DIMACS
DIMACS REU 2012

Student: Marissa Loving
Office: CoRE 434
School: University of Hawaii at Hilo
E-mail: loving7@hawaii.edu
Project: Fast Fourier Optimization in Designing Telescope Masks

About Me
I am a rising senior majoring in Mathematics and Computer Science at the University of Hawaii at Hilo. Pure mathematics is my passion, but I also enjoy a full life outside of academics with my wonderful parents and eleven siblings. I love the outdoors and when not pulling all nighters to finish a project or home work assignment I can often be found at the beach or lifeguarding at my university's pool. I am very excited to see what my summer at DIMACS will hold.

Project Description
In astronomy, an exciting area of study is the search for extra-solar habitable planets. This can be extremely difficult. The distance between a star and a planet within its habitable zone is so miniscule compared to the distance between the star and earth that distinguishing between the star and its planet becomes impossible due to physical limitations. Such limitations can be overcome through techniques in adaptive optics and high contrast imagining. For example, Fourier Transforms can be used to model the telescope masks that are designed to increase image resolution when viewing high contrast regions. However, Fourier Transforms are rather computationally intensive. One way to reduce the amount of computations needed in these models is to apply a greater number of constraints. Essentially a simpler model is sacrificed to allow simpler computation. This tradeoff can be avoided by employing a method of Fast Fourier Optimization developed by Dr. Robert Vanderbei. My summer project will focus on exploring some of the models that Dr. Vanderbei has created as well as using them to design masks of my own. I will also be delving into the world of linear programming under the guidance of Dr. Vanderbei.

Weekly Log
Week 1: Monday's orientation gave me a chance to meet many of the other REU students. It was exciting to hear about all of their projects. While waiting to meet with my mentor I read through a couple of papers describing Fast Fourier Optimization and its application to high contrast imaging. On Wednesday I met with my mentor, Dr. Vanderbei, and we discussed some of the possibilities for projects and were able to sketch out some summer plans. The rest of the week was spent exploring Rutgers, grocery shopping with my roommates, picking up my Rutgers ID card, and preparing my website and first presentation.
Week 2: Went to Princeton University to participate in the High Contrast Imaging Lab's first group meeting of the summer. During this meeting one of the lab's graduate students suggested a more focused project plan for my summer. The idea is to design a telescope mask, much as had been disussed previously, but with a specific instrument in mind. As of Thursday of this week I will be designing a pin hole mask for the CHARIS lenslet array. I can't wait to begin work on the main body of my project!
Week 3: I began running an AMPL model that Dr. Vanderbei gave me and reading up on some of the more specific aspects of pupil apodization, Fourier Transformations, Airy Patterns, and Point Spread Functions. On Monday we visited IBM's T. J. Watson Research Center, which was extremely exciting! We were actually able to see Blue Gene.
Week 4: The first portion of the week was spent learning the basics of AMPL while Wednesday through Friday was spent at the 2012 International Symposium of Veronoi Diagrams which was being hosted at DIMACS.
Week 5: Worked on designing my lenslet apodization model in AMPL. Encountered some issues with scaling from a single lens to the lenslet array. Aside from work I enjoyed the BBQ at Dr. Fiorini's house with the other REU kids and then proceeded to suffer from heat exhaustion in the crowds of Philidelphia. What an adventure!
Week 6: Met with my mentor at Princeton again this week and went over my model as well as designing a couple of other different approaches to the problem and discussing a few issues related to optimization and linear programming in general.
Week 7: Worked on my MATLAB code to visualize the results from our 2-dimensional optimization. Worked on my final presentation with Bob and Mary Ann and then presented on Thursday.
Week 8 and 9:Prague Report

Presentations:
First Presentation
Final Presentation

My Mentor: Dr. Robert Vanderbei