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Comparison of Possible Optimization Methods for Design of Optical Filters

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Wavefront coding for extending the depth of focus of imaging systems uses a cubic phase mask which has a single parameter phase variation. Using a single parameter puts a limitation on optimizing the function that serves as criteria for characterizing invariance in depth of focus of a filter. Pupil phase engineering builds on wavefront coding by using a multi-parameter filter. Global optimization of these multidimensional filters with a conventional sequentially implemented method like Simulated Annealing can take time in the order of several days and even weeks to optimize on a single machine. Hence there is a need to address this issue by an algorithm that can work over a network of computers in parallel. This thesis uses a freely available Genetic Algorithm package called SUGAL; which allows a lot of configurability and extensibility. By itself, SUGAL does not have a standard parallel run feature, but it allows extensibility so that it can be modified to give a parallel implementation. Due to extensibility of both SUGAL and MATLAB they have been integrated with each other in this thesis. Results of comparison of conventional optimization methods like the BFGS (Broyden-Fletcher-Goldfarb-Shanno) and (the similar but global optimization method) SA (Simulated Annealing) with GA (Genetic Algorithms) give us some important observations. Unlike BFGS, GA is a method for global optimization and when compared to a global optimization method like SA the parallel implementation of the GA did better not only in the time taken, but also in the number of function evaluations required. For functions which do not have gradients, BFGS fails totally and is not an option this highlights why GA are considered better for discrete optimization. In addition BFGS suffers from having to guess good starting points and is affected by fortuitous starts. However, in the vicinity of the solution and for convex problems it is often cheaper to use the BFGS method. It is also observed that GA converges very close to the solution but the final solution, if at all reached, by BFGS or SA is slightly more accurate. This research also suggests that, from among the different ways to run the GA, the hybrid genitor algorithm is better for a parallel implementation simply because the Genitor algorithm can not be implemented in parallel.
genetic algorithm
hybrid genitor
optical fiters
pupil phase engineering
Kediyal, Prashant C (author)
pkediyal@hotmail.com (authorEmail)
David John (committee chair)
Robert Plemmons (committee member)
Paul Pauca (committee member)
Kediyal, Prashant C
2008-09-28T10:49:48Z (accessioned)
2010-06-18T19:00:09Z (accessioned)
2005-08-19 (available)
2008-09-28T10:49:48Z (available)
2010-06-18T19:00:09Z (available)
2004-03-22 (issued)
null (defenseDate)
Computer Science (discipline)
Wake Forest University (grantor)
MS (level)
http://hdl.handle.net/10339/14929 (uri)
etd-05022004-113931 (oldETDId)
Release the entire work for access only to the Wake Forest University system for one year from the date of approval. After one year, release the entire work for access worldwide, unless I send notification to delay release. (accessRights)
I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Wake Forest University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. (license)
Comparison of Possible Optimization Methods for Design of Optical Filters

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