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dc.contributor.authorAftab, Maham
dc.contributor.authorGraves, Logan R.
dc.contributor.authorBurge, James H.
dc.contributor.authorSmith, Greg A.
dc.contributor.authorOh, Chang-Jin
dc.contributor.authorKim, Dae Wook
dc.date.accessioned2019-11-07T19:40:12Z
dc.date.available2019-11-07T19:40:12Z
dc.date.issued2019-09-24
dc.identifier.citationMaham Aftab, Logan R. Graves, James H. Burge, Greg A. Smith, Chang Jin Oh, and Dae Wook Kim "Rectangular domain curl polynomial set for optical vector data processing and analysis," Optical Engineering 58(9), 095105 (24 September 2019). https://doi.org/10.1117/1.OE.58.9.095105en_US
dc.identifier.issn0091-3286
dc.identifier.doi10.1117/1.oe.58.9.095105
dc.identifier.urihttp://hdl.handle.net/10150/635031
dc.description.abstractRectangular pupils are employed in many optical applications such as lasers and anamorphic optics, as well as for detection and metrology systems such as some Shack−Hartmann wavefront sensors and deflectometry systems. For optical fabrication, testing, and analysis in the rectangular domain, it is important to have a well-defined set of polynomials that are orthonormal over a rectangular pupil. Since we often measure the gradient of a wavefront or surface, it is necessary to have a polynomial set that is orthogonal over a rectangular pupil in the vector domain as well. We derive curl (called C) polynomials based on two-dimensional (2-D) versions of Chebyshev polynomials of the first kind. Previous work derived a set of polynomials (called G polynomials) that are obtained from the gradients of the 2-D Chebyshev polynomials. We show how the two sets together can be used as a complete representation of any vector data in the rectangular domain. The curl polynomials themselves or the complete set of G and C polynomials has many interesting applications. Two of those applications shown are systematic error analysis and correction in deflectometry systems and mapping imaging distortion.en_US
dc.language.isoenen_US
dc.publisherSPIE-SOC PHOTO-OPTICAL INSTRUMENTATION ENGINEERSen_US
dc.rightsCopyright © 2019 Society of Photo-Optical Instrumentation Engineers (SPIE).en_US
dc.subjectmeasurement and metrologyen_US
dc.subjectsurface measurementsen_US
dc.subjectnumerical approximation and analysisen_US
dc.subjectoptical instrumentationen_US
dc.subjectinformation processingen_US
dc.subjecttestingen_US
dc.titleRectangular domain curl polynomial set for optical vector data processing and analysisen_US
dc.typeArticleen_US
dc.contributor.departmentUniv Arizona, Steward Observen_US
dc.contributor.departmentUniv Arizona, Large Opt Fabricat & Testing Grpen_US
dc.identifier.journalOPTICAL ENGINEERINGen_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.volume58
dc.source.issue09
dc.source.beginpage1
refterms.dateFOA2019-11-07T19:40:13Z


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