Iterative nonlinear optimization techniques for diffractive optical applications and their implementations

Jieyao Zhuang, Purdue University

Abstract

This research focused on the development of iterative nonlinear optimization techniques for diffractive optical applications and their implementations. Five iterative optimization techniques for diffractive optical applications have been developed. The iterative interlacing technique (IIT) for synthesis of CGH involves dividing a hologram into a set of subholograms and designing them iteratively. This technique can be used with most existing algorithms for CGH synthesis and was shown to give a lower reconstruction error and a better reconstructed image in general. The fast decimation-in-frequency direct-binary-search (FDIFDBS) algorithms are fast DBS algorithms. They differ from the original DBS algorithm only in the way the hologram is scanned. The computational complexities for the FDIFDBS algorithms are substantially reduced. The FDIFDBS for complex amplitude-based error (FDIFDBS-CABE) algorithm was extended to the fast decimation-in-frequency direct-multilevel-search (FDIFDMS) algorithm which can be used to design multilevel CGH's without an increase in computational complexity. Based on the image geometry and the decimation-in-frequency property of the fast Fourier transform (FFT) algorithm, an optimal decimation-in-frequency IIT (ODIFIIT) algorithm was developed. As in the IIT technique, the ODIFIIT algorithm can be used with any currently existing CGH synthesis algorithm. In this thesis, the ODIFIIT algorithm together with POCS method (ODIFIIT-POCS) is developed. One version of the algorithm, the constant ODIFIIT-POCS algorithm was shown to give much higher diffraction efficiency and lower reconstruction error than previous CGH coding algorithms. An algorithm based on general linear transform systems, including both unitary and non-unitary linear optical transform systems, was developed. The algorithm was successfully applied to the phase retrieval problem. The designed diffractive optical elements were implemented using e-beam lithography and reactive ion etching.

Degree

Ph.D.

Advisors

Ersoy, Purdue University.

Subject Area

Electrical engineering|Optics

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