternatively, in some applications optimum focus as well as beam tilt should be considered, in this case resolution is improved by a factor of about 1.4 (again for n= 5/3). Finally, joint (tilt corrected) optimization over aperture length and taper is treated; however, as one might expect, the use of taper offers negligible resolution improvement.     

Sputtering processes: Erosion and chemical change

We review laboratory data and models on sputter-induced erosion and chemical alterations of ice films and apply the results to icy grains and satellites exposed to magnetospheric ion bombardment. We show that the source of the plasma in the inner magnetosphere of Saturn is likely to be the sputter erosion of the icy objects in this region and consider the sputter erosion and possible stabilization of the E-ring. Ion-induced polymerization is discussed as a source of the darkened rings of Uranus.     

Image Algebra and Automatic Shape Recognition

Shape recognition can be carried out with set theory operations. In addition to the usual set theory operations of union, complement, etc., the operation of erosion between two sets (or images) is incorporated. Then it is shown that these operations between sets serve as a basis for representation theorems for all, generally nonlinear, translation invariant transformations, (i.e., transformations which commute with translations). By treating images and shapes as point sets in n-dimensional Cartesian space (n = 2 for binary images, n = 3 for gray scale images, and larger n for images that incorporate color, polarization, and the like), the problem of shape or pattern recognition is converted to the problem of detecting the occurrences of specific sets within an image. This problem is closely related to the operation of erosion. By introducing complement images and complement shapes, a generic computer for automatic shape recognition is found which provides a constructive proof of the representation theorem and related results.     

Applied potential tomography

Applied Potential Tomography (APT) is a new method of imaging changes in the distribution of electrical resistivity within the human body. Such changes occur during respiration and, because of the movement of blood within the chest, during the cardiac cycle. Changes can also be observed due to redistribution of fluid within the body during simulated weightlessness. As very low electric currents are used to take measurements the method is safe. The equipment is simple and compact and ideal for use in space based measurement of physiological changes in the human body.     

Development and growth of potato tubers in microgravity.

A potato explant consisting of a leaf, its axillary bud, and a small segment of stem will develop a tuber in 10-14 days when grown on earth. The tubers develop from the axillary buds and accumulate starch derived from sugars produced through photosynthesis and/or mobilized from leaf tissue. Potato explants were harvested and maintained in the Astroculture (TM) unit, a plant growth chamber designed for spaceflight. The unit provides an environment with controlled temperature, humidity, CO2 level, light intensity, and a nutrient delivery system. The hardware was loaded onto the space shuttle Columbia 24 hours prior to the launch of the STS-73 mission. Explant leaf tissue appeared turgid and green for the first 11 days of flight, but then became chlorotic and eventually necrotic by the end of the mission. The same events occurred to ground control explants with approximately the same timing. At the end of the 16-day mission, tubers were present on each explant. The size and shape of the space-grown tubers were similar to the ground-control tubers. The arrangement of cells in the tuber interior and at the exterior in the periderm was similar in both environments. Starch and protein were present in the tubers grown in space and on the ground. The range in starch grain size was similar in tubers from both environments, but the distribution of grains into size classes differed somewhat, with the space-grown tubers having more small grains than the ground control tubers. Proteinaceous crystals were found in tubers formed in each condition.     

Cytochemical localization of calcium in soybean root cap cells in microgravity.

The antimonate precipitation technique was used to evaluate the effects of microgravity and ethylene on the cellular and subcellular distribution of free calcium ions in soybean root apices. Soybean (Glycine max L. [Merr.]) dry seeds were launched, activated by hydration, and germinated in the presence of KMnO4 (to remove ethylene) and in its absence onboard the space shuttle Columbia during the STS-87 mission. Primary root apices of 6-day old seedlings were fixed for electron microscopy after landing. Ultrastructural studies indicated that antimonate precipitation appeared as individual electron-dense particles which were more or less round in shape and varied in diameter from 10 nm (minimum size beginning from which the particles were well identified) to 90 nm. It was revealed that analyzed root cap cells varied in both the precipitate particle sizes and the amount particles per unit of the cellular area. In both flight and ground control treatments, antimonate precipitation level increases from apical meristem cells to peripheral (secretory) cells of root apices. In root cap statocytes, subcellular localization of precipitate particles was revealed in the cytoplasm, nucleus and small vacuoles. The quantitative analysis showed a reduction of precipitate density in the cytoplasm and the nucleus, and an increase in precipitate density in the vacuoles from statocytes of both spaceflight treatments in comparison with ground controls.