Zernike polynomials (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Zernike polynomials" in English language version.

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16doi.org

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11harvard.edu

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7nih.gov

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4arxiv.org

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4semanticscholar.org

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1books.google.com

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1uh.edu

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arxiv.org

Mathar, R. J. (2009). "Zernike Basis to Cartesian Transformations". Serbian Astronomical Journal. 179 (179): 107–120. arXiv:0809.2368. Bibcode:2009SerAJ.179..107M. doi:10.2298/SAJ0979107M. S2CID 115159231.
Tatulli, E. (2013). "Transformation of Zernike coefficients: a Fourier-based method for scaled, translated, and rotated wavefront apertures". J. Opt. Soc. Am. A. 30 (4): 726–32. arXiv:1302.7106. Bibcode:2013JOSAA..30..726T. doi:10.1364/JOSAA.30.000726. PMID 23595334. S2CID 23491106.
Janssen, A. J. E. M. (2011). "A generalization of the Zernike circle polynomials for forward and inverse problems in diffraction theory". arXiv:1110.2369 [math-ph].
Mathar, R. J. (2018). "Orthogonal basis function over the unit circle with the minimax property". arXiv:1802.09518 [math.NA].

books.google.com

Born, Max & Wolf, Emil (1999). Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th ed.). Cambridge, UK: Cambridge University Press. p. 986. ISBN 9780521642224. (see also at Google Books)

doi.org

Zernike, F. (1934). "Beugungstheorie des Schneidenverfahrens und Seiner Verbesserten Form, der Phasenkontrastmethode". Physica. 1 (8): 689–704. Bibcode:1934Phy.....1..689Z. doi:10.1016/S0031-8914(34)80259-5.
Mathar, R. J. (2009). "Zernike Basis to Cartesian Transformations". Serbian Astronomical Journal. 179 (179): 107–120. arXiv:0809.2368. Bibcode:2009SerAJ.179..107M. doi:10.2298/SAJ0979107M. S2CID 115159231.
Noll, R. J. (1976). "Zernike polynomials and atmospheric turbulence" (PDF). J. Opt. Soc. Am. 66 (3): 207. Bibcode:1976JOSA...66..207N. doi:10.1364/JOSA.66.000207.
Thibos, L. N.; Applegate, R. A.; Schwiegerling, J. T.; Webb, R. (2002). "Standards for reporting the optical aberrations of eyes" (PDF). Journal of Refractive Surgery. 18 (5): S652-60. doi:10.3928/1081-597X-20020901-30. PMID 12361175.
Genberg, V. L.; Michels, G. J.; Doyle, K. B. (2002). "Orthogonality of Zernike polynomials". Optomechanical design and Engineering 2002. Proc SPIE. Vol. 4771. pp. 276–286. doi:10.1117/12.482169.
Lakshminarayanan, V.; Fleck, Andre (2011). "Zernike polynomials: a guide". J. Mod. Opt. 58 (7): 545–561. Bibcode:2011JMOp...58..545L. doi:10.1080/09500340.2011.554896. S2CID 120905947.
Honarvar Shakibaei, Barmak (2013). "Recursive formula to compute Zernike radial polynomials". Opt. Lett. 38 (14): 2487–2489. Bibcode:2013OptL...38.2487H. doi:10.1364/OL.38.002487. PMID 23939089.
Kintner, E. C. (1976). "On the mathematical properties of the Zernike Polynomials". Opt. Acta. 23 (8): 679–680. Bibcode:1976AcOpt..23..679K. doi:10.1080/713819334.
Tatulli, E. (2013). "Transformation of Zernike coefficients: a Fourier-based method for scaled, translated, and rotated wavefront apertures". J. Opt. Soc. Am. A. 30 (4): 726–32. arXiv:1302.7106. Bibcode:2013JOSAA..30..726T. doi:10.1364/JOSAA.30.000726. PMID 23595334. S2CID 23491106.
Janssen, A. J. E. M. (2011). "New analytic results for the Zernike Circle Polynomials from a basic result in the Nijboer-Zernike diffraction theory". Journal of the European Optical Society: Rapid Publications. 6: 11028. Bibcode:2011JEOS....6E1028J. doi:10.2971/jeos.2011.11028.
Barakat, Richard (1980). "Optimum balanced wave-front aberrations for radially symmetric amplitude distributions: Generalizations of Zernike polynomials". J. Opt. Soc. Am. 70 (6): 739–742. Bibcode:1980JOSA...70..739B. doi:10.1364/JOSA.70.000739.
Akondi, Vyas; Dubra, Alfredo (22 June 2020). "Average gradient of Zernike polynomials over polygons". Optics Express. 28 (13): 18876–18886. Bibcode:2020OExpr..2818876A. doi:10.1364/OE.393223. ISSN 1094-4087. PMC 7340383. PMID 32672177.
Tahmasbi, A. (2010). An Effective Breast Mass Diagnosis System using Zernike Moments. 17th Iranian Conf. on Biomedical Engineering (ICBME'2010). Isfahan, Iran: IEEE. pp. 1–4. doi:10.1109/ICBME.2010.5704941.
Tahmasbi, A.; Saki, F.; Shokouhi, S.B. (2011). "Classification of Benign and Malignant Masses Based on Zernike Moments". Computers in Biology and Medicine. 41 (8): 726–735. doi:10.1016/j.compbiomed.2011.06.009. PMID 21722886.
Rdzanek, W. P. (2018). "Sound radiation of a vibrating elastically supported circular plate embedded into a flat screen revisited using the Zernike circle polynomials". J. Sound Vib. 434: 91–125. Bibcode:2018JSV...434...92R. doi:10.1016/j.jsv.2018.07.035. S2CID 125512636.
Alizadeh, Elaheh; Lyons, Samanthe M; Castle, Jordan M; Prasad, Ashok (2016). "Measuring systematic changes in invasive cancer cell shape using Zernike moments". Integrative Biology. 8 (11): 1183–1193. doi:10.1039/C6IB00100A. PMID 27735002.

harvard.edu

ui.adsabs.harvard.edu

Zernike, F. (1934). "Beugungstheorie des Schneidenverfahrens und Seiner Verbesserten Form, der Phasenkontrastmethode". Physica. 1 (8): 689–704. Bibcode:1934Phy.....1..689Z. doi:10.1016/S0031-8914(34)80259-5.
Mathar, R. J. (2009). "Zernike Basis to Cartesian Transformations". Serbian Astronomical Journal. 179 (179): 107–120. arXiv:0809.2368. Bibcode:2009SerAJ.179..107M. doi:10.2298/SAJ0979107M. S2CID 115159231.
Noll, R. J. (1976). "Zernike polynomials and atmospheric turbulence" (PDF). J. Opt. Soc. Am. 66 (3): 207. Bibcode:1976JOSA...66..207N. doi:10.1364/JOSA.66.000207.
Lakshminarayanan, V.; Fleck, Andre (2011). "Zernike polynomials: a guide". J. Mod. Opt. 58 (7): 545–561. Bibcode:2011JMOp...58..545L. doi:10.1080/09500340.2011.554896. S2CID 120905947.
Honarvar Shakibaei, Barmak (2013). "Recursive formula to compute Zernike radial polynomials". Opt. Lett. 38 (14): 2487–2489. Bibcode:2013OptL...38.2487H. doi:10.1364/OL.38.002487. PMID 23939089.
Kintner, E. C. (1976). "On the mathematical properties of the Zernike Polynomials". Opt. Acta. 23 (8): 679–680. Bibcode:1976AcOpt..23..679K. doi:10.1080/713819334.
Tatulli, E. (2013). "Transformation of Zernike coefficients: a Fourier-based method for scaled, translated, and rotated wavefront apertures". J. Opt. Soc. Am. A. 30 (4): 726–32. arXiv:1302.7106. Bibcode:2013JOSAA..30..726T. doi:10.1364/JOSAA.30.000726. PMID 23595334. S2CID 23491106.
Janssen, A. J. E. M. (2011). "New analytic results for the Zernike Circle Polynomials from a basic result in the Nijboer-Zernike diffraction theory". Journal of the European Optical Society: Rapid Publications. 6: 11028. Bibcode:2011JEOS....6E1028J. doi:10.2971/jeos.2011.11028.
Barakat, Richard (1980). "Optimum balanced wave-front aberrations for radially symmetric amplitude distributions: Generalizations of Zernike polynomials". J. Opt. Soc. Am. 70 (6): 739–742. Bibcode:1980JOSA...70..739B. doi:10.1364/JOSA.70.000739.
Akondi, Vyas; Dubra, Alfredo (22 June 2020). "Average gradient of Zernike polynomials over polygons". Optics Express. 28 (13): 18876–18886. Bibcode:2020OExpr..2818876A. doi:10.1364/OE.393223. ISSN 1094-4087. PMC 7340383. PMID 32672177.
Rdzanek, W. P. (2018). "Sound radiation of a vibrating elastically supported circular plate embedded into a flat screen revisited using the Zernike circle polynomials". J. Sound Vib. 434: 91–125. Bibcode:2018JSV...434...92R. doi:10.1016/j.jsv.2018.07.035. S2CID 125512636.

nih.gov

pubmed.ncbi.nlm.nih.gov

Thibos, L. N.; Applegate, R. A.; Schwiegerling, J. T.; Webb, R. (2002). "Standards for reporting the optical aberrations of eyes" (PDF). Journal of Refractive Surgery. 18 (5): S652-60. doi:10.3928/1081-597X-20020901-30. PMID 12361175.
Honarvar Shakibaei, Barmak (2013). "Recursive formula to compute Zernike radial polynomials". Opt. Lett. 38 (14): 2487–2489. Bibcode:2013OptL...38.2487H. doi:10.1364/OL.38.002487. PMID 23939089.
Tatulli, E. (2013). "Transformation of Zernike coefficients: a Fourier-based method for scaled, translated, and rotated wavefront apertures". J. Opt. Soc. Am. A. 30 (4): 726–32. arXiv:1302.7106. Bibcode:2013JOSAA..30..726T. doi:10.1364/JOSAA.30.000726. PMID 23595334. S2CID 23491106.
Akondi, Vyas; Dubra, Alfredo (22 June 2020). "Average gradient of Zernike polynomials over polygons". Optics Express. 28 (13): 18876–18886. Bibcode:2020OExpr..2818876A. doi:10.1364/OE.393223. ISSN 1094-4087. PMC 7340383. PMID 32672177.
Tahmasbi, A.; Saki, F.; Shokouhi, S.B. (2011). "Classification of Benign and Malignant Masses Based on Zernike Moments". Computers in Biology and Medicine. 41 (8): 726–735. doi:10.1016/j.compbiomed.2011.06.009. PMID 21722886.
Alizadeh, Elaheh; Lyons, Samanthe M; Castle, Jordan M; Prasad, Ashok (2016). "Measuring systematic changes in invasive cancer cell shape using Zernike moments". Integrative Biology. 8 (11): 1183–1193. doi:10.1039/C6IB00100A. PMID 27735002.

ncbi.nlm.nih.gov

Akondi, Vyas; Dubra, Alfredo (22 June 2020). "Average gradient of Zernike polynomials over polygons". Optics Express. 28 (13): 18876–18886. Bibcode:2020OExpr..2818876A. doi:10.1364/OE.393223. ISSN 1094-4087. PMC 7340383. PMID 32672177.

semanticscholar.org

api.semanticscholar.org

Mathar, R. J. (2009). "Zernike Basis to Cartesian Transformations". Serbian Astronomical Journal. 179 (179): 107–120. arXiv:0809.2368. Bibcode:2009SerAJ.179..107M. doi:10.2298/SAJ0979107M. S2CID 115159231.
Lakshminarayanan, V.; Fleck, Andre (2011). "Zernike polynomials: a guide". J. Mod. Opt. 58 (7): 545–561. Bibcode:2011JMOp...58..545L. doi:10.1080/09500340.2011.554896. S2CID 120905947.
Tatulli, E. (2013). "Transformation of Zernike coefficients: a Fourier-based method for scaled, translated, and rotated wavefront apertures". J. Opt. Soc. Am. A. 30 (4): 726–32. arXiv:1302.7106. Bibcode:2013JOSAA..30..726T. doi:10.1364/JOSAA.30.000726. PMID 23595334. S2CID 23491106.
Rdzanek, W. P. (2018). "Sound radiation of a vibrating elastically supported circular plate embedded into a flat screen revisited using the Zernike circle polynomials". J. Sound Vib. 434: 91–125. Bibcode:2018JSV...434...92R. doi:10.1016/j.jsv.2018.07.035. S2CID 125512636.

uh.edu

voi.opt.uh.edu

Thibos, L. N.; Applegate, R. A.; Schwiegerling, J. T.; Webb, R. (2002). "Standards for reporting the optical aberrations of eyes" (PDF). Journal of Refractive Surgery. 18 (5): S652-60. doi:10.3928/1081-597X-20020901-30. PMID 12361175.

worldcat.org

search.worldcat.org

Akondi, Vyas; Dubra, Alfredo (22 June 2020). "Average gradient of Zernike polynomials over polygons". Optics Express. 28 (13): 18876–18886. Bibcode:2020OExpr..2818876A. doi:10.1364/OE.393223. ISSN 1094-4087. PMC 7340383. PMID 32672177.