Abstract

In this paper, a precise phase-shift extraction method was introduced for the first time to measure the thickness distribution of transparent glass films. A spatial light modulator modulated the phases of the incident laser in a large lateral shearing interferometer. The phase shifting caused by the thickness of the films can be extracted ranging from 0 to 2π, in a recursive way suitable for real-time implementation. Incident lasers with different wavelengths were utilized to measure the spatial distribution of the thickness of the films, and they can be larger than one wavelength of the incident light. Both artificial and experimental results have verified that the resolution of the thickness measurement reaches up to 1 𝛍m.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (3)

J. A. Kim, J. W. Kim, C. S. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref] [PubMed]

C. Qi, S. Zheng, and H. Zhou, “Experimental investigation on gas-phase temperature of axisymmetric ethylene flames by large lateral shearing interferometry,” Int. J. Therm. Sci. 115, 104–111 (2017).
[Crossref]

S. Sun, Z. Cao, A. Huang, L. Xu, and W. Yang, “A high-speed digital electrical capacitance tomography system combining digital recursive demodulation and parallel capacitance measurement,” IEEE Sens. J. 17(20), 6690–6698 (2017).
[Crossref]

2016 (3)

A. Furtmann and G. Poll, “Evaluation of oil-film thickness along the path of contact in a gear mesh by capacitance measurement,” Tribol. Online 11(2), 189–194 (2016).
[Crossref]

Y. Li, Y. Wang, C. Liu, J. Yang, and Q. Ding, “Linear frequency modulation multi-beam laser heterodyne measurement for the glass thickness,” Appl. Phys. B 122(2), 1–5 (2016).

H. Wu, F. Zhang, T. Liu, and X. Qu, “Glass thickness and index measurement using optical sampling by cavity tuning,” Appl. Opt. 55(34), 9756–9763 (2016).
[Crossref] [PubMed]

2015 (1)

J. Zhu, J. Dai, X. Cheng, C. Cheng, J. Zhang, and Y. Li, “Temperature measurement of a horizontal cylinder in natural convection using a lateral shearing interferometer with a large shear amount,” Opt. Eng. 54(3), 034109 (2015).
[Crossref]

2014 (5)

Y. Li, W. Xiao, and F. Pan, “Multiple-wavelength-scanning-based phase unwrapping method for digital holographic microscopy,” Appl. Opt. 53(5), 979–987 (2014).
[Crossref] [PubMed]

B. Maniscalco, P. M. Kaminski, and J. M. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
[Crossref]

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[Crossref] [PubMed]

M. M. Neumann and D. L. Neumann, “Touch screen tablets and emergent literacy,” Early Child. Educ. J. 42(4), 231–239 (2014).
[Crossref]

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

2013 (4)

D. E. Scott, R. J. Grigsby, and S. M. Lunte, “Microdialysis sampling coupled to microchip electrophoresis with integrated amperometric detection on an all-glass substrate,” ChemPhysChem 14(10), 2288–2294 (2013).
[Crossref] [PubMed]

C. Knoth, B. Klein, T. Prinz, and T. Kleinebecker, “Unmanned aerial vehicles as innovative remote sensing platforms for high-resolution infrared imagery to support restoration monitoring in cut-over bogs,” Appl. Veg. Sci. 16(3), 509–517 (2013).
[Crossref]

Y. Huang, F. Li, M. Qin, L. Jiang, and Y. Song, “A multi-stopband photonic-crystal microchip for high-performance metal-ion recognition based on fluorescent detection,” Angew. Chem. Int. Ed. Engl. 52(28), 7296–7299 (2013).
[Crossref] [PubMed]

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo-Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51(5), 626–632 (2013).
[Crossref]

2012 (2)

2011 (1)

D. Zheng and F. Da, “A novel algorithm for branch cut phase unwrapping,” Opt. Lasers Eng. 49(5), 609–617 (2011).
[Crossref]

2010 (4)

Y. P. Kumar and S. Chatterjee, “Thickness measurement of transparent glass plates using a lateral shearing cyclic path optical configuration setup and polarization phase shifting interferometry,” Appl. Opt. 49(33), 6552–6557 (2010).
[Crossref] [PubMed]

D. Sastikumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42(6), 911–917 (2010).
[Crossref]

M. T. Fathi and S. Donati, “Thickness measurement of transparent plates by a self-mixing interferometer,” Opt. Lett. 35(11), 1844–1846 (2010).
[Crossref] [PubMed]

S. Chatterjee, “Measurement of surface profile of a long-radius optical surface with wedge phase shifting lateral shear interferometer,” Opt. Eng. 49(10), 103602 (2010).
[Crossref]

2009 (1)

2008 (1)

2007 (1)

2005 (1)

2004 (1)

2002 (2)

G. N. Peggs and A. Yacoot, “A review of recent work in sub-nanometre displacement measurement using optical and X-ray interferometry,” Philos Trans A Math Phys. Eng. Sci. 360(1794), 953–968 (2002).

H. Maruyama, S. Inoue, T. Mitsuyama, M. Ohmi, and M. Haruna, “Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness,” Appl. Opt. 41(7), 1315–1322 (2002).
[Crossref] [PubMed]

2000 (1)

A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29(1), 1–12 (2000).
[Crossref]

1997 (1)

S. Kim, “Accelerated phase-measuring algorithm of least squares for phase-shifting interferometry,” Opt. Eng. 36(11), 3101–3106 (1997).
[Crossref]

1987 (1)

1985 (2)

1982 (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Arévalo-Aguilar, L. M.

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo-Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51(5), 626–632 (2013).
[Crossref]

Brai, M.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Cao, Z.

S. Sun, Z. Cao, A. Huang, L. Xu, and W. Yang, “A high-speed digital electrical capacitance tomography system combining digital recursive demodulation and parallel capacitance measurement,” IEEE Sens. J. 17(20), 6690–6698 (2017).
[Crossref]

Chatterjee, S.

Chen, H.

Chen, J.

Cheng, C.

J. Zhu, J. Dai, X. Cheng, C. Cheng, J. Zhang, and Y. Li, “Temperature measurement of a horizontal cylinder in natural convection using a lateral shearing interferometer with a large shear amount,” Opt. Eng. 54(3), 034109 (2015).
[Crossref]

Cheng, X.

J. Zhu, J. Dai, X. Cheng, C. Cheng, J. Zhang, and Y. Li, “Temperature measurement of a horizontal cylinder in natural convection using a lateral shearing interferometer with a large shear amount,” Opt. Eng. 54(3), 034109 (2015).
[Crossref]

Cheng, Y. Y.

Ciesielski, B.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Da, F.

D. Zheng and F. Da, “A novel algorithm for branch cut phase unwrapping,” Opt. Lasers Eng. 49(5), 609–617 (2011).
[Crossref]

Dai, J.

J. Zhu, J. Dai, X. Cheng, C. Cheng, J. Zhang, and Y. Li, “Temperature measurement of a horizontal cylinder in natural convection using a lateral shearing interferometer with a large shear amount,” Opt. Eng. 54(3), 034109 (2015).
[Crossref]

Dai, M.

Dai, X.

Dainty, C.

De Angelis, C.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Delisle, C.

Della Monaca, S.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Ding, J.

Ding, Q.

Y. Li, Y. Wang, C. Liu, J. Yang, and Q. Ding, “Linear frequency modulation multi-beam laser heterodyne measurement for the glass thickness,” Appl. Phys. B 122(2), 1–5 (2016).

Donati, S.

Dubey, S. K.

Dubra, A.

Eiju, T.

Fan, Y. X.

Fathi, M. T.

Fattibene, P.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Furtmann, A.

A. Furtmann and G. Poll, “Evaluation of oil-film thickness along the path of contact in a gear mesh by capacitance measurement,” Tribol. Online 11(2), 189–194 (2016).
[Crossref]

Garcia, T.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Giammartini, S.

A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29(1), 1–12 (2000).
[Crossref]

Gobi, G.

D. Sastikumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42(6), 911–917 (2010).
[Crossref]

Grigsby, R. J.

D. E. Scott, R. J. Grigsby, and S. M. Lunte, “Microdialysis sampling coupled to microchip electrophoresis with integrated amperometric detection on an all-glass substrate,” ChemPhysChem 14(10), 2288–2294 (2013).
[Crossref] [PubMed]

Guerrero-Sánchez, F.

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo-Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51(5), 626–632 (2013).
[Crossref]

Guj, G.

A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29(1), 1–12 (2000).
[Crossref]

Guo, Y. F.

Gustafsson, H.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Haavardsholm, T.

Hariharan, P.

Haruna, M.

He, X.

Hole, E. O.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Hossain, M. M.

Huang, A.

S. Sun, Z. Cao, A. Huang, L. Xu, and W. Yang, “A high-speed digital electrical capacitance tomography system combining digital recursive demodulation and parallel capacitance measurement,” IEEE Sens. J. 17(20), 6690–6698 (2017).
[Crossref]

Huang, Y.

Y. Huang, F. Li, M. Qin, L. Jiang, and Y. Song, “A multi-stopband photonic-crystal microchip for high-performance metal-ion recognition based on fluorescent detection,” Angew. Chem. Int. Ed. Engl. 52(28), 7296–7299 (2013).
[Crossref] [PubMed]

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Inoue, S.

Ishii, Y.

Jiang, H.

Jiang, L.

Y. Huang, F. Li, M. Qin, L. Jiang, and Y. Song, “A multi-stopband photonic-crystal microchip for high-performance metal-ion recognition based on fluorescent detection,” Angew. Chem. Int. Ed. Engl. 52(28), 7296–7299 (2013).
[Crossref] [PubMed]

Jin, J.

J. A. Kim, J. W. Kim, C. S. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref] [PubMed]

Juarez-Salazar, R.

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo-Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51(5), 626–632 (2013).
[Crossref]

Juniewicz, M.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Kaminski, P. M.

B. Maniscalco, P. M. Kaminski, and J. M. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
[Crossref]

Kang, C. S.

J. A. Kim, J. W. Kim, C. S. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref] [PubMed]

Kåsen, I.

Kato, M.

Kim, J. A.

J. A. Kim, J. W. Kim, C. S. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref] [PubMed]

Kim, J. W.

J. A. Kim, J. W. Kim, C. S. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref] [PubMed]

Kim, M. K.

Kim, S.

S. Kim, “Accelerated phase-measuring algorithm of least squares for phase-shifting interferometry,” Opt. Eng. 36(11), 3101–3106 (1997).
[Crossref]

Klein, B.

C. Knoth, B. Klein, T. Prinz, and T. Kleinebecker, “Unmanned aerial vehicles as innovative remote sensing platforms for high-resolution infrared imagery to support restoration monitoring in cut-over bogs,” Appl. Veg. Sci. 16(3), 509–517 (2013).
[Crossref]

Kleinebecker, T.

C. Knoth, B. Klein, T. Prinz, and T. Kleinebecker, “Unmanned aerial vehicles as innovative remote sensing platforms for high-resolution infrared imagery to support restoration monitoring in cut-over bogs,” Appl. Veg. Sci. 16(3), 509–517 (2013).
[Crossref]

Knoth, C.

C. Knoth, B. Klein, T. Prinz, and T. Kleinebecker, “Unmanned aerial vehicles as innovative remote sensing platforms for high-resolution infrared imagery to support restoration monitoring in cut-over bogs,” Appl. Veg. Sci. 16(3), 509–517 (2013).
[Crossref]

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Kothiyal, M. P.

Krefft, K.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Kumar, Y. P.

Lee, J. Y.

J. A. Kim, J. W. Kim, C. S. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref] [PubMed]

Leveque, P.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Li, F.

Y. Huang, F. Li, M. Qin, L. Jiang, and Y. Song, “A multi-stopband photonic-crystal microchip for high-performance metal-ion recognition based on fluorescent detection,” Angew. Chem. Int. Ed. Engl. 52(28), 7296–7299 (2013).
[Crossref] [PubMed]

Li, Y.

Y. Li, Y. Wang, C. Liu, J. Yang, and Q. Ding, “Linear frequency modulation multi-beam laser heterodyne measurement for the glass thickness,” Appl. Phys. B 122(2), 1–5 (2016).

J. Zhu, J. Dai, X. Cheng, C. Cheng, J. Zhang, and Y. Li, “Temperature measurement of a horizontal cylinder in natural convection using a lateral shearing interferometer with a large shear amount,” Opt. Eng. 54(3), 034109 (2015).
[Crossref]

Y. Li, W. Xiao, and F. Pan, “Multiple-wavelength-scanning-based phase unwrapping method for digital holographic microscopy,” Appl. Opt. 53(5), 979–987 (2014).
[Crossref] [PubMed]

Liu, C.

Y. Li, Y. Wang, C. Liu, J. Yang, and Q. Ding, “Linear frequency modulation multi-beam laser heterodyne measurement for the glass thickness,” Appl. Phys. B 122(2), 1–5 (2016).

Liu, T.

Longo, A.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Lou, C.

Lund, E.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Lunte, S. M.

D. E. Scott, R. J. Grigsby, and S. M. Lunte, “Microdialysis sampling coupled to microchip electrophoresis with integrated amperometric detection on an all-glass substrate,” ChemPhysChem 14(10), 2288–2294 (2013).
[Crossref] [PubMed]

Lv, W.

Maniscalco, B.

B. Maniscalco, P. M. Kaminski, and J. M. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
[Crossref]

Marrale, M.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Maruyama, H.

Mehta, D. S.

Meneses-Fabian, C.

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo-Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51(5), 626–632 (2013).
[Crossref]

Michalec, B.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Mierzwinska, G.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Mitsuyama, T.

Neumann, D. L.

M. M. Neumann and D. L. Neumann, “Touch screen tablets and emergent literacy,” Early Child. Educ. J. 42(4), 231–239 (2014).
[Crossref]

Neumann, M. M.

M. M. Neumann and D. L. Neumann, “Touch screen tablets and emergent literacy,” Early Child. Educ. J. 42(4), 231–239 (2014).
[Crossref]

Nicolas, S.

Ohmi, M.

Opsahl, T.

Oreb, B. F.

Pan, F.

Paterson, C.

Peggs, G. N.

G. N. Peggs and A. Yacoot, “A review of recent work in sub-nanometre displacement measurement using optical and X-ray interferometry,” Philos Trans A Math Phys. Eng. Sci. 360(1794), 953–968 (2002).

Poll, G.

A. Furtmann and G. Poll, “Evaluation of oil-film thickness along the path of contact in a gear mesh by capacitance measurement,” Tribol. Online 11(2), 189–194 (2016).
[Crossref]

Prinz, T.

C. Knoth, B. Klein, T. Prinz, and T. Kleinebecker, “Unmanned aerial vehicles as innovative remote sensing platforms for high-resolution infrared imagery to support restoration monitoring in cut-over bogs,” Appl. Veg. Sci. 16(3), 509–517 (2013).
[Crossref]

Qi, C.

C. Qi, S. Zheng, and H. Zhou, “Experimental investigation on gas-phase temperature of axisymmetric ethylene flames by large lateral shearing interferometry,” Int. J. Therm. Sci. 115, 104–111 (2017).
[Crossref]

Qin, M.

Y. Huang, F. Li, M. Qin, L. Jiang, and Y. Song, “A multi-stopband photonic-crystal microchip for high-performance metal-ion recognition based on fluorescent detection,” Angew. Chem. Int. Ed. Engl. 52(28), 7296–7299 (2013).
[Crossref] [PubMed]

Qu, X.

Rao, J. L.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Renganathan, B.

D. Sastikumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42(6), 911–917 (2010).
[Crossref]

Robledo-Sánchez, C.

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo-Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51(5), 626–632 (2013).
[Crossref]

Rognmo, A.

Romanyukha, A. A.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Sastikumar, D.

D. Sastikumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42(6), 911–917 (2010).
[Crossref]

Scott, D. E.

D. E. Scott, R. J. Grigsby, and S. M. Lunte, “Microdialysis sampling coupled to microchip electrophoresis with integrated amperometric detection on an all-glass substrate,” ChemPhysChem 14(10), 2288–2294 (2013).
[Crossref] [PubMed]

Shakher, C.

Shao, X.

Skauli, T.

Song, Y.

Y. Huang, F. Li, M. Qin, L. Jiang, and Y. Song, “A multi-stopband photonic-crystal microchip for high-performance metal-ion recognition based on fluorescent detection,” Angew. Chem. Int. Ed. Engl. 52(28), 7296–7299 (2013).
[Crossref] [PubMed]

Stella, A.

A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29(1), 1–12 (2000).
[Crossref]

Sun, S.

S. Sun, Z. Cao, A. Huang, L. Xu, and W. Yang, “A high-speed digital electrical capacitance tomography system combining digital recursive demodulation and parallel capacitance measurement,” IEEE Sens. J. 17(20), 6690–6698 (2017).
[Crossref]

Takeda, M.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Torkildsen, H. E.

Trompier, F.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Tuner, H.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Wada, A.

Walls, J. M.

B. Maniscalco, P. M. Kaminski, and J. M. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
[Crossref]

Wang, H. T.

Wang, Y.

Y. Li, Y. Wang, C. Liu, J. Yang, and Q. Ding, “Linear frequency modulation multi-beam laser heterodyne measurement for the glass thickness,” Appl. Phys. B 122(2), 1–5 (2016).

Warnasooriya, N.

Wieser, A.

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Wu, H.

Wyant, J. C.

Xiao, W.

Xu, J.

Xu, L.

S. Sun, Z. Cao, A. Huang, L. Xu, and W. Yang, “A high-speed digital electrical capacitance tomography system combining digital recursive demodulation and parallel capacitance measurement,” IEEE Sens. J. 17(20), 6690–6698 (2017).
[Crossref]

Yacoot, A.

G. N. Peggs and A. Yacoot, “A review of recent work in sub-nanometre displacement measurement using optical and X-ray interferometry,” Philos Trans A Math Phys. Eng. Sci. 360(1794), 953–968 (2002).

Yang, F.

Yang, J.

Y. Li, Y. Wang, C. Liu, J. Yang, and Q. Ding, “Linear frequency modulation multi-beam laser heterodyne measurement for the glass thickness,” Appl. Phys. B 122(2), 1–5 (2016).

Yang, W.

S. Sun, Z. Cao, A. Huang, L. Xu, and W. Yang, “A high-speed digital electrical capacitance tomography system combining digital recursive demodulation and parallel capacitance measurement,” IEEE Sens. J. 17(20), 6690–6698 (2017).
[Crossref]

Yuan, T.

Yun, H.

Zhai, S. H.

Zhang, F.

Zhang, J.

J. Zhu, J. Dai, X. Cheng, C. Cheng, J. Zhang, and Y. Li, “Temperature measurement of a horizontal cylinder in natural convection using a lateral shearing interferometer with a large shear amount,” Opt. Eng. 54(3), 034109 (2015).
[Crossref]

Zheng, D.

D. Zheng and F. Da, “A novel algorithm for branch cut phase unwrapping,” Opt. Lasers Eng. 49(5), 609–617 (2011).
[Crossref]

Zheng, S.

C. Qi, S. Zheng, and H. Zhou, “Experimental investigation on gas-phase temperature of axisymmetric ethylene flames by large lateral shearing interferometry,” Int. J. Therm. Sci. 115, 104–111 (2017).
[Crossref]

Zhou, H.

C. Qi, S. Zheng, and H. Zhou, “Experimental investigation on gas-phase temperature of axisymmetric ethylene flames by large lateral shearing interferometry,” Int. J. Therm. Sci. 115, 104–111 (2017).
[Crossref]

W. Lv, H. Zhou, C. Lou, and J. Zhu, “Spatial and temporal film thickness measurement of a soap bubble based on large lateral shearing displacement interferometry,” Appl. Opt. 51(36), 8863–8872 (2012).
[Crossref] [PubMed]

Zhu, J.

J. Zhu, J. Dai, X. Cheng, C. Cheng, J. Zhang, and Y. Li, “Temperature measurement of a horizontal cylinder in natural convection using a lateral shearing interferometer with a large shear amount,” Opt. Eng. 54(3), 034109 (2015).
[Crossref]

W. Lv, H. Zhou, C. Lou, and J. Zhu, “Spatial and temporal film thickness measurement of a soap bubble based on large lateral shearing displacement interferometry,” Appl. Opt. 51(36), 8863–8872 (2012).
[Crossref] [PubMed]

Angew. Chem. Int. Ed. Engl. (1)

Y. Huang, F. Li, M. Qin, L. Jiang, and Y. Song, “A multi-stopband photonic-crystal microchip for high-performance metal-ion recognition based on fluorescent detection,” Angew. Chem. Int. Ed. Engl. 52(28), 7296–7299 (2013).
[Crossref] [PubMed]

Appl. Opt. (12)

H. Maruyama, S. Inoue, T. Mitsuyama, M. Ohmi, and M. Haruna, “Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness,” Appl. Opt. 41(7), 1315–1322 (2002).
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H. Wu, F. Zhang, T. Liu, and X. Qu, “Glass thickness and index measurement using optical sampling by cavity tuning,” Appl. Opt. 55(34), 9756–9763 (2016).
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T. Skauli, H. E. Torkildsen, S. Nicolas, T. Opsahl, T. Haavardsholm, I. Kåsen, and A. Rognmo, “Compact camera for multispectral and conventional imaging based on patterned filters,” Appl. Opt. 53(13), C64–C71 (2014).
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A. Dubra, C. Paterson, and C. Dainty, “Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform,” Appl. Opt. 43(5), 1108–1113 (2004).
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Y. Y. Cheng and J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,” Appl. Opt. 24(18), 3049–3052 (1985).
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P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26(13), 2504–2506 (1987).
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M. P. Kothiyal and C. Delisle, “Shearing interferometer for phase shifting interferometry with polarization phase shifter,” Appl. Opt. 24(24), 4439–4442 (1985).
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D. S. Mehta, S. K. Dubey, M. M. Hossain, and C. Shakher, “Simple multifrequency and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry for three-dimensional profilometry,” Appl. Opt. 44(35), 7515–7521 (2005).
[Crossref] [PubMed]

A. Wada, M. Kato, and Y. Ishii, “Multiple-wavelength digital holographic interferometry using tunable laser diodes,” Appl. Opt. 47(12), 2053–2060 (2008).
[Crossref] [PubMed]

Y. Li, W. Xiao, and F. Pan, “Multiple-wavelength-scanning-based phase unwrapping method for digital holographic microscopy,” Appl. Opt. 53(5), 979–987 (2014).
[Crossref] [PubMed]

W. Lv, H. Zhou, C. Lou, and J. Zhu, “Spatial and temporal film thickness measurement of a soap bubble based on large lateral shearing displacement interferometry,” Appl. Opt. 51(36), 8863–8872 (2012).
[Crossref] [PubMed]

Y. P. Kumar and S. Chatterjee, “Thickness measurement of transparent glass plates using a lateral shearing cyclic path optical configuration setup and polarization phase shifting interferometry,” Appl. Opt. 49(33), 6552–6557 (2010).
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Appl. Phys. B (1)

Y. Li, Y. Wang, C. Liu, J. Yang, and Q. Ding, “Linear frequency modulation multi-beam laser heterodyne measurement for the glass thickness,” Appl. Phys. B 122(2), 1–5 (2016).

Appl. Veg. Sci. (1)

C. Knoth, B. Klein, T. Prinz, and T. Kleinebecker, “Unmanned aerial vehicles as innovative remote sensing platforms for high-resolution infrared imagery to support restoration monitoring in cut-over bogs,” Appl. Veg. Sci. 16(3), 509–517 (2013).
[Crossref]

ChemPhysChem (1)

D. E. Scott, R. J. Grigsby, and S. M. Lunte, “Microdialysis sampling coupled to microchip electrophoresis with integrated amperometric detection on an all-glass substrate,” ChemPhysChem 14(10), 2288–2294 (2013).
[Crossref] [PubMed]

Chin. Opt. Lett. (1)

Early Child. Educ. J. (1)

M. M. Neumann and D. L. Neumann, “Touch screen tablets and emergent literacy,” Early Child. Educ. J. 42(4), 231–239 (2014).
[Crossref]

Exp. Fluids (1)

A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29(1), 1–12 (2000).
[Crossref]

IEEE Sens. J. (1)

S. Sun, Z. Cao, A. Huang, L. Xu, and W. Yang, “A high-speed digital electrical capacitance tomography system combining digital recursive demodulation and parallel capacitance measurement,” IEEE Sens. J. 17(20), 6690–6698 (2017).
[Crossref]

Int. J. Therm. Sci. (1)

C. Qi, S. Zheng, and H. Zhou, “Experimental investigation on gas-phase temperature of axisymmetric ethylene flames by large lateral shearing interferometry,” Int. J. Therm. Sci. 115, 104–111 (2017).
[Crossref]

J. Opt. Soc. Am. A (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Opt. Eng. (3)

J. Zhu, J. Dai, X. Cheng, C. Cheng, J. Zhang, and Y. Li, “Temperature measurement of a horizontal cylinder in natural convection using a lateral shearing interferometer with a large shear amount,” Opt. Eng. 54(3), 034109 (2015).
[Crossref]

S. Chatterjee, “Measurement of surface profile of a long-radius optical surface with wedge phase shifting lateral shear interferometer,” Opt. Eng. 49(10), 103602 (2010).
[Crossref]

S. Kim, “Accelerated phase-measuring algorithm of least squares for phase-shifting interferometry,” Opt. Eng. 36(11), 3101–3106 (1997).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

D. Sastikumar, G. Gobi, and B. Renganathan, “Determination of the thickness of a transparent plate using a reflective fiber optic displacement sensor,” Opt. Laser Technol. 42(6), 911–917 (2010).
[Crossref]

Opt. Lasers Eng. (2)

R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, and L. M. Arévalo-Aguilar, “Generalized phase-shifting interferometry by parameter estimation with the least squares method,” Opt. Lasers Eng. 51(5), 626–632 (2013).
[Crossref]

D. Zheng and F. Da, “A novel algorithm for branch cut phase unwrapping,” Opt. Lasers Eng. 49(5), 609–617 (2011).
[Crossref]

Opt. Lett. (1)

Philos Trans A Math Phys. Eng. Sci. (1)

G. N. Peggs and A. Yacoot, “A review of recent work in sub-nanometre displacement measurement using optical and X-ray interferometry,” Philos Trans A Math Phys. Eng. Sci. 360(1794), 953–968 (2002).

Radiat. Environ. Biophys. (1)

P. Fattibene, F. Trompier, A. Wieser, M. Brai, B. Ciesielski, C. De Angelis, S. Della Monaca, T. Garcia, H. Gustafsson, E. O. Hole, M. Juniewicz, K. Krefft, A. Longo, P. Leveque, E. Lund, M. Marrale, B. Michalec, G. Mierzwińska, J. L. Rao, A. A. Romanyukha, and H. Tuner, “EPR dosimetry intercomparison using smart phone touch screen glass,” Radiat. Environ. Biophys. 53(2), 311–320 (2014).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

J. A. Kim, J. W. Kim, C. S. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref] [PubMed]

Thin Solid Films (1)

B. Maniscalco, P. M. Kaminski, and J. M. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
[Crossref]

Tribol. Online (1)

A. Furtmann and G. Poll, “Evaluation of oil-film thickness along the path of contact in a gear mesh by capacitance measurement,” Tribol. Online 11(2), 189–194 (2016).
[Crossref]

Other (3)

V. N. Khramov and A. Adamov, “Modification of the laser triangulation method for measuring the thickness of optical layers,” in Saratov Fall Meeting (SPIE, 2018), 1071703.
[Crossref]

H. Guo, “TFT substrate glass geometrical parameter measurement and data processing,” in Proceedings of the 2015 International Conference on Power Electronics and Energy Engineering (Atlantis, 2015), pp. 129–133.
[Crossref]

D. Underwood, Elementary number theory (W. H. Freeman and Company, 1969).

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Figures (12)

Fig. 1
Fig. 1 Schematic diagram of large lateral shearing interferometry to obtain the thickness distribution of measured film.
Fig. 2
Fig. 2 Phase-shift extraction from the interferograms via using the spatial light modulator (SLM). The initial interferogram (a) details the pattern before using the SLM modulation and (d) is an enlarged view of its part. The SLM (b) modulates the interferogram (a) into a new interferogram (c), and the phase of the wavefront in each pixel in (d) was modulated to a different angle, see (e). As a result, the phase at the same pixel was changed and the modulated interferogram (f) was achieved. In this case, the initial phase in (e) can be extracted by using the data fitting methods, and incident light at different wavelengths can be used to improve the precision of the phase extraction.
Fig. 3
Fig. 3 Three-dimensional optical alignment for the thickness distribution measurement of the target glass film by using the light tracing method.
Fig. 4
Fig. 4 Flowchart of the proposed thickness reconstruction method.
Fig. 5
Fig. 5 Reconstructed thickness distributions recovered with three-wavelength phase-extraction method. (a) was thickness distribution of glass film, (b) the error of thickness distributions.
Fig. 6
Fig. 6 The error distributions of reconstructed thickness calculated with multi-wavelength phase-extraction method. (a) four wavelengths, (b) five wavelengths.
Fig. 7
Fig. 7 (a) was thickness distribution of glass film, (b) the error of thickness distributions.
Fig. 8
Fig. 8 (a) was thickness distribution of glass film, (b) the error of thickness distributions.
Fig. 9
Fig. 9 Experiment setup fabricated for thickness distribution measurement of the glass films. The arrows indicate the light path of the lasers.
Fig. 10
Fig. 10 Reconstructed thickness distributions recovered with three-wavelength phase-extraction method with the frequency stability of the laser. (a) thickness distribution of glass film, (b) the error of thickness distributions.
Fig. 11
Fig. 11 Thickness distribution reconstructed based on the three-wavelength phase-extraction method. (a) the layout diagram of one film, (b) image of one film, (c) thickness distribution of glass film based on three wavelengths, (d) standard deviation distribution of glass film.
Fig. 12
Fig. 12 Thickness distribution measured from the three-wavelength phase-shift extractions. (a) the layout diagram of the five films, (b) image of five tacked films, (c) thickness distribution of glass film from phase-shift extractions of three wavelengths, (d) standard deviation distribution of thickness of the glass films.

Equations (20)

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Θ ( x , y ) = θ ( x , y ) θ ( x s , y ) + 2 π Δ z λ .
Θ 0 ( x , y ) = θ sys t e m ( x , y ) θ s y s t e m ( x s , y ) + 2 π Δ z λ .
Θ 1 ( x , y ) = θ f i l m ( x , y ) θ f i l m ( x s , y ) + Θ 0 ( x , y ) .
θ f i l m ( x , y ) { [ Θ 1 ( x , y ) Θ 0 ( x , y ) ] mod ( 2 π ) , W 2 < x < W 2 o r W 2 s < x < W 2 s 0 , others .
I 0 = A + B + 2 A B cos ( φ 0 ) .
I α = A + B + 2 A B cos ( φ 0 + α ) .
[ I 1 I 2 I M ] = [ u 1 u 2 u M ] Q .
Q = [ 2 A B cos φ 2 A B sin φ A + B ] .
{ K 1 = u 1 T u 1 P 1 = u 1 T I 1 .
{ K m = K m 1 + u m T u m P m = P m 1 + u m T I m .
Q = ( K M ) 1 P M .
φ = arc tan ( Q [ 2 ] Q [ 1 ] ) .
θ f i l m ( φ 1 φ 0 ) mod ( 2 π ) .
{ ( n 1 n 0 ) d λ 1 2 π = N 1 2 π + θ 1 ( n 2 n 0 ) d λ 2 2 π = N 2 2 π + θ 2 ( n 3 n 0 ) d λ 3 2 π = N 3 2 π + θ 3 ( n K n 0 ) d λ K 2 π = N K 2 π + θ K .
λ 1 N 1 = a k N k + b k ( N k Z ) .
N 1 p k mod ( a k d k ) .
{ N 1 p 2 mod ( a 2 d 2 ) N 1 p 3 mod ( a 3 d 3 ) .
N 1 ( p 3 z a 3 ( p 3 p 2 ) d 3 e + u a 2 a 3 d 2 d 3 e ) mod ( a 2 a 3 e d 2 d 3 ) .
{ N k = λ 1 N 1 b k a k d = λ 1 ( N 1 2 π + θ 1 ) 2 π ( n 1 n 0 ) .
S = Δ f f = Δ f c / λ = Δ f × λ c .

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