Papers by Robert Vanderbei
Sequencing the Stars
Sky and Telescope, Dec 1, 2010
Sensitivity of Shaped Pupil Coronagraphs to Wavefront Errors
American Astronomical Society Meeting Abstracts, Dec 1, 2003
Abstract In recent years, coronagraphy has emerged as a viable alternative for future space based... more Abstract In recent years, coronagraphy has emerged as a viable alternative for future space based extrasolar planet imaging missions. In particular, NASA is currently studying the tradeoffs between utilizing a nulling interferometer or a coronagraph for its Terrestrial Planet Finder Mission. One particularly promising approach to coronagraphy is the use of shaped pupils for high contrast. In a companion paper we present various optimal shapes for achieving high contrast in the focal plane. In this paper we present the sensitivity of these ...
Design of Pure and Hybrid Occulter Systems for THEIA
American Astronomical Society Meeting Abstracts #213, 2009
Abstract The proposed THEIA mission is an effort to image terrestrial planets around other stars ... more Abstract The proposed THEIA mission is an effort to image terrestrial planets around other stars using a space-based telescope and an occulter flying in formation. This system is known as a" hybrid" system, as it proposes to use both the occulter and an apodized pupil Lyot coronagraph in the telescope to suppress the starlight; it is contrasted with a" pure" occulter system, which does all of the starlight suppression with the occulter. We present a general procedure for creating a hybrid system, and compare the size, distance, and ...
Wavefront Estimation and Control Algorithms for High-Contrast Imaging
American Astronomical Society Meeting Abstracts, Dec 1, 2003
Abstract The ultimate limitation of high-dynamic-range imaging systems is the residual scatter du... more Abstract The ultimate limitation of high-dynamic-range imaging systems is the residual scatter due to imperfections in the optical surfaces and the non-uniform reflectivity of those surfaces. The first step in correcting the wavefront errors from scattering is the estimation of the phase aberrations. Its parameters are estimated using a global search with a genetic algorithm and a local optimization with the BFGS quasi-Newton method with a mixed quadratic and cubic line search procedure. Assuming one uses a deformable mirror to ...
Elsevier eBooks, 2004
Due to the success of the first editions of this book I have been asked on numerous occasions to ... more Due to the success of the first editions of this book I have been asked on numerous occasions to update and expand on the information in it. With the recent introduction of two new kata to the ZNKR curriculum and changes in grading requirements the time now seems right to do so. This new edition draws heavily on the first and second. Information concening Koryu has not been changed, but appendices have been brought up to date, the descriptions of Zen Ken Ren kata have been revised and expanded with photographs to assist in interpreting the descriptions. Also the first chapter, particularly that concerning ettiquette has been considerably enlarged, with photographs of torei, and drawings of methods of folding Hakama, tying obi etc. Explanations of terms have been expanded too.
S&T, 2007
Two astronomers, using amateur equipment, determined the scale of the solar system to better than... more Two astronomers, using amateur equipment, determined the scale of the solar system to better than 1%. So can you. By Robert J. Vanderbei and Ruslan Belikov Left: This diagram shows the changing right ascension (RAJ of PfUdentia as it moved across the sky. Its motion with respect to the background stars was nearly linear. The outhors took cluslers of measurements (red crosses) on the evening of August 9, 2006 UT, the next morning, and the next evening. RighI: After uniform linear motion was subtracted out, what remained were the residuals: the apparent sinusoidal oscillations of Prudenlia in right oscension due to the observers' changing position os Earth turned.
Pupil Mapping for Planet Finding: A Diffraction Analysis
AAS, Dec 1, 2005
Abstract Pupil-mapping is a technique whereby a uniformly-illuminated input pupil, such as from s... more Abstract Pupil-mapping is a technique whereby a uniformly-illuminated input pupil, such as from starlight, is mapped to a non-uniformly illuminated exit pupil such that the image formed from this pupil has sidelobes that are suppressed many orders of magnitude relative to the main lobe. Pupil mapping is therefore a candidate technique for coronagraphic imaging of extrasolar planets around nearby stars. Unlike most other high-contrast imaging techniques, pupil mapping is lossless and preserves the full angular resolution of the collecting ...
Laboratory Demonstration of Occulter-Based High Contrast Imaging
AAS, 2012
Abstract The direct imaging of Earth-like planets in neighbouring solar systems requires generati... more Abstract The direct imaging of Earth-like planets in neighbouring solar systems requires generating 10 orders of magnitude in contrast. Using an optimized external occulter, such high levels of contrast suppression can be theoretically achieved using a space telescope. At Princeton, we have designed an experimental testbed where we scaled a 400 mas occulter to fit in the laboratory. We present monochromatic results obtained using a HeNe laser that achieves 10 orders of magnitude of contrast in parts of an annular discovery ...

The students will learn some basic concepts in statistical thinking about data, with emphasis on ... more The students will learn some basic concepts in statistical thinking about data, with emphasis on exploratory data analysis. The module will analyze daily temperature data collected over 55 years at a single location -McGuire Air Force Base (AFB) in southern New Jersey. The analysis explores the question, "Is there any observable temperature trend over this time period at McGuire AFB?" The challenge is to see a potentially small change within a data set that has both seasonal variability and high daily variability. We will do basic plots to help the students view data in different ways, introduce methods for removing seasonality, and use averaging to reduce day-to-day variability. This module might be viewed as a "case study" in data analysis. It will give students a taste of what it's like to do "real world" data analysis. Students will work with a large noisy data set and look at it in different ways to try to answer a specific question. The module does not, however, provide an answer to the question on temperature change that it addresses -it is about the process of data analysis. Each individual analysis (corresponding to a figure in the module) leads us to a new set of questions, which in turn leads to further analyses. This is often the way data analysis proceeds in practice. As the adage goes, "It's not the destination, it's the journey." This module is created in association with the Mathematics of Planet Earth project. Target Audience: Introductory undergraduate statistics students; students in a first course on exploratory data analysis. Prerequisites: Graphing, basic statistical ideas like averages, medians, and variance. It would be helpful for the students to be familiar with basic mathematical notation, such as summations and subscripting to denote terms in a series. This is especially true for the discussion on moving averages in Inset 3. Mathematical Fields: Statistics, specifically exploratory data analysis, graphical data analysis, and very basic ideas in viewing and working with time series data.
Amateur Science Project: Sequencing the Stars
Sky and telescope, 2010
Using images of star clusters acquired with CCD cameras, amateurs can create their own Hertzsprun... more Using images of star clusters acquired with CCD cameras, amateurs can create their own Hertzsprung-Russell diagrams.
Physics Today, Apr 1, 2015
Efficiency of the Simplex Method
Springer eBooks, 2014
In the previous chapter, we saw that the simplex method (with appropriate pivoting rules to guara... more In the previous chapter, we saw that the simplex method (with appropriate pivoting rules to guarantee no cycling) will solve any linear programming problem for which an optimal solution exists. In this chapter, we investigate just how fast it will solve a problem of a given size.
Mathematical Programming, 1993
We present a unified framework for solving linear and convex quadratic programs via interior poin... more We present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is [_~-2 A v] instead of reducing to obtain the usual AD2A v system. This methodology affords two advantages: (1) it avoids the fill created by explicitly forming the product AD2A v when A has dense columns; and (2) it can easily be used to solve nonseparable quadratic programs since it requires only that D be symmetric. We also present a procedure for converting nonseparable quadratic programs to separable ones which yields computational savings when the matrix of quadratic coefficients is dense.
The Simplex Method in Matrix Notation
Springer eBooks, 2008
So far, we have avoided using matrix notation to present linear programming problems and the simp... more So far, we have avoided using matrix notation to present linear programming problems and the simplex method. In this chapter, we shall recast everything into matrix notation. At the same time, we will emphasize the close relations between the primal and the dual problems. ... As usual, we begin our discussion with the standard-form linear programming problem: ... In the past, we have generally denoted slack variables by wi's but have noted that sometimes it is convenient just to string them onto the end of the list of original variables. Such is the case now, and ...
Transactions of the American Mathematical Society, Feb 1, 1983
Let </> be a real valued function defined on the state space of a Markov process x,. Let t, be th... more Let </> be a real valued function defined on the state space of a Markov process x,. Let t, be the first time x, gets to a level set of <J> which is ; units higher than the one on which it started. We call the time changed process x, = x, a stochastic wave. We give conditions under which this process is Markovian and we evaluate its infinitesimal operator.

Shaped pupil design for future space telescopes
Proceedings of SPIE, Aug 28, 2014
ABSTRACT Several years ago at Princeton we invented a technique to optimize shaped pupil (SP) cor... more ABSTRACT Several years ago at Princeton we invented a technique to optimize shaped pupil (SP) coronagraphs for any telescope aperture. In the last year, our colleagues at the Jet Propulsion Laboratory (JPL) invented a method to produce these non-freestanding mask designs on a substrate. These two advances allowed us to design SPs for two possible space telescopes for the direct imaging of exoplanets and disks, WFIRST-AFTA and Exo-C. In December 2013, the SP was selected along with the hybrid Lyot coronagraph for placement in the AFTA coronagraph instrument. Here we describe our designs and analysis of the SPs being manufactured and tested in the High Contrast Imaging Testbed at JPL.We also explore hybrid SP coronagraph designs for AFTA that would improve performance with minimal or no changes to the optical layout. These possibilities include utilizing a Lyot stop after the focal plane mask or applying large, static deformations to the deformable mirrors (nominally for wavefront correction) already in the system.

Lyot coronagraph design study for large, segmented space telescope apertures
Proceedings of SPIE, Jul 29, 2016
Recent efforts combining the optimization techniques of apodized pupil Lyot coronagraphs (APLC) a... more Recent efforts combining the optimization techniques of apodized pupil Lyot coronagraphs (APLC) and shaped pupils have demonstrated the viability of a binary-transmission mask architecture for extremely high contrast (10-10) exoplanet imaging. We are now building on those innovations to carry out a survey of Lyot coronagraph performance for large, segmented telescope apertures. These apertures are of the same kind under considera- tion for NASA's Large UV/Optical/IR (LUVOIR) observatory concept. To map the multi-dimensional design parameter space, we have developed a software toolkit to manage large sets of mask optimization programs and execute them on a computing cluster. Here we summarize a preliminary survey of 500 APLC solutions for 4 reference hexagonal telescope apertures. Several promising designs produce annular, 10-10 contrast dark zones down to inner working angle 4λ0=D over a 15% bandpass, while delivering a half-max PSF core throughput of 18%. We also report our progress on devising solutions to the challenges of Lyot stop alignment/fabrication tolerance that arise in this contrast regime.
Mathematics of Operations Research, Aug 1, 1995
We consider optimization problems of the following type: min{tr(CX) : A(X) = B, X positive semide... more We consider optimization problems of the following type: min{tr(CX) : A(X) = B, X positive semidefinite}. Here, tr(•) denotes the trace operator, C and X are symmetric n × n matrices, B is a symmetric m × m matrix and A(•) denotes a linear operator. Such problems are called semidefinite programs and have recently become the object of considerable interest due to important connections with max-min eigenvalue problems and with new bounds for integer programming. In the context of symmetric matrices, the simplest linear operators have the following form: where M is an arbitrary m × n matrix. In this paper, we show that for such linear operators the optimization problem is trivial in the sense that an explicit solution can be given.

The Astrophysical Journal, 2006
Pupil-mapping is a technique whereby a uniformly-illuminated input pupil, such as from starlight,... more Pupil-mapping is a technique whereby a uniformly-illuminated input pupil, such as from starlight, can be mapped into a non-uniformly illuminated exit pupil, such that the image formed from this pupil will have suppressed sidelobes, many orders of magnitude weaker than classical Airy ring intensities. Pupil mapping is therefore a candidate technique for coronagraphic imaging of extrasolar planets around nearby stars. Unlike most other high-contrast imaging techniques, pupil mapping is lossless and preserves the full angular resolution of the collecting telescope. So, it could possibly give the highest signal-to-noise ratio of any proposed single-telescope system for detecting extrasolar planets. Prior analyses based on pupil-to-pupil ray-tracing indicate that a planet fainter than 10 -10 times its parent star, and as close as about 2λ/D, should be detectable. In this paper, we describe the results of careful diffraction analysis of pupil mapping systems. These results reveal a serious unresolved issue. Namely, high-contrast pupil mappings distribute light from very near the edge of the first pupil to a broad area of the second pupil and this dramatically amplifies diffraction-based edge effects resulting in a limiting attainable contrast of about 10 -5 . We hope that by identifying this problem others will provide a solution.
Mathematical Programming, 1989
The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free ... more The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual.
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Papers by Robert Vanderbei