Medición del índice de refracción de láminas planas en un interferómetro de división de frente de onda en configuración confocal
Two proposals were studied for measuring the refractive index of flat plates in a wavefront-splitting interferometer in confocal configuration by the identification of the best focused interferogram in two configurations: when the light passing through the plate is measured (transmission method), an...
- Autores:
-
Rueda Parra, Santiago
- Tipo de recurso:
- Work document
- Fecha de publicación:
- 2020
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- Universidad Nacional de Colombia
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- Universidad Nacional de Colombia
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- 530 - Física::535 - Luz y radiación relacionada
índice de refracción
interferencia
difracción
enfoque
sistema confocal
profundidad de foco
aberración esférica
refractive index
interference
diffraction
focusing
confocal system
depth of focus
spherical aberration
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- openAccess
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- Atribución-NoComercial 4.0 Internacional
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Medición del índice de refracción de láminas planas en un interferómetro de división de frente de onda en configuración confocal |
| title |
Medición del índice de refracción de láminas planas en un interferómetro de división de frente de onda en configuración confocal |
| spellingShingle |
Medición del índice de refracción de láminas planas en un interferómetro de división de frente de onda en configuración confocal 530 - Física::535 - Luz y radiación relacionada índice de refracción interferencia difracción enfoque sistema confocal profundidad de foco aberración esférica refractive index interference diffraction focusing confocal system depth of focus spherical aberration |
| title_short |
Medición del índice de refracción de láminas planas en un interferómetro de división de frente de onda en configuración confocal |
| title_full |
Medición del índice de refracción de láminas planas en un interferómetro de división de frente de onda en configuración confocal |
| title_fullStr |
Medición del índice de refracción de láminas planas en un interferómetro de división de frente de onda en configuración confocal |
| title_full_unstemmed |
Medición del índice de refracción de láminas planas en un interferómetro de división de frente de onda en configuración confocal |
| title_sort |
Medición del índice de refracción de láminas planas en un interferómetro de división de frente de onda en configuración confocal |
| dc.creator.fl_str_mv |
Rueda Parra, Santiago |
| dc.contributor.advisor.spa.fl_str_mv |
Mejía Barbosa, Yobani |
| dc.contributor.author.spa.fl_str_mv |
Rueda Parra, Santiago |
| dc.contributor.researchgroup.spa.fl_str_mv |
Optica Aplicada - UN |
| dc.subject.ddc.spa.fl_str_mv |
530 - Física::535 - Luz y radiación relacionada |
| topic |
530 - Física::535 - Luz y radiación relacionada índice de refracción interferencia difracción enfoque sistema confocal profundidad de foco aberración esférica refractive index interference diffraction focusing confocal system depth of focus spherical aberration |
| dc.subject.proposal.spa.fl_str_mv |
índice de refracción interferencia difracción enfoque sistema confocal profundidad de foco aberración esférica |
| dc.subject.proposal.eng.fl_str_mv |
refractive index interference diffraction focusing confocal system depth of focus spherical aberration |
| description |
Two proposals were studied for measuring the refractive index of flat plates in a wavefront-splitting interferometer in confocal configuration by the identification of the best focused interferogram in two configurations: when the light passing through the plate is measured (transmission method), and when the light reflecting on the surfaces of the plate is measured (reflection method). The interference pattern in defocused planes were analyzed numerically by solving the Rayleigh–Sommerfeld diffraction integral and by performing a ray tracing of the system using the exact form of Snell's law, and analytically by using the Fresnel approximations for point sources. Also, an analytical description of the Spherical Aberration influence on the Axial Irradiance was done. Using the transmission method, two significant figures for the refractive index were measured. The percentage uncertainties found using the transmission method were about 1.11 % and 4.19 %; the percentage differences between the reference value (N-BK7) and measured values, were about 1.41 % and 3.21 %. Using the reflection method, there was found an experimental error in the refractive index in the second significant figure and the percentage uncertainties were about 1.04 % and 3.58 %, and the percentage differences related with the expected value were about 1.40 % and 7.04 %. The experimental factors that limit the precision of the methods were analyzed. In the transmission method different positions in the plate are correlated. Because of that, the refractive index measurement is highly affected by variations in the thickness of the plate. By the other hand, the reflection method is a local measurement in a single position of the plate. For that reason, the refractive index measurement is highly affected by the local thickness of the plate. Because the origin of the experimental errors in both methods are different, it is not possible to use both methods simultaneously to improve the measurement. Our main conclusion is that our proposal is not well suited as high precision metrology for refractive index measurement of plates with a given thickness. Instead of that, it is possible to use the transmission method to measure differences in thickness, and the reflection method to measure local thickness, with sensitivities in the order of the nanometers. It is recommended to keep researching in that direction. |
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2020 |
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2020-08-04T15:34:27Z |
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2020-08-04T15:34:27Z |
| dc.date.issued.spa.fl_str_mv |
2020-06-10 |
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Documento de trabajo |
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info:eu-repo/semantics/workingPaper |
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| dc.relation.references.spa.fl_str_mv |
Y. Yoshizawa, Handbook of Optical Metrology. CRC Press, 2 ed., 2015. P. Hariharan, Basics of Interferometry. San Diego: Academic Press, 2 ed., 2007. S. Singh, “Refractive index measurement and its applications,” Physica Scripta, vol. 65, pp. 167–180, jan 2002. A. Arimoto, “Intensity distribution of aberration-free diffraction patterns due to circular apertures in large f-number optical systems,” Optica Acta: International Journal of Optics, vol. 23, no. 3, pp. 245–250, 1976. J. H. Erkkila and M. E. Rogers, “Diffracted fields in the focal volume of a converging wave,” J. Opt. Soc. Am., vol. 71, pp. 904–905, Jul 1981. V. N. Mahajan, “Axial irradiance and optimun focusing of laser beams,” Appl. Opt, vol. 22, no. 19, pp. 3042–3053, 1983. Y. Li and E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different fresnel numbers,” J. Opt. Soc. Am. A, vol. 1, pp. 801–808, Aug 1984. C. J. R. Sheppard and P. Török, “Dependence of fresnel number on aperture stop position,” J. Opt. Soc. Am. A, vol. 15, pp. 3016–3019, Dec 1998. M. Born and E. Wolf, Principles of Optics. Cambridge: Cambridge University Press, 1999. E. Collett and E. Wolf, “Symmetry properties of focused fields,” Opt. Lett., vol. 5, pp. 264–266, Jun 1980. A. F. Jiménez, “Diseño de un sistema para la medición de potencia refractiva de lentes progresivas empleando la prueba de hartmann,” Master’s thesis, Universidad Nacional de Colombia, Facultad de Ciencias - Fı́sica, Bogotá, 2011. Y. Mejı́a, “Extrapolation, interpolation, and identification of spots in hartmann patterns,” Appl. Opt., vol. 53, pp. 6073–6082, Sep 2014. Y. Mejı́a-Barbosa and D. Malacara-Hernández, “Object surface for applying a modified hartmann test to measure corneal topography,” Appl. Opt., vol. 40, pp. 5778–5786, Nov 2001. Y. Mejı́a and J. C. Galeano, “Corneal topographer based on the hartmann test,” Optometry and Vision Science, vol. 86, no. 4, pp. 370–381, 2009. Y. Mejı́a, “El frente de onda y su representación con polinomios de zernike,” Ciencia y Tecnologı́a para la Salud Visual y Ocular, vol. 9, pp. 145–166, 2011. Y. Mejı́a, “Exact relations between wave aberration and the sagitta difference, and between ray aberration and the slope difference,” Optik, vol. 123, no. 8, pp. 726–730, 2012. Y. Mejı́a, “La prueba de hartmann en ciencias de la visión,” Ciencia y Tecnologı́a para la Salud Visual y Ocular, vol. 10, pp. 149–165, 2012. J. Schmit, K. Creath, and J. Wyant, “Surface profilers, multiple wavelength, and white light intereferometry,” in Optical Shop Testing (D. Malacara, ed.), ch. 15, pp. 667,755, John Wiley & Sons, Inc., 3 ed., 2007. J. G. Fujimoto, C. Pitris, S. A. Boppart, and M. E. Brezinski, “Optical coherence tomography: An emerging technology for biomedical imaging and optical biopsy,” Neoplasia, vol. 2, no. 1, pp. 9 – 25, 2000. V. Chen, “Not using laser light for confocal microscopy and how to use laser light when it’s all you have,” in Handbook of Biological Confocal Microscopy (J. B. Pawley, ed.), ch. 6, pp. 99,109, Springer US, 3 ed., 2006. S. Rueda and Y. Mejı́a, “Measurement of surface position by focusing an interference pattern of multiple apertures with a confocal system,” Appl. Opt., vol. 57, pp. 498–506, Jan 2018. J. Terrien, “News from the bureau international des poids et mesures,” Metrologia, vol. 11, pp. 179–183, oct 1975. P. Giacomo, “News from the BIPM,” Metrologia, vol. 20, pp. 25–30, jan 1984. S. S. Batanov, E. D. Ruchkin, and P. I. A., Refractive Indices of solids. Springer, 2016. W. Boyes, Instrumentation Reference Book. Elsevier Science, 2002. L. W. Tilton, “Standard conditions for precise prism refractometry,” Journal of Research of the National Bureau of Standards, vol. 14, pp. 393–418, 1935. O. Medenbach and R. D. Shannon, “Refractive indices and optical dispersion of 103 synthetic and mineral oxides and silicates measured by a small-prism technique,” J. Opt. Soc. Am. B, vol. 14, pp. 3299–3318, Dec 1997. O. Medenbach, D. Dettmar, R. D. Shannon, R. X. Fischer, and W. M. Yen, “Refractive index and optical dispersion of rare earth oxides using a small-prism technique,” Journal of Optics A: Pure and Applied Optics, vol. 3, pp. 174–177, mar 2001. M. S. Shumate, “Interferometric measurement of large indices of refraction,” Appl. Opt., vol. 5, pp. 327–331, Feb 1966. L. A. Gerasimova, “Interferometric measurement of the refractive-index gradient distribution in gradient-index optical blanks,” Appl. Opt., vol. 35, pp. 2997–3001, Jun 1996. G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt., vol. 36, pp. 8184–8189, Nov 1997. H. G. Tompkins and E. A. Irene, Handbook of ellipsometry. Springer, 2005. R. A. Paselk, “The evolution of abbe refractometer,” Bulletin of the Scientific Instrument Society, vol. 62, pp. 19–22, 1999. H. Onodera, I. Awai, and J. ichi Ikenoue, “Refractive-index measurement of bulk materials: prism coupling method,” Appl. Opt., vol. 22, pp. 1194–1197, Apr 1983. G. H. Meeten, “Refractive index errors in the critical-angle and the brewster-angle methods applied to absorbing and heterogeneous materials,” Measurement Science and Technology, vol. 8, pp. 728–733, jul 1997. G. D. Gillen and S. Guha, “Refractive-index measurements of zinc germanium diphosphide at 300 and 77 k by use of a modified michelson interferometer,” Appl. Opt., vol. 43, pp. 2054–2058, Apr 2004. J. J. Lunazzi and M. Garavaglia, “Fabry-perot laser interferometry to measure refractive index or thickness of transparent materials,” vol. 6, pp. 237–240, mar 1973. G. D. Gillen and S. Guha, “Use of michelson and fabry–perot interferometry for independent determination of the refractive index and physical thickness of wafers,” Appl. Opt., vol. 44, pp. 344–347, Jan 2005. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys., vol. 59, pp. 427–471,1996. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science, vol. 254, pp. 1178–1181, 1991. D. Malacara-Hernández and Z. Malacara-Hernández, Handbook of Optical Design, Third Edition. Optical science and engineering, Taylor & Francis, 2013. V. N. Mahajan, Aberration Theory Made Simple. SPIE tutorial texts, SPIE, 2011. A. Sommerfeld, Optics, Lectures on Theoretical Physics, vol. IV. Academic Press, 1954. J. Goodman, Introduction to Fourier Optics. McGraw-Hill, 1996. H. Osterberg and L. W. Smith, “Closed solutions of rayleigh’s diffraction integrals for axial points,” Journal of the Optical Society of America, vol. 51, no. 10, pp. 1050–1054,1961. H. Urey, “Spot size, depth-of-focus, and diffraction ring intensity formulas for truncated gaussian beams,” Appl. Opt, vol. 43, no. 3, pp. 620–625, 2004. V. N. Mahajan, “Axial irradiance of a focused beam,” J. Opt. Soc. Am. A, vol. 22, pp. 1814–1823, Sep 2005. D. Malacara, M. Servin, and Z. Malacara, “Two-wave interferometers and configurations used in optical testing,” in Interferogram analysis for optical testing, ch. 1.1, Taylor & Francis, 2 ed., 2005. H. M. Mora Escobar, Introducción a C y a métodos numéricos. Bogotá: Universidad Nacional de Colombia, 2004. N. H. Asmar, Partial Differential Equations with Fourier Series and Boundary Value Problems. Saddle River, New Jersey: Pearson Prentice, 2000. E. Hecht and A. Zajac, Optics. Reading, Massachusetts: Addison-Wesley Publishing Company, 4 ed., 2002. Edmund Optics, Optics and Photonics Catalog and Resource Guide. 2019. M. N. Polyanskiy, “Refractive index database.” https://refractiveindex.info. Accessed on 2019-10-14. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” Journal of Biomedical Optics, vol. 10, no. 4, pp. 1 – 8, 2005. A. M. Ardila, Fı́sica Experimental. Bogotá: Universidad Nacional de Colombia, 2007. Nikon, “Nexiv vmz-k series.” https://www.nikonmetrology.com/en-gb/product/nexiv-vmz-k6555, 2018. E. T. Whittaker, A History of the Theories of Aether and Electricity. London: Longmans, Green, and Co., 1910. O. Stavroudis, The Mathematics of Geometrical and Physical Optics. Mörlenbach: WILEY-VCH, 2006. M. Herzberger, “Optics from euclid to hyugens,” Applied Optics, vol. 5, pp. 1383–1393, 1966. W. B. Joyce and A. Joyce, “Descartes, newton, and snell’s law,” J. Opt. Soc. Am, vol. 66, no. 1, pp. 1–8, 1976. M. Spivak, Calculus. Calculus, Cambridge University Press, 2006. |
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Derechos reservados - Universidad Nacional de Colombia |
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de ColombiaAcceso abiertohttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Mejía Barbosa, Yobanic0dbee1e-bab8-45cb-a8cb-4d4fc9d81e1c-1Rueda Parra, Santiago76a6f81c-9e9f-481d-a953-2d5b7fbb3e5eOptica Aplicada - UN2020-08-04T15:34:27Z2020-08-04T15:34:27Z2020-06-10https://repositorio.unal.edu.co/handle/unal/77917Two proposals were studied for measuring the refractive index of flat plates in a wavefront-splitting interferometer in confocal configuration by the identification of the best focused interferogram in two configurations: when the light passing through the plate is measured (transmission method), and when the light reflecting on the surfaces of the plate is measured (reflection method). The interference pattern in defocused planes were analyzed numerically by solving the Rayleigh–Sommerfeld diffraction integral and by performing a ray tracing of the system using the exact form of Snell's law, and analytically by using the Fresnel approximations for point sources. Also, an analytical description of the Spherical Aberration influence on the Axial Irradiance was done. Using the transmission method, two significant figures for the refractive index were measured. The percentage uncertainties found using the transmission method were about 1.11 % and 4.19 %; the percentage differences between the reference value (N-BK7) and measured values, were about 1.41 % and 3.21 %. Using the reflection method, there was found an experimental error in the refractive index in the second significant figure and the percentage uncertainties were about 1.04 % and 3.58 %, and the percentage differences related with the expected value were about 1.40 % and 7.04 %. The experimental factors that limit the precision of the methods were analyzed. In the transmission method different positions in the plate are correlated. Because of that, the refractive index measurement is highly affected by variations in the thickness of the plate. By the other hand, the reflection method is a local measurement in a single position of the plate. For that reason, the refractive index measurement is highly affected by the local thickness of the plate. Because the origin of the experimental errors in both methods are different, it is not possible to use both methods simultaneously to improve the measurement. Our main conclusion is that our proposal is not well suited as high precision metrology for refractive index measurement of plates with a given thickness. Instead of that, it is possible to use the transmission method to measure differences in thickness, and the reflection method to measure local thickness, with sensitivities in the order of the nanometers. It is recommended to keep researching in that direction.Se estudiaron dos propuestas para medir el índice de refracción de láminas planas en un interferómetro de división de frente de onda de múltiples aperturas en configuración confocal. Los métodos planteados consisten en identificar el plano de mejor enfoque del patrón de interferencia en dos configuraciones: cuando se observa la trasmisión de luz a través de la lámina (método de transmisión) y cuando se observan reflexiones en las caras de la lámina (método de reflexión). La formación de patrones de interferencia en planos desenfocados se estudió de forma numérica, mediante la solución numérica a la integral de difracción de Rayleigh–Sommerfeld usando el método de cuadratura de Gauss y mediante un trazado de rayos geométrico aplicando la ley de Snell exacta y, de forma analítica, mediante el uso de las aproximaciones de Fresnel para fuentes puntuales. También se hizo un tratamiento analítico del efecto de la aberración esférica sobre el patrón de irradiancia axial producido en un interferómetro de tres aperturas en configuración confocal. Con el método de transmisión se lograron medir con exactitud dos cifras significativas del índice de refracción de las láminas empleadas, obteniendo errores porcentuales entre 1.11 % y 4.19 % y diferencias porcentuales respecto al valor de referencia (N-BK7) entre 1.41 % y 3.21 % . Por el método de reflexión, el error cometido se encuentra en la segunda cifra significativa; los errores porcentuales de este método están acotados entre 1.04 % y 3.58 % y las diferencias porcentuales respecto al valor de referencia entre 1.40 % y 7.04 %. Los factores que afectan la precisión y la exactitud de los métodos planteados para medir índices de refracción fueron analizados. Debido a que en la medida de transmisión se están correlacionando distintas posiciones de la lámina, se encontró que la medida del índice de refracción está fuertemente afectada por variaciones del espesor de la lámina a lo largo de su superficie; por el contrario, el método de reflexión es una medida local sobre una posición de la lámina, por lo que el resultado se ve fuertemente afectado por el valor del espesor de la lámina en la posición que se mide. Debido a que el origen del error en ambos casos es distinto, no se pueden usar los dos métodos de forma simultánea para mejorar el resultado. Se concluye que, como método para medir el índice de refracción de láminas con espesor conocido, nuestra propuesta no puede ser considerada como metrología de alta precisión. En lugar de esto, si se desean medir láminas con índice de refracción conocido, el método de transmisión puede dar buenos resultados para medir variaciones en el espesor y el método de reflexión se puede usar para medir el espesor local de láminas, con sensibilidades en el orden de los nanómetros. Se recomienda continuar investigando en esta dirección.Línea de Investigación: Metrología óptica .Maestría201application/pdfspa530 - Física::535 - Luz y radiación relacionadaíndice de refraccióninterferenciadifracciónenfoquesistema confocalprofundidad de focoaberración esféricarefractive indexinterferencediffractionfocusingconfocal systemdepth of focusspherical aberrationMedición del índice de refracción de láminas planas en un interferómetro de división de frente de onda en configuración confocalDocumento de trabajoinfo:eu-repo/semantics/workingPaperinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_8042Texthttp://purl.org/redcol/resource_type/WPBogotá - Ciencias - Maestría en Ciencias - FísicaDepartamento de FísicaUniversidad Nacional de Colombia - Sede BogotáY. Yoshizawa, Handbook of Optical Metrology. CRC Press, 2 ed., 2015.P. Hariharan, Basics of Interferometry. San Diego: Academic Press, 2 ed., 2007.S. Singh, “Refractive index measurement and its applications,” Physica Scripta, vol. 65, pp. 167–180, jan 2002.A. Arimoto, “Intensity distribution of aberration-free diffraction patterns due to circular apertures in large f-number optical systems,” Optica Acta: International Journal of Optics, vol. 23, no. 3, pp. 245–250, 1976.J. H. Erkkila and M. E. Rogers, “Diffracted fields in the focal volume of a converging wave,” J. Opt. Soc. Am., vol. 71, pp. 904–905, Jul 1981.V. N. Mahajan, “Axial irradiance and optimun focusing of laser beams,” Appl. Opt, vol. 22, no. 19, pp. 3042–3053, 1983.Y. Li and E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different fresnel numbers,” J. Opt. Soc. Am. A, vol. 1, pp. 801–808, Aug 1984.C. J. R. Sheppard and P. Török, “Dependence of fresnel number on aperture stop position,” J. Opt. Soc. Am. A, vol. 15, pp. 3016–3019, Dec 1998.M. Born and E. Wolf, Principles of Optics. Cambridge: Cambridge University Press, 1999.E. Collett and E. Wolf, “Symmetry properties of focused fields,” Opt. Lett., vol. 5, pp. 264–266, Jun 1980.A. F. Jiménez, “Diseño de un sistema para la medición de potencia refractiva de lentes progresivas empleando la prueba de hartmann,” Master’s thesis, Universidad Nacional de Colombia, Facultad de Ciencias - Fı́sica, Bogotá, 2011.Y. Mejı́a, “Extrapolation, interpolation, and identification of spots in hartmann patterns,” Appl. Opt., vol. 53, pp. 6073–6082, Sep 2014.Y. Mejı́a-Barbosa and D. Malacara-Hernández, “Object surface for applying a modified hartmann test to measure corneal topography,” Appl. Opt., vol. 40, pp. 5778–5786, Nov 2001.Y. Mejı́a and J. C. Galeano, “Corneal topographer based on the hartmann test,” Optometry and Vision Science, vol. 86, no. 4, pp. 370–381, 2009.Y. Mejı́a, “El frente de onda y su representación con polinomios de zernike,” Ciencia y Tecnologı́a para la Salud Visual y Ocular, vol. 9, pp. 145–166, 2011.Y. 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