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dc.contributor.authorAftab, Maham
dc.contributor.authorBurge, James H.
dc.contributor.authorSmith, Greg A.
dc.contributor.authorGraves, Logan R.
dc.contributor.authorOh, Chang Jin
dc.contributor.authorKim, Dae Wook
dc.date.accessioned2019-05-16T22:12:12Z
dc.date.available2019-05-16T22:12:12Z
dc.date.issued2018
dc.identifier.citationMaham Aftab, James H. Burge, Greg A. Smith, Logan Graves, Chang-jin Oh, and Dae Wook Kim "Chebyshev gradient polynomials for high resolution surface and wavefront reconstruction", Proc. SPIE 10742, Optical Manufacturing and Testing XII, 1074211 (14 September 2018); doi: 10.1117/12.2320804; https://doi.org/10.1117/12.2320804en_US
dc.identifier.issn9781510620551
dc.identifier.issn9781510620568
dc.identifier.doi10.1117/12.2320804
dc.identifier.doi10.1117/12.2320804.5836031818001
dc.identifier.urihttp://hdl.handle.net/10150/632303
dc.description.abstractA new data processing method based on orthonormal rectangular gradient polynomials is introduced in this work. This methodology is capable of effectively reconstructing surfaces or wavefronts with data obtained from deflectometry systems, especially during fabrication and metrology of high resolution and freeform surfaces. First, we derived a complete and computationally efficient vector polynomial set, called G polynomials. These polynomials are obtained from gradients of Chebyshev polynomials of the first kind - a basis set with many qualities that are useful for modal fitting. In our approach both the scalar and vector polynomials, that are defined and manipulated easily, have a straightforward relationship due to which the polynomial coefficients of both sets are the same. This makes conversion between the two sets highly convenient. Another powerful attribute of this technique is the ability to quickly generate a very large number of polynomial terms, with high numerical efficiency. Since tens of thousands of polynomials can be generated, mid-to-high spatial frequencies of surfaces can be reconstructed from high-resolution metrology data. We will establish the strengths of our approach with examples involving simulations as well as real metrology data from the Daniel K. Inouye Solar Telescope (DKIST) primary mirror.en_US
dc.description.sponsorshipKorea Basic Science Institute; II-VI Foundation Block granten_US
dc.language.isoenen_US
dc.publisherSPIE-INT SOC OPTICAL ENGINEERINGen_US
dc.relation.urlhttps://spiedigitallibrary.org/conference-proceedings-of-spie/10742/2320804/Chebyshev-gradient-polynomials-for-high-resolution-surface-and-wavefront-reconstruction/10.1117/12.2320804.fullen_US
dc.relation.urlhttps://spiedigitallibrary.org/conference-presentations/10742/1074211/Chebyshev-gradient-polynomials-for-high-resolution-surface-and-wavefront-reconstruction/10.1117/12.2320804.5836031818001en_US
dc.rights© (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).en_US
dc.subjectSurface reconstructionen_US
dc.subjectSurface measurementsen_US
dc.subjectOptical metrologyen_US
dc.subjectInformation processingen_US
dc.subjectDeflectometryen_US
dc.subjectTestingen_US
dc.subjectModal fittingen_US
dc.subjectNumerical approximation and analysisen_US
dc.titleChebyshev gradient polynomials for high resolution surface and wavefront reconstructionen_US
dc.typeArticleen_US
dc.contributor.departmentUniv Arizona, Coll Opt Scien_US
dc.contributor.departmentUniv Arizona, Steward Observen_US
dc.identifier.journalOPTICAL MANUFACTURING AND TESTING XIIen_US
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en_US
dc.eprint.versionFinal published versionen_US
dc.source.beginpage40
refterms.dateFOA2019-05-16T22:12:13Z


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