## Image Analysis using One Binary Ring Mask Invariant to Rotation and Scale

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Click here for journal-ordered list. Research My research spans from probability to optimization, from pure math to astronomy. I am particularly interested in designing optical systems for high-contrast imaging with the hope of using such systems to one day take direct images, and eventually spectra, of Earth-like exoplanets. Exploiting the Efficiency of Simplex and Sparsification Methods. We propose two approaches to solve large-scale compressed sensing problems.

The first approach uses the parametric simplex method to recover very sparse signals by taking a small number of simplex pivots, while the second approach reformulates the problem using Kronecker products to achieve image analysis using one binary ring mask invariant to rotation and scale computation via a sparser problem formulation.

In particular, we focus on the computational aspects of these methods in compressed sensing. Various problems, especially in the field of machine learning, involve an unknown regularization parameter. Dantzig selector estimation, LAD-Lasso, and constrained l 1 minimization estimation. For such problems, we show that the parametric simplex method can be used to solve these problems for all values of the regularization parameter a continuum of optimization problems in the same time that other variants of the simplex method can solve just one instance.

Machine Learning Research15 1, The parametric simplex method is applied to solve sparse precision matrix estimation problems very efficiently. We describe a statistical procedure to account for differences in grading practices from one course to another.

The goal is to define a course "inflatedness" image analysis using one binary ring mask invariant to rotation and scale a student "aptitude" that image analysis using one binary ring mask invariant to rotation and scale captures ones intuitive notions of these concepts.

Climate Change Local Warming. Using 55 years of daily average temperatures from a local weather station, I made a least-absolute-deviations LAD regression model that accounts for three effects: The model was formulated as a linear programming problem and solved using widely available optimization software.

To appear in J. Coronagraphs of the Apodized Pupil and Shaped Pupil varieties use the Fraunhofer diffraction properties of amplitude masks to create regions of high contrast in the vicinity of a target star.

Optimal Pupil Apodizations for Arbitrary Apertures. In the context of exoplanet direct detection and characterization, where high-contrast imaging is mandatory, we present fully optimized two-dimensional pupil apodizations for which no specific geometric con- straints are put on the pupil plane apodization, apart from the shape of the aperture itself.

Masks for circular and segmented apertures are displayed, with and without a central obstruction and spiders. We present a new method for numerical propagations through Lyot-style coronagraphs using finite size occulting masks. Standard methods for coronagraphic simulations involve Fast Fourier Transforms FFT of very large arrays, and computing power is an issue for the design and tolerancing of coronagraphs on Extremely Large Telescopes ELT in order to handle both the speed and memory requirements.

Our method combines a semi-analytical approach with non-FFT based Fourier transform algorithms. It enables both fast and memory-efficient computations without introducing any additional approximations.

Typical speed improvements based on computation costs are of twenty to fifty for propagations from pupil image analysis using one binary ring mask invariant to rotation and scale Lyot plane, with image analysis using one binary ring mask invariant to rotation and scale to sixty times less memory jeeded.

Our method makes it possible to perform numerical coronagraphic studies even in the case of ELTs using a contemporary commercial laptop computer, or any standard commercial workstation computer. Mathematical Programming Series B In this paper I describe a new and exciting application of optimization technology. The problem is to design a space telescope capable of imaging Earth-like planets around nearby stars. Because of limitations inherent in the wave nature of light, the design problem is one of diffraction control so as to provide the extremely high contrast needed to image a faint planet positioned very close to its much brighter star.

The mathematics behind the diffraction control problem are described. We summarize the design procedure for shaped pupils and review the various families of designs we have found. We describe the manufacturing processes we have used to make free standing shaped pupil masks and review our most recent laboratory results with and without wavefront control.

We also discuss the factors limiting high contrast in the laboratory and our plans for mitigating them. The shaped pupil coronagraph for planet finding coronagraphy: Microwave and Terahertz Photonics.

Proceedings of the SPIE, This paper summarizes our work designing optimal shaped pupils for high-contrast imaging. We show how any effective apodization can be created using shaped pupils and present a variety of both one-dimensional and azimuthally symmetric pupil shapes.

Each pupil has its own performance advantage and we discuss the tradeoffs among various designs. Optimizations are typically performed by maximizing a measure of system throughput under constraints on contrast and inner working angle. We mention the question of sensitivity to aberrations. Controlling aberrations will be critical for any implementation of a planet-finding coronagraph. Finally, we present our first laboratory results testing a shaped pupil coronagraph.

Astrophysical Journal1: We present yet another new family of masks for high-contrast imaging as required for the to-be-built terrestrial planet finder space telescope.

We call these masks checkerboard masks. They consist of two barcode masks, one rotated 90 degrees with respect to the other. Each barcode mask provides contrast to the 10 -5 level. The checkboard mask then achieves a 10 level of contrast everywhere except along the two axes of symmetry where the contrast remains at the 10 -5 level.

We show that by combining a Lyot-plane checkboard mask with an image-plane occulter we can achieve even tighter inner working angles, although as with occulting designs in general pointing error and stellar size become nontrivial issues. Checkerboard masks can be thought of as the binary-mask analogue of Nisenson's apodized square aperture concept. New pupil masks for high-contrast imaging.

Motivated by the desire to image exosolar planets, recent work by us and others has shown that high-contrast imaging can be achieved using specially shaped pupil masks. To date, our masks have been symmetric with respect to a cartesian coordinate system but were not rotationally invariant, thus requiring that one take multiple images at different angles of rotation about the central point in order to obtain high-contrast in all directions.

In this talk, we present two new classes of masks that have rotational symmetry and provide high-contrast in all directions with just one image. They are also well-suited for use on ground-based telescopes, and perhaps NGST as well, since they can accommodate central obstructions and associated support spiders.

Advances in Space Research34 3: NASA's current strategic plan calls for the launching of a space observatory, The Terrestrial Planet Finder TPFby the middle of the next decade; it will search for terrestrial planets in the habitable zone of roughly nearby stars and characterize them for the potential to harbor life.

This concept consists of a 4 meter by 10 meter coronagraphic telescope in a deep space orbit. Circularly Symmetric Apodization via Starshaped Masks. Astrophysical Journal In a recent paper, we introduced a class of shaped pupil masks, called spider-web masks, that produce point spread functions having annular dark zones.

With such masks, a single image can be used to probe a star for extrasolar planets. In this paper, we introduce a new class of shaped pupil masks that also provide annular dark zones.

We call these masks starshaped masks. Given any circularly symmetric apodization function, we show how to construct a corresponding starshaped mask that has the same point-spread function as obtained by the apodization. Spiderweb Masks for High Contrast Imaging. To date, the masks we have designed have been symmetric with respect to a cartesian coordinate system but were not rotationally invariant, thus requiring that one take multiple images at different angles of rotation about the central point in order to obtain high-contrast in all directions.

In this paper, we present a new class of masks that have rotational symmetry and provide high-contrast in all directions with just one image. They are also well-suited for use on ground-based telescopes, and perhaps NGST too, since they can accommodate central obstructions and associated support spiders.

In this paper we examine several different apodization approaches to achieving high-contrast imaging of extrasolar planets and compare different designs on a selection of performance metrics.

These approaches are characterized by their use of the pupil's transmission function to focus the starlight rather than by masking the star in the image plane as in a classical coronagraph. There are two broad classes of pupil coronagraphs examined in this paper: The latter are much easier to manufacture to the needed tolerances. In addition to comparing existing approaches, numerical optimization is used to design new pupil shapes. These new designs can achieve nearly as high a throughput as the best apodized pupils and perform significantly better than the apodized square aperture design.

Pupils are shown for terrestrial planet discovery using square, rectangular, circular, and elliptical apertures. A mask is also presented targeted at Jovian planet discovery, where contrast is given up to yield greater throughput.

An external flower-shaped occulter flying in formation with a space telescope can theoretically provide sufficient starlight suppression to enable direct imaging of an Earth-like planet.

Occulter shapes are scaled to enable experimental validation of their performance at laboratory dimensions. Previous experimental results have shown promising performance but have not realized the full theoretical potential of occulter designs.

Here, image analysis using one binary ring mask invariant to rotation and scale develop a two-dimensional diffraction model for optical propagations for occulters incorporating experimental errors. We perform a sensitivity analysis, and comparison with experimental results from a scaled-occulter testbed **image analysis using one binary ring mask invariant to rotation and scale** the optical model to the 10 contrast level.

The manufacturing accuracy along the edge of the occulter shape is identified as the limiting factor to achieving the theoretical potential of the occulter design. Eliminating Poisson's Spot with Linear Programming. Operations Research and Cyber-Infrastructure. A leading design concept for NASA's upcoming planet-finding space telescope involves placing an occulter 72, km in front of a 4-m telescope.

The purpose of the occulter is to block the bright starlight thereby enabling the telescope to take pictures of planets orbiting the blocked star. In this paper, I explain how to reduce this shape-optimization problem to a large-scale linear programming problem that can be solved with modern LP tools.

One method for finding terrestrial planets around nearby stars is to use two spacecrafta telescope and a specially shaped occulter, whose shape is specially designed to prevent all but a tiny fraction of the starlight from diffracting into the telescope. As the cost and observing cadence for such a mission will be driven largely by the separation between the two spacecraft, it is critically important to design an occulter that can meet the observing goals while flying as close to the telescope as possible.

In this paper, we explore this tradeoff between separation and occulter diameter. More specifically, we present a method for designing the shape of the outer edge of an occulter that is as small as possible and gives a shadow that is deep enough and large enough for a 4m telescope to survey the habitable zones of many stars for Earth-like planets.

In particular, we show that in order for a 4m telescope to detect in broadband visible light a planet 0. Astrophysical Journal2: We begin by reviewing the general derivation of the design equations driving PIAA.