John E. Dorband

Hubble Space Telescope Faint Object Camera calculated point-spread functions

A set of observed noisy Hubble Space Telescope Faint Object Camera point-spread functions is used to recover the combined Hubble and Faint Object Camera wave-front error. The low-spatial-frequency wave-front error is parameterized in terms of a set of 32 annular Zernike polynomials. The midlevel and higher spatial frequencies are parameterized in terms of set of 891 polar-Fourier polynomials. The parameterized wave-front error is used to generate accurate calculated point-spread functions, both pre- and post-COSTAR (corrective optics space telescope axial replacement), suitable for image restoration at arbitrary wavelengths. We describe the phase-retrieval-based recovery process and the phase parameterization. Resultant calculated precorrection and postcorrection point-spread functions are shown along with an estimate of both pre- and post-COSTAR spherical aberration.

Tetrahedral Robotics for Space Exploration

A reconfigurable space filling robotic architecture has a wide range of possible applications. One of the more intriguing possibilities is mobility in very irregular and otherwise impassable terrain. NASA Goddard Space Flight Center is developing the third generation of its addressable reconfigurable technology (ART) tetrahedral robotics architecture. An ART-based variable geometry truss consisting of 12 tetrahedral elements made from 26 smart struts on a wireless network has been developed. The primary goal of this development is the demonstration of a new kind of robotic mobility that can provide access and articulation that complement existing capabilities. An initial set of gaits and other behaviors are being tested, and accommodations for payloads such as sensor and telemetry packages are being studied. Herein, we describe our experience with the ART tetrahedral robotics architecture and the improvements implemented in the third generation of this technology. Applications of these robots to space exploration and the tradeoffs involved with this architecture will be discussed.

MOTION OF THE ULTRAVIOLET R AQUARII JET

We present evidence for subarcsecond changes in the ultraviolet (~2550 A) morphology of the inner 5 arcseconds of the R Aqr jet over a 2 yr period. These data were taken with the Hubble Space Telescope (HST) Faint Object Camera (FOC) when the primary mirror flow was still affecting observations. Images of the R Aqr stellar jet were successfully restored to the original design resolution by completely characterizing the telescope-camera point spread function (PSF) with the aid of phase-retrieval techniques. Thus, a noise-free PSF was employed in the final restorations which utilized the maximum entropy method (MEM). We also present recent imagery obtained with the HST/FOC system after the COSTAR correction mission that provides confirmation of the validity of our restoration methodology. The restored results clearly show that the jet is flowing along the northeast (NE)-southwest (SW) axis with a prominent helical-like structure evident on the stronger NE side of the jet. Transverse velocities increase with increasing distance from the central source, providing a velocity range of 36-235 km s-1. From an analysis of proper motions of the two major ultraviolet jet components, we detect an ~40.2 yr event separation of this apparent enhanced material ejection occurring probably at periastron which is consistent with the suspected ~44 yr binary period; this same analysis shows that the jet is undergoing nonlinear acceleration which suggests that the propulsive force probably results from magnetohydromagnetic effects. The restoration computations and the algorithms employed demonstrate that mining of flawed HST data can be scientifically worthwhile.

A MAXIMUM ENTROPY METHOD WITH A PRIORI MAXIMUM LIKELIHOOD CONSTRAINTS

Implementations of the maximum entropy method for data reconstruction have almost universally used the approach of maximizing the statistic S - λχ2, where S is the Shannon entropy of the reconstructed distribution and χ2 is the usual statistical measure associated with agreement between certain properties of the reconstructed distribution and the data. We develop here an alternative approach which maximizes the entropy subject to the set of constraints that χ2 be at a minimum with respect to the reconstructed distribution. This in turn modifies the fitting statistic to be S - λ ∇χ2 where λ is now a vector. This new method provides a unique solution to both the well-posed and ill-posed problem, provides a natural convergence criterion which has previously been lacking in other implementations of maximum entropy, and provides the most conservative (least informative) data reconstruction result consistent with both maximum entropy and maximum likelihood methods, thereby mitigating against over-interpretation of reconstruction results. A spectroscopic example is shown as a demonstration.

Maximum entropy restoration of blurred and oversaturated Hubble Space Telescope imagery

A brief introduction to image reconstruction is made and the basic concepts of the maximum entropy method are outlined. A statistical inference algorithm based on this method is presented. The algorithm is tested on simulated data and applied to real data. The latter is from a 1024 × 1024 Hubble Space Telescope image of the binary stellar system R Aquarii, which suffers from both spherical aberration and detector saturation. Under these constraints the maximum entropy method produces an image that agrees closely with observed results. The calculations were performed on the MasPar MP-1 single-instruction/multiple-data computer.

The [N II] Kinematics of R Aquarii

We report a kinematic study of the symbiotic star system R Aqr derived from [N II] λ6584 emission observations with a Fabry-Perot imaging spectrometer. The [N II] spatial structure of the R Aqr jet, first observed circa 1977, and surrounding hourglass-shaped nebulosity, due to an explosion ~660 yr ago, are derived from 41 velocity planes spaced at ~12 km s-1 intervals. Fabry-Perot imagery shows that the elliptical nebulosity making up the waist of the hourglass shell is consistent with a circular ring expanding radially at 55 km s-1 as seen at an inclination angle i ~ 70°. With respect to the position of R Aqr, at optical and radio wavelengths the jet is made up of a northeast component and a less intense, more amorphous southwest component. The [N II] Fabry-Perot data cube demonstrates that the two jet components possess quite different intensity-velocity structures which represent collimated flow in opposite directions. We offer an idealized schematic model for the R Aqr jet motion which results in a small-scale helical structure forming around a larger scale helical path. The implications of such a jet model are discussed. We present a movie showing a side-by-side comparison of the spatial structure of the model and the data as a function of the 41 velocity planes.

Unification of Legendre, Laguerre, Hermite, and binomial discrete transforms using Pascal's matrix

Pascals matrix plays an important role in the computation of the discrete Legendre, Laguerre, Hermite, and binomial transforms. In particular, Pascals matrix helps to unify the formulation of these orthogonal transforms and demonstrate the similarity of the computation of the transform matrices. It also allows the identification of the identical computations needed for these transforms. The fundamental finding is based on the discovery of the relationship between Pascals matrix and the binomial coefficient.

Sparse matrix approximation method for an active optical control system

We develop a sparse matrix approximation method to decompose a wave front into a basis set of actuator influence functions for an active optical system consisting of a deformable mirror and a segmented primary mirror. The wave front used is constructed by Zernike polynomials to simulate the output of a phase-retrieval algorithm. Results of a Monte Carlo simulation of the optical control loop are compared with the standard, nonsparse approach in terms of accuracy and precision, as well as computational speed and memory. The sparse matrix approximation method can yield more than a 50-fold increase in the speed and a 20-fold reduction in matrix size and a commensurate decrease in required memory, with less than 10% degradation in solution accuracy. Our method is also shown to be better than when elements are selected for the sparse matrix on a magnitude basis alone. We show that the method developed is a viable alternative to use of the full control matrix in a phase-retrieval-based active optical control system.

Asymptotically optimal probabilistic embedding algorithms for supporting tree structured computations in hypercubes

We show two asymptotically optimal probabilistic tree embedding algorithms in hypercubes with constant dilation. These algorithms are slight extension of the random walk algorithm. The first algorithm allows a tree node to have a stay option during each step of a random walk. The second algorithm permits varying length of random walks. Numerical data are given to demonstrate performance improvement.

Applications of the MasPar MP-1 at NASA/Goddard

Massively parallel systems are targeted for accelerated development and maturation by NASAs upcoming five-year High Performance Computing Initiative. A summary of the broad range of applications currently running on the MP-1 is presented along with descriptions of the parallel algorithmic techniques employed in five of them. The following applications are described in some detail: finite element simulation, tridiagonal solver, neural networks, image deblurring, and point plotting. The MasPar MP-1 has replaced the MPP (Massively Parallel Processor) and with 8K processors installed is providing more than twice the megaflop power and 64 times the high-speed memory. All the MPP users have migrated their development activities to the MasPar along with many of their application codes. User feedback has been positive due to the more capable hardware and its excellent reliability.<<ETX>>