Optimal Asymmetric 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 ourselves have contributed several design ideas, all of which can be described as shaped pupil coronagraphs. In this paper, we offer a complete and unified survey of asymmetric shaped pupils designs, some of which have been published in our previous papers. We also introduce a promising new design, which we call barcode masks. These masks 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 a refined analysis based on vector propogation techniques.Comment: 17 pages, 11 figures, submitted to Applied Optic

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: seasonal variations, the 11-year solar cycle, and a linear trend. The model was formulated as a linear programming problem and solved using widely available optimization software. The solution indicates that temperatures have gone up by about 2 degrees Fahrenheit over the 55 years covered by the data. It also correctly identifies the known phase of the solar cycle; i.e., the date of the last solar minimum. It turns out that the maximum slope of the solar cycle sinusoid in the regression model is about the same size as the slope produced by the linear trend. The fact that the solar cycle was correctly extracted by the model is a strong indicator that effects of this size, in particular the slope of the linear trend, can be accurately determined from the 55 years of data analyzed. The main purpose for doing this analysis is to demonstrate that it is easy to find and analyze archived temperature data for oneself. In particular, this problem makes a good class project for upper-level undergraduate courses in optimization or in statistics. It is worth noting that a similar least-squares model failed to characterize the solar cycle correctly and hence even though it too indicates that temperatures have been rising locally, one can be less confident in this result. The paper ends with a section presenting similar results from a few thousand sites distributed world-wide, some results from a modification of the model that includes both temperature and humidity, as well as a number of suggestions for future work and/or ideas for enhancements that could be used as classroom projects.Comment: 12 pages, 5 figures, to appear in SIAM Revie

Laboratory Experiment of Checkerboard Pupil Mask Coronagraph

We present the results of the first laboratory experiment of checkerboard shaped pupil binary mask coronagraphs using visible light, in the context of the R&D activities for future mid-infrared space missions such as the 3.5 m SPICA telescope. The primary aim of this work is to demonstrate the coronagraphic performance of checkerboard masks down to a $10^{-6}$ peak-to-peak contrast, which is required to detect self-luminous extra-solar planets in the mid-infrared region. Two masks, consisting of aluminum films on a glass substrates, were manufactured using nano-fabrication techniques with electron beam lithography: one mask was optimized for a pupil with a 30% central obstruction and the other was for a pupil without obstruction. The theoretical contrast for both masks was $10^{-7}$ and no adaptive optics system was employed. For both masks, the observed point spread functions were quite consistent with the theoretical ones. The average contrast measured within the dark regions was $2.7 {\times} 10^{-7}$ and $1.1 {\times} 10^{-7}$. The coronagraphic performance significantly outperformed the $10^{-6}$ requirement and almost reached the theoretical limit determined by the mask designs. We discuss the potential application of checkerboard masks for mid-infrared coronagraphy, and conclude that binary masks are promising for future high-contrast space telescopes.Comment: 6 pages, 6 figure

A Parametric Simplex Algorithm for Linear Vector Optimization Problems

In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (Evans-Steuer) algorithm [12]. Different from it, the proposed algorithm works in the parameter space and does not aim to find the set of all efficient solutions. Instead, it finds a solution in the sense of Loehne [16], that is, it finds a subset of efficient solutions that allows to generate the whole frontier. In that sense, it can also be seen as a generalization of the parametric self-dual simplex algorithm, which originally is designed for solving single objective linear optimization problems, and is modified to solve two objective bounded LVOPs with the positive orthant as the ordering cone in Ruszczynski and Vanderbei [21]. The algorithm proposed here works for any dimension, any solid pointed polyhedral ordering cone C and for bounded as well as unbounded problems. Numerical results are provided to compare the proposed algorithm with an objective space based LVOP algorithm (Benson algorithm in [13]), that also provides a solution in the sense of [16], and with Evans-Steuer algorithm [12]. The results show that for non-degenerate problems the proposed algorithm outperforms Benson algorithm and is on par with Evan-Steuer algorithm. For highly degenerate problems Benson's algorithm [13] excels the simplex-type algorithms; however, the parametric simplex algorithm is for these problems computationally much more efficient than Evans-Steuer algorithm.Comment: 27 pages, 4 figures, 5 table