Biomedical subjects

Robert J Vanderbei

Publications and source records attributed to Robert J Vanderbei.

4 recordsLinked to original sources

PubMed2006

On representing and correcting wavefront errors in high-contrast imaging systems.

Conventional adaptive-optics systems correct the wavefront by adjusting a deformable mirror (DM) based on measurements of the phase aberration taken in a pupil plane. The ability of this technique, known as phase conjugation, to correct aberrations is normally limited by the maximum spatial frequency of the DM. In this paper we show that conventional phase conjugation is not able to achieve the dark nulls needed for high-contrast imaging. Linear combinations of high frequencies in the aberration at the pupil plane "fold" and appear as low-frequency aberrations at the image plane. After describing the frequency-folding phenomenon, we present an alternative optimized solution for the shape of the deformable mirror based on the Fourier decomposition of the effective phase and amplitude aberrations.

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PubMed2005

Optimal one-dimensional apodizations and shaped pupils for planet finding coronagraphy.

The realization that direct imaging of extrasolar planets could be technologically feasible within the next decade or so has inspired a great deal of recent research into high-contrast imaging. We have contributed several design ideas, all of which can be described as shaped pupil coronagraphs. We offer a complete and unified survey of one-dimensional shaped pupil designs, some of which have been published in our previous papers. We also introduce a promising new design, which we call bar-code masks. With these masks we can achieve the required contrast with a fairly large discovery zone and throughput, but most importantly they are perhaps the easiest to manufacture and might therefore stand up best to refined analyses.

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PubMed2005

Horsing around on Saturn.

On the basis of simple statistical mechanical models, the prevailing view of the rings of Saturn is that they are unstable and must therefore have been formed rather recently. In this paper, we argue that the Saturn rings and inner moons are in much more stable orbits than previously thought and, therefore, that they likely formed together as part of the initial formation of the solar system. To make this argument, we give a detailed description of so-called horseshoe orbits and show that this horseshoeing phenomenon greatly stabilizes the rings of Saturn. This paper is part of a collaborative effort with E. Belbruno and J.R. Gott III. For a description of their part of the work, see their papers in these proceedings.

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PubMed2004

New orbits for the n-body problem.

In this paper, we consider minimizing the action functional as a method for numerically discovering periodic solutions to the n-body problem. With this method, we can find a large number of choreographies and other more general solutions. We show that most of the solutions found, including all but one of the choreographies, are unstable. It appears to be much easier to find unstable solutions to the n-body problem than stable ones. Simpler solutions are more likely to be stable than exotic ones.

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