Abstract

Characterization of the displacement response is critical for accurate chromatic confocal measurement. Current characterization methods usually provide a linear or polynomial relationship between the extracted peak wavelengths of the spectral signal and displacement. However, these methods are susceptible to errors in the peak extraction algorithms and errors in the selected model. In this paper, we propose a hybrid radial basis function network method to characterise the displacement response. With this method, the peak wavelength of the spectral signal is firstly extracted with a state-of-art peak extraction algorithm, following which, a higher-accuracy chromatic dispersion model is applied to determine the displacement-wavelength relationship. Lastly, a radial basis function network is optimized to provide a mapping between the spectral signals and the residual fitting errors of the chromatic dispersion model. Using experimental tests, we show that the hybrid radial basis function network method significantly improves the measurement accuracy, when compared to the existing characterizing methods.

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

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References

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  1. M. Gu, Principles of three-dimensional imaging in confocal microscopes (World Scientific, 1996).
  2. J. B. Pawley, Handbook of biological confocal microscopy (Springer, 2006).
  3. B.V.R. Tata and B. Raj, “Confocal laser scanning microscopy: Applications in material science and technology,” Bull. Mater. Sci. 21(4), 263–278 (1998).
    [Crossref]
  4. L. Qiu, D. Liu, W. Zhao, H. Cui, and Z. Sheng, “Real-time laser differential confocal microscopy without sample reflectivity effects,” Opt. Express 22(18), 21626–21640 (2014).
    [Crossref]
  5. J. Chesna, B. Wiedmaier, J. Wang, A. Samara, R. Leach, T. Her, and S. Smith, “Aerial wetting contact angle measurement using confocal microscopy,” Meas. Sci. Technol. 27(12), 125202 (2016).
    [Crossref]
  6. L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
    [Crossref]
  7. J. Yang, L. Qiu, W. Zhao, Y. Shen, and H. Jiang, “Laser differential confocal paraboloidal vertex radius measurement,” Opt. Lett. 39(4), 830–833 (2014).
    [Crossref]
  8. J. Liu, Y. Wang, K. Gu, X. You, M. Zhang, M. Li, and J. Tan, “Measuring profile of large hybrid aspherical diffractive infrared elements using confocal profilometer,” Meas. Sci. Technol. 27(12), 125011 (2016).
    [Crossref]
  9. J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Opt. Express 20(23), 26027–26036 (2012).
    [Crossref]
  10. R.K. Leach, Optical Measurement of Surface Topography (Springer, 2011).
  11. J. Yang, L. Qiu, W. Zhao, R. Shao, and Z. Li, “Measuring the lens focal length by laser reflection-confocal technology,” Appl. Opt. 52(16), 3812–3817 (2013).
    [Crossref]
  12. T. R. Corle, C. H. Chou, and G. S. Kino, “Depth response of confocal optical microscope,” Opt. Lett. 11(12), 770–772 (1986).
    [Crossref]
  13. A. Ruprecht, K. Koerner, T. Wiesendanger, H. Tiziani, and W. Osten, “Chromatic confocal detection for high-speed microtopography measurements,” Proc. SPIE 5302, 53–60 (2004).
    [Crossref]
  14. Q. Yu, K. Zhang, C. Cui, R. Zhou, F. Cheng, R. Ye, and Y. Zhang, “Method of thickness measurement for transparent specimens with chromatic confocal microscopy,” Appl. Opt. 57(33), 9722–9728 (2018).
    [Crossref]
  15. M. Hillenbrand, L. Lorenz, R. Kleindienst, A. Grewe, and S. Sinzinger, “Spectrally multiplexed chromatic confocal multipoint sensing,” Opt. Lett. 38(22), 4694–4697 (2013).
    [Crossref]
  16. K. Ang, Z. Fang, and A. Tay, “Note: Real-time three-dimensional topography measurement of microfluidic devices with pillar structures using confocal microscope,” Rev. Sci. Instrum. 85(2), 026108 (2014).
    [Crossref]
  17. L. Chen, Y. Chang, and H. Li, “Full-field chromatic confocal surface profilometry employing digital micromirror device correspondence for minimizing lateral cross talks,” Opt. Eng. 51(8), 081507 (2012).
    [Crossref]
  18. B. Jiao, X. Li, Q. Zhou, K. Ni, and X. Wang, “Improved chromatic confocal displacement-sensor based on a spatial-bandpass-filter and an X-shaped fiber-coupler,” Opt. Express 27(8), 10961–10973 (2019).
    [Crossref]
  19. B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum. 80(7), 073706 (2009).
    [Crossref]
  20. Q. Yu, K. Zhang, R. Zhou, C. Cui, F. Cheng, S. Fu, and R. Ye, “Calibration of a chromatic confocal microscope for measuring a colored specimen,” IEEE Photonics J. 10(6), 1–9 (2018).
    [Crossref]
  21. S.L. Dobson, P. Sun, and Y. Fainman, “Diffractive lenses for chromatic confocal imaging,” Appl. Opt. 36(20), 4744–4748 (1997).
    [Crossref]
  22. P. C. Lin, P. Sun, L. Zhu, and Y. Fainman, “Single-shot depth-section imaging through chromatic slit-scan confocal microscopy,” Appl. Opt. 37(28), 6764–6770 (1998).
    [Crossref]
  23. S. Cha, P. C. Lin, L. Zhu, P. Sun, and Y. Fainman, “Nontranslational three-dimensional profilometry by chromatic confocal microscopy with dynamically configurable micromirror scanning,” Appl. Opt. 39(16), 2605–2613 (2000).
    [Crossref]
  24. K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic Confocal Microscopy using supercontinuum light,” Opt. Express 12(10), 2096–2101 (2004).
    [Crossref]
  25. D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol. 44(4), 788–793 (2012).
    [Crossref]
  26. X. Chen, T. Nakamura, Y. Shimizu, C. Chen, Y. Chen, H. Matsukuma, and W. Gao, “A chromatic confocal probe with a mode-locked femtosecond laser source,” Opt. Laser Technol. 103, 359–366 (2018).
    [Crossref]
  27. U. Minoni, G. Manili, S. Bettoni, E. Varrenti, D. Modotto, and C. De Angelis, “Chromatic confocal setup for displacement measurement using a supercontinuum light source,” Opt. Laser Technol. 49, 91–94 (2013).
    [Crossref]
  28. C. Olsovsky, R. Shelton, O. Carrasco-Zevallos, B. E. Applegate, and K. C. Maitland, “Chromatic confocal microscopy for multi-depth imaging of epithelial tissue,” Biomed. Opt. Express 4(5), 732–740 (2013).
    [Crossref]
  29. J. Garzón, T. Gharbi, and J. Meneses, “Real-time determination of the optical thickness and topography of tissues by chromatic confocal microscopy,” J. Opt. A: Pure Appl. Opt. 10(10), 104028 (2008).
    [Crossref]
  30. D.W. Sesko, “Intensity compensation for interchangeable chromatic point sensor components,” U.S.patent US7, 876, 456 B2 (Jan. 25, 2011).
  31. A. K. Ruprecht, T. F. Wiesendanger, and H. J. Tiziani, “Signal evaluation for high-speed confocal measurements,” Appl. Opt. 41(35), 7410–7415 (2002).
    [Crossref]
  32. C. Chen, J. Wang, X. J. Liu, W. L. Lu, H. Zhu, and X. Q. Jiang, “Influence of sample surface height for evaluation of peak extraction algorithms in confocal microscopy,” Appl. Opt. 57(22), 6516–6526 (2018).
    [Crossref]
  33. M. Hillenbrand, B. Mitschunas, F. Brill, A. Grewe, and S. Sinzinger, “Spectral characteristics of chromatic confocal imaging systems,” Appl. Opt. 53(32), 7634–7642 (2014).
    [Crossref]
  34. C. Liu, Y. Liu, T. Zheng, J. Tan, and J. Liu, “Monte Carlo based analysis of confocal peak extraction uncertainty,” Meas. Sci. Technol. 28(10), 105016 (2017).
    [Crossref]
  35. J. Liu and J. Tan, Confocal Microscopy (Morgan & Claypool, 2016).
  36. H. Nouira, N. E. Hayek, X. Yuan, and N. Anwer, “Characterization of the main error sources of chromatic confocal probes for dimensional measurement,” Meas. Sci. Technol. 25(4), 044011 (2014).
    [Crossref]
  37. G. Zhuo, C. Hsu, Y. Wang, and M. Chan, “Chromatic confocal microscopy to rapidly reveal nanoscale surface/interface topography by position-sensitive detection,” Appl. Phys. Lett. 113(8), 083106 (2018).
    [Crossref]
  38. M. J. Baker, J. T. Xi, and J. F. Chicharo, “Neural Network digital fringe calibration technique for structured light profilometers,” Appl. Opt. 46(8), 1233–1243 (2007).
    [Crossref]
  39. X. Chen, Y. Chen, K. Gupta, J. Zhou, and H. Najjaran, “SliceNet: A proficient model for real-time 3D shape-based recognition,” Neurocomputing 316, 144–155 (2018).
    [Crossref]
  40. K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2(5), 359–366 (1989).
    [Crossref]
  41. I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, Deep learning (MIT press, Cambridge, 2016).
  42. H. Zhao, S. Shi, H. Jiang, Y. Zhang, and Z. Xu, “Calibration of AOTF-based 3D measurement system using multiplane model based on phase fringe and BP neural network,” Opt. Express 25(9), 10413–10433 (2017).
    [Crossref]
  43. D. Luo and M. W. Kudenov, “Neural network calibration of a snapshot birefringent Fourier transform spectrometer with periodic phase errors,” Opt. Express 24(10), 11266 (2016).
    [Crossref]
  44. L. Fan, W. Li, A. Dahlback, J. J. Stamnes, S. Stamnes, and K. Stamnes, “New neural-network-based method to infer total ozone column amounts and cloud effects from multi-channel, moderate bandwidth filter instruments,” Opt. Express 22(16), 19595–19609 (2014).
    [Crossref]
  45. M. Grunwald, P. Laube, M. Schall, G. Umlauf, and M.O. Franz, “Radiometric calibration of digital cameras using neural networks,” Proc. SPIE 10395, 1039505 (2017).
    [Crossref]
  46. C. Zhang, Y. Niu, H. Zhang, and J. Lu, “Optimized star sensors laboratory calibration method using a regularization neural network,” Appl. Opt. 57(5), 1067–1074 (2018).
    [Crossref]
  47. W. J. Xiang, Z. X. Zhou, D. Y. Ge, Q. Y. Zhang, and Q. H. Yao, “Camera calibration by hybrid Hopfield network and self-adaptive genetic algorithm,” Meas. Sci. Rev. 12(6), 302–308 (2012).
    [Crossref]
  48. S. Xie, X. Zhang, S. Chen, and C. Zhu, “Hybrid neural network models of transducers,” Meas. Sci. Technol. 22(10), 105201 (2011).
    [Crossref]
  49. L. C. Chen, D.T. Nguyen, and Y.W. Chang, “Precise optical surface profilometry using innovative chromatic differential confocal microscopy,” Opt. Lett. 41(24), 5660–5663 (2016).
    [Crossref]
  50. C. Chen, W. Yang, J. Wang, W. Lu, X. Liu, and X. Jiang, “Accurate and efficient height extraction in chromatic confocal microscopy using corrected fitting of the differential signal,” Precis. Eng. 56, 447–454 (2019).
    [Crossref]
  51. M. Rahlves, B. Roth, and E. Reithmeier, “Confocal signal evaluation algorithms for surface metrology: uncertainty and numerical efficiency,” Appl. Opt. 56(21), 5920–5926 (2017).
    [Crossref]
  52. C. Chen, J. Wang, R. Leach, W. Lu, X. Liu, and X. Jiang, “Corrected parabolic fitting for height extraction in confocal microscopy,” Opt. Express 27(3), 3682–3697 (2019).
    [Crossref]
  53. M. Rayer and D. Mansfield, “Chromatic confocal microscopy using staircase diffractive surface,” Appl. Opt. 53(23), 5123–5130 (2014).
    [Crossref]
  54. W. J. Smith, Modern Optical Engineering: The Design of Optical Systems (McGraw-Hill, New York, 1990).
  55. B. Tatian, “Fitting Refractive-Index Data With The Sellmeier Dispersion Formula,” Appl. Opt. 23(24), 4477–4485 (1984).
    [Crossref]
  56. P. N. Robb and R. I. Mercado, “Calculation of refractive indices using Buchdahl’s chromatic coordinate,” Appl. Opt. 22(8), 1198–1215 (1983).
    [Crossref]
  57. Schott glass catalog (2011), http://www.us.schott.com .
  58. C.L. Li and J. Sasián, “Adaptive dispersion formula for index interpolation and chromatic aberration correction,” Opt. Express 22(1), 1193–1202 (2014).
    [Crossref]
  59. D. N. Fuller, A. L. Kellner, and J. H. Price, “Exploiting chromatic aberration for image-based microscope autofocus,” Appl. Opt. 50(25), 4967–4976 (2011).
    [Crossref]
  60. J. Novak and A. Miks, “Hyperchromats with linear dependence of longitudinal chromatic aberration on wavelength,” Optik 116(4), 165–168 (2005).
    [Crossref]
  61. M. Hillenbrand, B. Mitschunas, C. Wenzel, A. Grewe, X. Ma, P. Feßer, M. Bichra, and S. Sinzinger, “Hybrid hyperchromats for chromatic confocal sensor systems,” Adv. Opt. Technol. 1(3), 187 (2012).
    [Crossref]
  62. C. Chen, J. Wang, C. Zhang, W. Lu, X. Liu, Z. Lei, and X. Jiang, “Influence of optical aberrations on the peak extraction in confocal microscopy,” Opt. Commun. 449, 24–32 (2019).
    [Crossref]
  63. M. J. L. Orr, "Introduction to radial basis function networks," University of Edinburgh, Edinburgh, Scotland, 1996.
  64. S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2(2), 302–309 (1991).
    [Crossref]
  65. D. Manrique, J. Rios, and A. Rodriguez-Paton, “Evolutionary system for automatically constructing and adapting radial basis function networks,” Neurocomputing 69(16-18), 2268–2283 (2006).
    [Crossref]
  66. J. A. Hartigan and M. A. Wong, “Algorithm AS 136: A K-means clustering algorithm,” J. R. Stat. Soc. Series C 28(1), 100–108 (1979).
    [Crossref]
  67. F. A. Tobar, S. Y. Kung, and D. P. Mandic, “Multikernel least mean square algorithm,” IEEE Trans. Neural Netw. Learning Syst. 25(2), 265–277 (2014).
    [Crossref]
  68. S. T. Roweis and S. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290(5500), 2323–2326 (2000).
    [Crossref]
  69. H. Abdi and L. J. Williams, “Principal component analysis,” Wiley Interdiscip. Rev. Comput. Stat. 2(4), 433–459 (2010).
    [Crossref]
  70. I. T. Jolliffe, Principle Component Analysis (Springer, 1986).
  71. R. K. Leach, Fundamental Principles of Engineering Nanometrology (Elsevier, 2014).
  72. D. Claus, G. Pedrini, T. Boettcher, M. Taphanel, W. Osten, and R. Hibst, “Development of a realistic wave propagation-based chromatic confocal microscopy model,” Proc. SPIE 10677, 106770X (2018).
    [Crossref]
  73. D. Duque and J. Garzon, “Effects of both diffractive element and fiber optic based detector in a chromatic confocal system,” Opt. Laser Technol. 50, 182–189 (2013).
    [Crossref]

2019 (4)

C. Chen, W. Yang, J. Wang, W. Lu, X. Liu, and X. Jiang, “Accurate and efficient height extraction in chromatic confocal microscopy using corrected fitting of the differential signal,” Precis. Eng. 56, 447–454 (2019).
[Crossref]

C. Chen, J. Wang, C. Zhang, W. Lu, X. Liu, Z. Lei, and X. Jiang, “Influence of optical aberrations on the peak extraction in confocal microscopy,” Opt. Commun. 449, 24–32 (2019).
[Crossref]

C. Chen, J. Wang, R. Leach, W. Lu, X. Liu, and X. Jiang, “Corrected parabolic fitting for height extraction in confocal microscopy,” Opt. Express 27(3), 3682–3697 (2019).
[Crossref]

B. Jiao, X. Li, Q. Zhou, K. Ni, and X. Wang, “Improved chromatic confocal displacement-sensor based on a spatial-bandpass-filter and an X-shaped fiber-coupler,” Opt. Express 27(8), 10961–10973 (2019).
[Crossref]

2018 (9)

C. Zhang, Y. Niu, H. Zhang, and J. Lu, “Optimized star sensors laboratory calibration method using a regularization neural network,” Appl. Opt. 57(5), 1067–1074 (2018).
[Crossref]

C. Chen, J. Wang, X. J. Liu, W. L. Lu, H. Zhu, and X. Q. Jiang, “Influence of sample surface height for evaluation of peak extraction algorithms in confocal microscopy,” Appl. Opt. 57(22), 6516–6526 (2018).
[Crossref]

Q. Yu, K. Zhang, C. Cui, R. Zhou, F. Cheng, R. Ye, and Y. Zhang, “Method of thickness measurement for transparent specimens with chromatic confocal microscopy,” Appl. Opt. 57(33), 9722–9728 (2018).
[Crossref]

D. Claus, G. Pedrini, T. Boettcher, M. Taphanel, W. Osten, and R. Hibst, “Development of a realistic wave propagation-based chromatic confocal microscopy model,” Proc. SPIE 10677, 106770X (2018).
[Crossref]

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

Q. Yu, K. Zhang, R. Zhou, C. Cui, F. Cheng, S. Fu, and R. Ye, “Calibration of a chromatic confocal microscope for measuring a colored specimen,” IEEE Photonics J. 10(6), 1–9 (2018).
[Crossref]

X. Chen, T. Nakamura, Y. Shimizu, C. Chen, Y. Chen, H. Matsukuma, and W. Gao, “A chromatic confocal probe with a mode-locked femtosecond laser source,” Opt. Laser Technol. 103, 359–366 (2018).
[Crossref]

G. Zhuo, C. Hsu, Y. Wang, and M. Chan, “Chromatic confocal microscopy to rapidly reveal nanoscale surface/interface topography by position-sensitive detection,” Appl. Phys. Lett. 113(8), 083106 (2018).
[Crossref]

X. Chen, Y. Chen, K. Gupta, J. Zhou, and H. Najjaran, “SliceNet: A proficient model for real-time 3D shape-based recognition,” Neurocomputing 316, 144–155 (2018).
[Crossref]

2017 (4)

C. Liu, Y. Liu, T. Zheng, J. Tan, and J. Liu, “Monte Carlo based analysis of confocal peak extraction uncertainty,” Meas. Sci. Technol. 28(10), 105016 (2017).
[Crossref]

M. Grunwald, P. Laube, M. Schall, G. Umlauf, and M.O. Franz, “Radiometric calibration of digital cameras using neural networks,” Proc. SPIE 10395, 1039505 (2017).
[Crossref]

H. Zhao, S. Shi, H. Jiang, Y. Zhang, and Z. Xu, “Calibration of AOTF-based 3D measurement system using multiplane model based on phase fringe and BP neural network,” Opt. Express 25(9), 10413–10433 (2017).
[Crossref]

M. Rahlves, B. Roth, and E. Reithmeier, “Confocal signal evaluation algorithms for surface metrology: uncertainty and numerical efficiency,” Appl. Opt. 56(21), 5920–5926 (2017).
[Crossref]

2016 (4)

D. Luo and M. W. Kudenov, “Neural network calibration of a snapshot birefringent Fourier transform spectrometer with periodic phase errors,” Opt. Express 24(10), 11266 (2016).
[Crossref]

L. C. Chen, D.T. Nguyen, and Y.W. Chang, “Precise optical surface profilometry using innovative chromatic differential confocal microscopy,” Opt. Lett. 41(24), 5660–5663 (2016).
[Crossref]

J. Liu, Y. Wang, K. Gu, X. You, M. Zhang, M. Li, and J. Tan, “Measuring profile of large hybrid aspherical diffractive infrared elements using confocal profilometer,” Meas. Sci. Technol. 27(12), 125011 (2016).
[Crossref]

J. Chesna, B. Wiedmaier, J. Wang, A. Samara, R. Leach, T. Her, and S. Smith, “Aerial wetting contact angle measurement using confocal microscopy,” Meas. Sci. Technol. 27(12), 125202 (2016).
[Crossref]

2014 (9)

K. Ang, Z. Fang, and A. Tay, “Note: Real-time three-dimensional topography measurement of microfluidic devices with pillar structures using confocal microscope,” Rev. Sci. Instrum. 85(2), 026108 (2014).
[Crossref]

H. Nouira, N. E. Hayek, X. Yuan, and N. Anwer, “Characterization of the main error sources of chromatic confocal probes for dimensional measurement,” Meas. Sci. Technol. 25(4), 044011 (2014).
[Crossref]

F. A. Tobar, S. Y. Kung, and D. P. Mandic, “Multikernel least mean square algorithm,” IEEE Trans. Neural Netw. Learning Syst. 25(2), 265–277 (2014).
[Crossref]

C.L. Li and J. Sasián, “Adaptive dispersion formula for index interpolation and chromatic aberration correction,” Opt. Express 22(1), 1193–1202 (2014).
[Crossref]

J. Yang, L. Qiu, W. Zhao, Y. Shen, and H. Jiang, “Laser differential confocal paraboloidal vertex radius measurement,” Opt. Lett. 39(4), 830–833 (2014).
[Crossref]

M. Rayer and D. Mansfield, “Chromatic confocal microscopy using staircase diffractive surface,” Appl. Opt. 53(23), 5123–5130 (2014).
[Crossref]

L. Fan, W. Li, A. Dahlback, J. J. Stamnes, S. Stamnes, and K. Stamnes, “New neural-network-based method to infer total ozone column amounts and cloud effects from multi-channel, moderate bandwidth filter instruments,” Opt. Express 22(16), 19595–19609 (2014).
[Crossref]

L. Qiu, D. Liu, W. Zhao, H. Cui, and Z. Sheng, “Real-time laser differential confocal microscopy without sample reflectivity effects,” Opt. Express 22(18), 21626–21640 (2014).
[Crossref]

M. Hillenbrand, B. Mitschunas, F. Brill, A. Grewe, and S. Sinzinger, “Spectral characteristics of chromatic confocal imaging systems,” Appl. Opt. 53(32), 7634–7642 (2014).
[Crossref]

2013 (5)

2012 (5)

L. Chen, Y. Chang, and H. Li, “Full-field chromatic confocal surface profilometry employing digital micromirror device correspondence for minimizing lateral cross talks,” Opt. Eng. 51(8), 081507 (2012).
[Crossref]

D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol. 44(4), 788–793 (2012).
[Crossref]

M. Hillenbrand, B. Mitschunas, C. Wenzel, A. Grewe, X. Ma, P. Feßer, M. Bichra, and S. Sinzinger, “Hybrid hyperchromats for chromatic confocal sensor systems,” Adv. Opt. Technol. 1(3), 187 (2012).
[Crossref]

W. J. Xiang, Z. X. Zhou, D. Y. Ge, Q. Y. Zhang, and Q. H. Yao, “Camera calibration by hybrid Hopfield network and self-adaptive genetic algorithm,” Meas. Sci. Rev. 12(6), 302–308 (2012).
[Crossref]

J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Opt. Express 20(23), 26027–26036 (2012).
[Crossref]

2011 (2)

D. N. Fuller, A. L. Kellner, and J. H. Price, “Exploiting chromatic aberration for image-based microscope autofocus,” Appl. Opt. 50(25), 4967–4976 (2011).
[Crossref]

S. Xie, X. Zhang, S. Chen, and C. Zhu, “Hybrid neural network models of transducers,” Meas. Sci. Technol. 22(10), 105201 (2011).
[Crossref]

2010 (1)

H. Abdi and L. J. Williams, “Principal component analysis,” Wiley Interdiscip. Rev. Comput. Stat. 2(4), 433–459 (2010).
[Crossref]

2009 (1)

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum. 80(7), 073706 (2009).
[Crossref]

2008 (1)

J. Garzón, T. Gharbi, and J. Meneses, “Real-time determination of the optical thickness and topography of tissues by chromatic confocal microscopy,” J. Opt. A: Pure Appl. Opt. 10(10), 104028 (2008).
[Crossref]

2007 (1)

2006 (1)

D. Manrique, J. Rios, and A. Rodriguez-Paton, “Evolutionary system for automatically constructing and adapting radial basis function networks,” Neurocomputing 69(16-18), 2268–2283 (2006).
[Crossref]

2005 (1)

J. Novak and A. Miks, “Hyperchromats with linear dependence of longitudinal chromatic aberration on wavelength,” Optik 116(4), 165–168 (2005).
[Crossref]

2004 (2)

A. Ruprecht, K. Koerner, T. Wiesendanger, H. Tiziani, and W. Osten, “Chromatic confocal detection for high-speed microtopography measurements,” Proc. SPIE 5302, 53–60 (2004).
[Crossref]

K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic Confocal Microscopy using supercontinuum light,” Opt. Express 12(10), 2096–2101 (2004).
[Crossref]

2002 (1)

2000 (2)

1998 (2)

B.V.R. Tata and B. Raj, “Confocal laser scanning microscopy: Applications in material science and technology,” Bull. Mater. Sci. 21(4), 263–278 (1998).
[Crossref]

P. C. Lin, P. Sun, L. Zhu, and Y. Fainman, “Single-shot depth-section imaging through chromatic slit-scan confocal microscopy,” Appl. Opt. 37(28), 6764–6770 (1998).
[Crossref]

1997 (1)

1991 (1)

S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2(2), 302–309 (1991).
[Crossref]

1989 (1)

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2(5), 359–366 (1989).
[Crossref]

1986 (1)

1984 (1)

1983 (1)

1979 (1)

J. A. Hartigan and M. A. Wong, “Algorithm AS 136: A K-means clustering algorithm,” J. R. Stat. Soc. Series C 28(1), 100–108 (1979).
[Crossref]

Abdi, H.

H. Abdi and L. J. Williams, “Principal component analysis,” Wiley Interdiscip. Rev. Comput. Stat. 2(4), 433–459 (2010).
[Crossref]

Ang, K.

K. Ang, Z. Fang, and A. Tay, “Note: Real-time three-dimensional topography measurement of microfluidic devices with pillar structures using confocal microscope,” Rev. Sci. Instrum. 85(2), 026108 (2014).
[Crossref]

Anwer, N.

H. Nouira, N. E. Hayek, X. Yuan, and N. Anwer, “Characterization of the main error sources of chromatic confocal probes for dimensional measurement,” Meas. Sci. Technol. 25(4), 044011 (2014).
[Crossref]

Applegate, B. E.

Baker, M. J.

Bengio, Y.

I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, Deep learning (MIT press, Cambridge, 2016).

I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, Deep learning (MIT press, Cambridge, 2016).

Bettoni, S.

U. Minoni, G. Manili, S. Bettoni, E. Varrenti, D. Modotto, and C. De Angelis, “Chromatic confocal setup for displacement measurement using a supercontinuum light source,” Opt. Laser Technol. 49, 91–94 (2013).
[Crossref]

Bichra, M.

M. Hillenbrand, B. Mitschunas, C. Wenzel, A. Grewe, X. Ma, P. Feßer, M. Bichra, and S. Sinzinger, “Hybrid hyperchromats for chromatic confocal sensor systems,” Adv. Opt. Technol. 1(3), 187 (2012).
[Crossref]

Boettcher, T.

D. Claus, G. Pedrini, T. Boettcher, M. Taphanel, W. Osten, and R. Hibst, “Development of a realistic wave propagation-based chromatic confocal microscopy model,” Proc. SPIE 10677, 106770X (2018).
[Crossref]

Brill, F.

Carrasco-Zevallos, O.

Cha, S.

Chan, M.

G. Zhuo, C. Hsu, Y. Wang, and M. Chan, “Chromatic confocal microscopy to rapidly reveal nanoscale surface/interface topography by position-sensitive detection,” Appl. Phys. Lett. 113(8), 083106 (2018).
[Crossref]

Chang, Y.

L. Chen, Y. Chang, and H. Li, “Full-field chromatic confocal surface profilometry employing digital micromirror device correspondence for minimizing lateral cross talks,” Opt. Eng. 51(8), 081507 (2012).
[Crossref]

Chang, Y.W.

Chen, C.

C. Chen, J. Wang, R. Leach, W. Lu, X. Liu, and X. Jiang, “Corrected parabolic fitting for height extraction in confocal microscopy,” Opt. Express 27(3), 3682–3697 (2019).
[Crossref]

C. Chen, W. Yang, J. Wang, W. Lu, X. Liu, and X. Jiang, “Accurate and efficient height extraction in chromatic confocal microscopy using corrected fitting of the differential signal,” Precis. Eng. 56, 447–454 (2019).
[Crossref]

C. Chen, J. Wang, C. Zhang, W. Lu, X. Liu, Z. Lei, and X. Jiang, “Influence of optical aberrations on the peak extraction in confocal microscopy,” Opt. Commun. 449, 24–32 (2019).
[Crossref]

X. Chen, T. Nakamura, Y. Shimizu, C. Chen, Y. Chen, H. Matsukuma, and W. Gao, “A chromatic confocal probe with a mode-locked femtosecond laser source,” Opt. Laser Technol. 103, 359–366 (2018).
[Crossref]

C. Chen, J. Wang, X. J. Liu, W. L. Lu, H. Zhu, and X. Q. Jiang, “Influence of sample surface height for evaluation of peak extraction algorithms in confocal microscopy,” Appl. Opt. 57(22), 6516–6526 (2018).
[Crossref]

Chen, L.

L. Chen, Y. Chang, and H. Li, “Full-field chromatic confocal surface profilometry employing digital micromirror device correspondence for minimizing lateral cross talks,” Opt. Eng. 51(8), 081507 (2012).
[Crossref]

Chen, L. C.

Chen, S.

S. Xie, X. Zhang, S. Chen, and C. Zhu, “Hybrid neural network models of transducers,” Meas. Sci. Technol. 22(10), 105201 (2011).
[Crossref]

S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2(2), 302–309 (1991).
[Crossref]

Chen, X.

X. Chen, Y. Chen, K. Gupta, J. Zhou, and H. Najjaran, “SliceNet: A proficient model for real-time 3D shape-based recognition,” Neurocomputing 316, 144–155 (2018).
[Crossref]

X. Chen, T. Nakamura, Y. Shimizu, C. Chen, Y. Chen, H. Matsukuma, and W. Gao, “A chromatic confocal probe with a mode-locked femtosecond laser source,” Opt. Laser Technol. 103, 359–366 (2018).
[Crossref]

Chen, Y.

X. Chen, T. Nakamura, Y. Shimizu, C. Chen, Y. Chen, H. Matsukuma, and W. Gao, “A chromatic confocal probe with a mode-locked femtosecond laser source,” Opt. Laser Technol. 103, 359–366 (2018).
[Crossref]

X. Chen, Y. Chen, K. Gupta, J. Zhou, and H. Najjaran, “SliceNet: A proficient model for real-time 3D shape-based recognition,” Neurocomputing 316, 144–155 (2018).
[Crossref]

Cheng, F.

Q. Yu, K. Zhang, R. Zhou, C. Cui, F. Cheng, S. Fu, and R. Ye, “Calibration of a chromatic confocal microscope for measuring a colored specimen,” IEEE Photonics J. 10(6), 1–9 (2018).
[Crossref]

Q. Yu, K. Zhang, C. Cui, R. Zhou, F. Cheng, R. Ye, and Y. Zhang, “Method of thickness measurement for transparent specimens with chromatic confocal microscopy,” Appl. Opt. 57(33), 9722–9728 (2018).
[Crossref]

Chesna, J.

J. Chesna, B. Wiedmaier, J. Wang, A. Samara, R. Leach, T. Her, and S. Smith, “Aerial wetting contact angle measurement using confocal microscopy,” Meas. Sci. Technol. 27(12), 125202 (2016).
[Crossref]

Chicharo, J. F.

Chou, C. H.

Chun, B. S.

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum. 80(7), 073706 (2009).
[Crossref]

Claus, D.

D. Claus, G. Pedrini, T. Boettcher, M. Taphanel, W. Osten, and R. Hibst, “Development of a realistic wave propagation-based chromatic confocal microscopy model,” Proc. SPIE 10677, 106770X (2018).
[Crossref]

Corle, T. R.

Courville, A.

I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, Deep learning (MIT press, Cambridge, 2016).

Cowan, C. F. N.

S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2(2), 302–309 (1991).
[Crossref]

Cui, C.

Q. Yu, K. Zhang, R. Zhou, C. Cui, F. Cheng, S. Fu, and R. Ye, “Calibration of a chromatic confocal microscope for measuring a colored specimen,” IEEE Photonics J. 10(6), 1–9 (2018).
[Crossref]

Q. Yu, K. Zhang, C. Cui, R. Zhou, F. Cheng, R. Ye, and Y. Zhang, “Method of thickness measurement for transparent specimens with chromatic confocal microscopy,” Appl. Opt. 57(33), 9722–9728 (2018).
[Crossref]

Cui, H.

Dahlback, A.

De Angelis, C.

U. Minoni, G. Manili, S. Bettoni, E. Varrenti, D. Modotto, and C. De Angelis, “Chromatic confocal setup for displacement measurement using a supercontinuum light source,” Opt. Laser Technol. 49, 91–94 (2013).
[Crossref]

Dobson, S.L.

Duque, D.

D. Duque and J. Garzon, “Effects of both diffractive element and fiber optic based detector in a chromatic confocal system,” Opt. Laser Technol. 50, 182–189 (2013).
[Crossref]

Fainman, Y.

Fan, L.

Fang, Z.

K. Ang, Z. Fang, and A. Tay, “Note: Real-time three-dimensional topography measurement of microfluidic devices with pillar structures using confocal microscope,” Rev. Sci. Instrum. 85(2), 026108 (2014).
[Crossref]

Feßer, P.

M. Hillenbrand, B. Mitschunas, C. Wenzel, A. Grewe, X. Ma, P. Feßer, M. Bichra, and S. Sinzinger, “Hybrid hyperchromats for chromatic confocal sensor systems,” Adv. Opt. Technol. 1(3), 187 (2012).
[Crossref]

Franz, M.O.

M. Grunwald, P. Laube, M. Schall, G. Umlauf, and M.O. Franz, “Radiometric calibration of digital cameras using neural networks,” Proc. SPIE 10395, 1039505 (2017).
[Crossref]

Fu, S.

Q. Yu, K. Zhang, R. Zhou, C. Cui, F. Cheng, S. Fu, and R. Ye, “Calibration of a chromatic confocal microscope for measuring a colored specimen,” IEEE Photonics J. 10(6), 1–9 (2018).
[Crossref]

Fuller, D. N.

Gao, W.

X. Chen, T. Nakamura, Y. Shimizu, C. Chen, Y. Chen, H. Matsukuma, and W. Gao, “A chromatic confocal probe with a mode-locked femtosecond laser source,” Opt. Laser Technol. 103, 359–366 (2018).
[Crossref]

Garzon, J.

D. Duque and J. Garzon, “Effects of both diffractive element and fiber optic based detector in a chromatic confocal system,” Opt. Laser Technol. 50, 182–189 (2013).
[Crossref]

Garzón, J.

J. Garzón, T. Gharbi, and J. Meneses, “Real-time determination of the optical thickness and topography of tissues by chromatic confocal microscopy,” J. Opt. A: Pure Appl. Opt. 10(10), 104028 (2008).
[Crossref]

Ge, D. Y.

W. J. Xiang, Z. X. Zhou, D. Y. Ge, Q. Y. Zhang, and Q. H. Yao, “Camera calibration by hybrid Hopfield network and self-adaptive genetic algorithm,” Meas. Sci. Rev. 12(6), 302–308 (2012).
[Crossref]

Gharbi, T.

J. Garzón, T. Gharbi, and J. Meneses, “Real-time determination of the optical thickness and topography of tissues by chromatic confocal microscopy,” J. Opt. A: Pure Appl. Opt. 10(10), 104028 (2008).
[Crossref]

Goodfellow, I.

I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, Deep learning (MIT press, Cambridge, 2016).

Grant, P. M.

S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2(2), 302–309 (1991).
[Crossref]

Grewe, A.

Grunwald, M.

M. Grunwald, P. Laube, M. Schall, G. Umlauf, and M.O. Franz, “Radiometric calibration of digital cameras using neural networks,” Proc. SPIE 10395, 1039505 (2017).
[Crossref]

Gu, K.

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

J. Liu, Y. Wang, K. Gu, X. You, M. Zhang, M. Li, and J. Tan, “Measuring profile of large hybrid aspherical diffractive infrared elements using confocal profilometer,” Meas. Sci. Technol. 27(12), 125011 (2016).
[Crossref]

Gu, M.

M. Gu, Principles of three-dimensional imaging in confocal microscopes (World Scientific, 1996).

Gupta, K.

X. Chen, Y. Chen, K. Gupta, J. Zhou, and H. Najjaran, “SliceNet: A proficient model for real-time 3D shape-based recognition,” Neurocomputing 316, 144–155 (2018).
[Crossref]

Gweon, D.

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum. 80(7), 073706 (2009).
[Crossref]

Hartigan, J. A.

J. A. Hartigan and M. A. Wong, “Algorithm AS 136: A K-means clustering algorithm,” J. R. Stat. Soc. Series C 28(1), 100–108 (1979).
[Crossref]

Hayek, N. E.

H. Nouira, N. E. Hayek, X. Yuan, and N. Anwer, “Characterization of the main error sources of chromatic confocal probes for dimensional measurement,” Meas. Sci. Technol. 25(4), 044011 (2014).
[Crossref]

Her, T.

J. Chesna, B. Wiedmaier, J. Wang, A. Samara, R. Leach, T. Her, and S. Smith, “Aerial wetting contact angle measurement using confocal microscopy,” Meas. Sci. Technol. 27(12), 125202 (2016).
[Crossref]

Hibst, R.

D. Claus, G. Pedrini, T. Boettcher, M. Taphanel, W. Osten, and R. Hibst, “Development of a realistic wave propagation-based chromatic confocal microscopy model,” Proc. SPIE 10677, 106770X (2018).
[Crossref]

Hillenbrand, M.

Hornik, K.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2(5), 359–366 (1989).
[Crossref]

Hsu, C.

G. Zhuo, C. Hsu, Y. Wang, and M. Chan, “Chromatic confocal microscopy to rapidly reveal nanoscale surface/interface topography by position-sensitive detection,” Appl. Phys. Lett. 113(8), 083106 (2018).
[Crossref]

Jiang, H.

Jiang, X.

C. Chen, J. Wang, R. Leach, W. Lu, X. Liu, and X. Jiang, “Corrected parabolic fitting for height extraction in confocal microscopy,” Opt. Express 27(3), 3682–3697 (2019).
[Crossref]

C. Chen, W. Yang, J. Wang, W. Lu, X. Liu, and X. Jiang, “Accurate and efficient height extraction in chromatic confocal microscopy using corrected fitting of the differential signal,” Precis. Eng. 56, 447–454 (2019).
[Crossref]

C. Chen, J. Wang, C. Zhang, W. Lu, X. Liu, Z. Lei, and X. Jiang, “Influence of optical aberrations on the peak extraction in confocal microscopy,” Opt. Commun. 449, 24–32 (2019).
[Crossref]

Jiang, X. Q.

Jiao, B.

Jolliffe, I. T.

I. T. Jolliffe, Principle Component Analysis (Springer, 1986).

Kellner, A. L.

Kim, K.

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum. 80(7), 073706 (2009).
[Crossref]

Kino, G. S.

Kleindienst, R.

Koerner, K.

A. Ruprecht, K. Koerner, T. Wiesendanger, H. Tiziani, and W. Osten, “Chromatic confocal detection for high-speed microtopography measurements,” Proc. SPIE 5302, 53–60 (2004).
[Crossref]

Kuang, C. F.

D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol. 44(4), 788–793 (2012).
[Crossref]

Kudenov, M. W.

Kung, S. Y.

F. A. Tobar, S. Y. Kung, and D. P. Mandic, “Multikernel least mean square algorithm,” IEEE Trans. Neural Netw. Learning Syst. 25(2), 265–277 (2014).
[Crossref]

Laube, P.

M. Grunwald, P. Laube, M. Schall, G. Umlauf, and M.O. Franz, “Radiometric calibration of digital cameras using neural networks,” Proc. SPIE 10395, 1039505 (2017).
[Crossref]

Leach, R.

C. Chen, J. Wang, R. Leach, W. Lu, X. Liu, and X. Jiang, “Corrected parabolic fitting for height extraction in confocal microscopy,” Opt. Express 27(3), 3682–3697 (2019).
[Crossref]

J. Chesna, B. Wiedmaier, J. Wang, A. Samara, R. Leach, T. Her, and S. Smith, “Aerial wetting contact angle measurement using confocal microscopy,” Meas. Sci. Technol. 27(12), 125202 (2016).
[Crossref]

Leach, R. K.

R. K. Leach, Fundamental Principles of Engineering Nanometrology (Elsevier, 2014).

Leach, R.K.

R.K. Leach, Optical Measurement of Surface Topography (Springer, 2011).

Lei, Z.

C. Chen, J. Wang, C. Zhang, W. Lu, X. Liu, Z. Lei, and X. Jiang, “Influence of optical aberrations on the peak extraction in confocal microscopy,” Opt. Commun. 449, 24–32 (2019).
[Crossref]

Li, C.L.

Li, H.

L. Chen, Y. Chang, and H. Li, “Full-field chromatic confocal surface profilometry employing digital micromirror device correspondence for minimizing lateral cross talks,” Opt. Eng. 51(8), 081507 (2012).
[Crossref]

Li, L.

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

Li, M.

J. Liu, Y. Wang, K. Gu, X. You, M. Zhang, M. Li, and J. Tan, “Measuring profile of large hybrid aspherical diffractive infrared elements using confocal profilometer,” Meas. Sci. Technol. 27(12), 125011 (2016).
[Crossref]

Li, P.

Li, W.

Li, X.

Li, Z.

Lin, P. C.

Liu, C.

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

C. Liu, Y. Liu, T. Zheng, J. Tan, and J. Liu, “Monte Carlo based analysis of confocal peak extraction uncertainty,” Meas. Sci. Technol. 28(10), 105016 (2017).
[Crossref]

Liu, D.

Liu, J.

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

C. Liu, Y. Liu, T. Zheng, J. Tan, and J. Liu, “Monte Carlo based analysis of confocal peak extraction uncertainty,” Meas. Sci. Technol. 28(10), 105016 (2017).
[Crossref]

J. Liu, Y. Wang, K. Gu, X. You, M. Zhang, M. Li, and J. Tan, “Measuring profile of large hybrid aspherical diffractive infrared elements using confocal profilometer,” Meas. Sci. Technol. 27(12), 125011 (2016).
[Crossref]

J. Liu and J. Tan, Confocal Microscopy (Morgan & Claypool, 2016).

Liu, X.

C. Chen, J. Wang, C. Zhang, W. Lu, X. Liu, Z. Lei, and X. Jiang, “Influence of optical aberrations on the peak extraction in confocal microscopy,” Opt. Commun. 449, 24–32 (2019).
[Crossref]

C. Chen, W. Yang, J. Wang, W. Lu, X. Liu, and X. Jiang, “Accurate and efficient height extraction in chromatic confocal microscopy using corrected fitting of the differential signal,” Precis. Eng. 56, 447–454 (2019).
[Crossref]

C. Chen, J. Wang, R. Leach, W. Lu, X. Liu, and X. Jiang, “Corrected parabolic fitting for height extraction in confocal microscopy,” Opt. Express 27(3), 3682–3697 (2019).
[Crossref]

D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol. 44(4), 788–793 (2012).
[Crossref]

Liu, X. J.

Liu, Y.

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

C. Liu, Y. Liu, T. Zheng, J. Tan, and J. Liu, “Monte Carlo based analysis of confocal peak extraction uncertainty,” Meas. Sci. Technol. 28(10), 105016 (2017).
[Crossref]

Liu, Z.

Lorenz, L.

Lu, J.

Lu, W.

C. Chen, J. Wang, R. Leach, W. Lu, X. Liu, and X. Jiang, “Corrected parabolic fitting for height extraction in confocal microscopy,” Opt. Express 27(3), 3682–3697 (2019).
[Crossref]

C. Chen, W. Yang, J. Wang, W. Lu, X. Liu, and X. Jiang, “Accurate and efficient height extraction in chromatic confocal microscopy using corrected fitting of the differential signal,” Precis. Eng. 56, 447–454 (2019).
[Crossref]

C. Chen, J. Wang, C. Zhang, W. Lu, X. Liu, Z. Lei, and X. Jiang, “Influence of optical aberrations on the peak extraction in confocal microscopy,” Opt. Commun. 449, 24–32 (2019).
[Crossref]

Lu, W. L.

Luo, D.

D. Luo and M. W. Kudenov, “Neural network calibration of a snapshot birefringent Fourier transform spectrometer with periodic phase errors,” Opt. Express 24(10), 11266 (2016).
[Crossref]

D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol. 44(4), 788–793 (2012).
[Crossref]

Ma, X.

M. Hillenbrand, B. Mitschunas, C. Wenzel, A. Grewe, X. Ma, P. Feßer, M. Bichra, and S. Sinzinger, “Hybrid hyperchromats for chromatic confocal sensor systems,” Adv. Opt. Technol. 1(3), 187 (2012).
[Crossref]

Maitland, K. C.

Mandic, D. P.

F. A. Tobar, S. Y. Kung, and D. P. Mandic, “Multikernel least mean square algorithm,” IEEE Trans. Neural Netw. Learning Syst. 25(2), 265–277 (2014).
[Crossref]

Manili, G.

U. Minoni, G. Manili, S. Bettoni, E. Varrenti, D. Modotto, and C. De Angelis, “Chromatic confocal setup for displacement measurement using a supercontinuum light source,” Opt. Laser Technol. 49, 91–94 (2013).
[Crossref]

Manrique, D.

D. Manrique, J. Rios, and A. Rodriguez-Paton, “Evolutionary system for automatically constructing and adapting radial basis function networks,” Neurocomputing 69(16-18), 2268–2283 (2006).
[Crossref]

Mansfield, D.

Matsukuma, H.

X. Chen, T. Nakamura, Y. Shimizu, C. Chen, Y. Chen, H. Matsukuma, and W. Gao, “A chromatic confocal probe with a mode-locked femtosecond laser source,” Opt. Laser Technol. 103, 359–366 (2018).
[Crossref]

Meneses, J.

J. Garzón, T. Gharbi, and J. Meneses, “Real-time determination of the optical thickness and topography of tissues by chromatic confocal microscopy,” J. Opt. A: Pure Appl. Opt. 10(10), 104028 (2008).
[Crossref]

Mercado, R. I.

Miks, A.

J. Novak and A. Miks, “Hyperchromats with linear dependence of longitudinal chromatic aberration on wavelength,” Optik 116(4), 165–168 (2005).
[Crossref]

Minoni, U.

U. Minoni, G. Manili, S. Bettoni, E. Varrenti, D. Modotto, and C. De Angelis, “Chromatic confocal setup for displacement measurement using a supercontinuum light source,” Opt. Laser Technol. 49, 91–94 (2013).
[Crossref]

Mitschunas, B.

M. Hillenbrand, B. Mitschunas, F. Brill, A. Grewe, and S. Sinzinger, “Spectral characteristics of chromatic confocal imaging systems,” Appl. Opt. 53(32), 7634–7642 (2014).
[Crossref]

M. Hillenbrand, B. Mitschunas, C. Wenzel, A. Grewe, X. Ma, P. Feßer, M. Bichra, and S. Sinzinger, “Hybrid hyperchromats for chromatic confocal sensor systems,” Adv. Opt. Technol. 1(3), 187 (2012).
[Crossref]

Modotto, D.

U. Minoni, G. Manili, S. Bettoni, E. Varrenti, D. Modotto, and C. De Angelis, “Chromatic confocal setup for displacement measurement using a supercontinuum light source,” Opt. Laser Technol. 49, 91–94 (2013).
[Crossref]

Najjaran, H.

X. Chen, Y. Chen, K. Gupta, J. Zhou, and H. Najjaran, “SliceNet: A proficient model for real-time 3D shape-based recognition,” Neurocomputing 316, 144–155 (2018).
[Crossref]

Nakamura, T.

X. Chen, T. Nakamura, Y. Shimizu, C. Chen, Y. Chen, H. Matsukuma, and W. Gao, “A chromatic confocal probe with a mode-locked femtosecond laser source,” Opt. Laser Technol. 103, 359–366 (2018).
[Crossref]

Nguyen, D.T.

Ni, K.

Niu, Y.

Nouira, H.

H. Nouira, N. E. Hayek, X. Yuan, and N. Anwer, “Characterization of the main error sources of chromatic confocal probes for dimensional measurement,” Meas. Sci. Technol. 25(4), 044011 (2014).
[Crossref]

Novak, J.

J. Novak and A. Miks, “Hyperchromats with linear dependence of longitudinal chromatic aberration on wavelength,” Optik 116(4), 165–168 (2005).
[Crossref]

Olsovsky, C.

Orr, M. J. L.

M. J. L. Orr, "Introduction to radial basis function networks," University of Edinburgh, Edinburgh, Scotland, 1996.

Osten, W.

D. Claus, G. Pedrini, T. Boettcher, M. Taphanel, W. Osten, and R. Hibst, “Development of a realistic wave propagation-based chromatic confocal microscopy model,” Proc. SPIE 10677, 106770X (2018).
[Crossref]

A. Ruprecht, K. Koerner, T. Wiesendanger, H. Tiziani, and W. Osten, “Chromatic confocal detection for high-speed microtopography measurements,” Proc. SPIE 5302, 53–60 (2004).
[Crossref]

Pawley, J. B.

J. B. Pawley, Handbook of biological confocal microscopy (Springer, 2006).

Pedrini, G.

D. Claus, G. Pedrini, T. Boettcher, M. Taphanel, W. Osten, and R. Hibst, “Development of a realistic wave propagation-based chromatic confocal microscopy model,” Proc. SPIE 10677, 106770X (2018).
[Crossref]

Price, J. H.

Qiu, L.

Rahlves, M.

Raj, B.

B.V.R. Tata and B. Raj, “Confocal laser scanning microscopy: Applications in material science and technology,” Bull. Mater. Sci. 21(4), 263–278 (1998).
[Crossref]

Rayer, M.

Reithmeier, E.

Rios, J.

D. Manrique, J. Rios, and A. Rodriguez-Paton, “Evolutionary system for automatically constructing and adapting radial basis function networks,” Neurocomputing 69(16-18), 2268–2283 (2006).
[Crossref]

Robb, P. N.

Rodriguez-Paton, A.

D. Manrique, J. Rios, and A. Rodriguez-Paton, “Evolutionary system for automatically constructing and adapting radial basis function networks,” Neurocomputing 69(16-18), 2268–2283 (2006).
[Crossref]

Roth, B.

Roweis, S. T.

S. T. Roweis and S. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290(5500), 2323–2326 (2000).
[Crossref]

Ruprecht, A.

A. Ruprecht, K. Koerner, T. Wiesendanger, H. Tiziani, and W. Osten, “Chromatic confocal detection for high-speed microtopography measurements,” Proc. SPIE 5302, 53–60 (2004).
[Crossref]

Ruprecht, A. K.

Samara, A.

J. Chesna, B. Wiedmaier, J. Wang, A. Samara, R. Leach, T. Her, and S. Smith, “Aerial wetting contact angle measurement using confocal microscopy,” Meas. Sci. Technol. 27(12), 125202 (2016).
[Crossref]

Sasián, J.

Saul, S. K.

S. T. Roweis and S. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290(5500), 2323–2326 (2000).
[Crossref]

Schall, M.

M. Grunwald, P. Laube, M. Schall, G. Umlauf, and M.O. Franz, “Radiometric calibration of digital cameras using neural networks,” Proc. SPIE 10395, 1039505 (2017).
[Crossref]

Sesko, D.W.

D.W. Sesko, “Intensity compensation for interchangeable chromatic point sensor components,” U.S.patent US7, 876, 456 B2 (Jan. 25, 2011).

Shao, R.

Shelton, R.

Shen, Y.

Sheng, Z.

Shi, K.

Shi, S.

Shimizu, Y.

X. Chen, T. Nakamura, Y. Shimizu, C. Chen, Y. Chen, H. Matsukuma, and W. Gao, “A chromatic confocal probe with a mode-locked femtosecond laser source,” Opt. Laser Technol. 103, 359–366 (2018).
[Crossref]

Sinzinger, S.

Smith, S.

J. Chesna, B. Wiedmaier, J. Wang, A. Samara, R. Leach, T. Her, and S. Smith, “Aerial wetting contact angle measurement using confocal microscopy,” Meas. Sci. Technol. 27(12), 125202 (2016).
[Crossref]

Smith, W. J.

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems (McGraw-Hill, New York, 1990).

Stamnes, J. J.

Stamnes, K.

Stamnes, S.

Stinchcombe, M.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2(5), 359–366 (1989).
[Crossref]

Sun, P.

Tan, J

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

Tan, J.

C. Liu, Y. Liu, T. Zheng, J. Tan, and J. Liu, “Monte Carlo based analysis of confocal peak extraction uncertainty,” Meas. Sci. Technol. 28(10), 105016 (2017).
[Crossref]

J. Liu, Y. Wang, K. Gu, X. You, M. Zhang, M. Li, and J. Tan, “Measuring profile of large hybrid aspherical diffractive infrared elements using confocal profilometer,” Meas. Sci. Technol. 27(12), 125011 (2016).
[Crossref]

J. Liu and J. Tan, Confocal Microscopy (Morgan & Claypool, 2016).

Taphanel, M.

D. Claus, G. Pedrini, T. Boettcher, M. Taphanel, W. Osten, and R. Hibst, “Development of a realistic wave propagation-based chromatic confocal microscopy model,” Proc. SPIE 10677, 106770X (2018).
[Crossref]

Tata, B.V.R.

B.V.R. Tata and B. Raj, “Confocal laser scanning microscopy: Applications in material science and technology,” Bull. Mater. Sci. 21(4), 263–278 (1998).
[Crossref]

Tatian, B.

Tay, A.

K. Ang, Z. Fang, and A. Tay, “Note: Real-time three-dimensional topography measurement of microfluidic devices with pillar structures using confocal microscope,” Rev. Sci. Instrum. 85(2), 026108 (2014).
[Crossref]

Tiziani, H.

A. Ruprecht, K. Koerner, T. Wiesendanger, H. Tiziani, and W. Osten, “Chromatic confocal detection for high-speed microtopography measurements,” Proc. SPIE 5302, 53–60 (2004).
[Crossref]

Tiziani, H. J.

Tobar, F. A.

F. A. Tobar, S. Y. Kung, and D. P. Mandic, “Multikernel least mean square algorithm,” IEEE Trans. Neural Netw. Learning Syst. 25(2), 265–277 (2014).
[Crossref]

Umlauf, G.

M. Grunwald, P. Laube, M. Schall, G. Umlauf, and M.O. Franz, “Radiometric calibration of digital cameras using neural networks,” Proc. SPIE 10395, 1039505 (2017).
[Crossref]

Varrenti, E.

U. Minoni, G. Manili, S. Bettoni, E. Varrenti, D. Modotto, and C. De Angelis, “Chromatic confocal setup for displacement measurement using a supercontinuum light source,” Opt. Laser Technol. 49, 91–94 (2013).
[Crossref]

Wang, J.

C. Chen, W. Yang, J. Wang, W. Lu, X. Liu, and X. Jiang, “Accurate and efficient height extraction in chromatic confocal microscopy using corrected fitting of the differential signal,” Precis. Eng. 56, 447–454 (2019).
[Crossref]

C. Chen, J. Wang, C. Zhang, W. Lu, X. Liu, Z. Lei, and X. Jiang, “Influence of optical aberrations on the peak extraction in confocal microscopy,” Opt. Commun. 449, 24–32 (2019).
[Crossref]

C. Chen, J. Wang, R. Leach, W. Lu, X. Liu, and X. Jiang, “Corrected parabolic fitting for height extraction in confocal microscopy,” Opt. Express 27(3), 3682–3697 (2019).
[Crossref]

C. Chen, J. Wang, X. J. Liu, W. L. Lu, H. Zhu, and X. Q. Jiang, “Influence of sample surface height for evaluation of peak extraction algorithms in confocal microscopy,” Appl. Opt. 57(22), 6516–6526 (2018).
[Crossref]

J. Chesna, B. Wiedmaier, J. Wang, A. Samara, R. Leach, T. Her, and S. Smith, “Aerial wetting contact angle measurement using confocal microscopy,” Meas. Sci. Technol. 27(12), 125202 (2016).
[Crossref]

Wang, X.

Wang, Y.

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

G. Zhuo, C. Hsu, Y. Wang, and M. Chan, “Chromatic confocal microscopy to rapidly reveal nanoscale surface/interface topography by position-sensitive detection,” Appl. Phys. Lett. 113(8), 083106 (2018).
[Crossref]

J. Liu, Y. Wang, K. Gu, X. You, M. Zhang, M. Li, and J. Tan, “Measuring profile of large hybrid aspherical diffractive infrared elements using confocal profilometer,” Meas. Sci. Technol. 27(12), 125011 (2016).
[Crossref]

Wenzel, C.

M. Hillenbrand, B. Mitschunas, C. Wenzel, A. Grewe, X. Ma, P. Feßer, M. Bichra, and S. Sinzinger, “Hybrid hyperchromats for chromatic confocal sensor systems,” Adv. Opt. Technol. 1(3), 187 (2012).
[Crossref]

White, H.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2(5), 359–366 (1989).
[Crossref]

Wiedmaier, B.

J. Chesna, B. Wiedmaier, J. Wang, A. Samara, R. Leach, T. Her, and S. Smith, “Aerial wetting contact angle measurement using confocal microscopy,” Meas. Sci. Technol. 27(12), 125202 (2016).
[Crossref]

Wiesendanger, T.

A. Ruprecht, K. Koerner, T. Wiesendanger, H. Tiziani, and W. Osten, “Chromatic confocal detection for high-speed microtopography measurements,” Proc. SPIE 5302, 53–60 (2004).
[Crossref]

Wiesendanger, T. F.

Williams, L. J.

H. Abdi and L. J. Williams, “Principal component analysis,” Wiley Interdiscip. Rev. Comput. Stat. 2(4), 433–459 (2010).
[Crossref]

Wong, M. A.

J. A. Hartigan and M. A. Wong, “Algorithm AS 136: A K-means clustering algorithm,” J. R. Stat. Soc. Series C 28(1), 100–108 (1979).
[Crossref]

Wu, H.

Xi, J. T.

Xiang, W. J.

W. J. Xiang, Z. X. Zhou, D. Y. Ge, Q. Y. Zhang, and Q. H. Yao, “Camera calibration by hybrid Hopfield network and self-adaptive genetic algorithm,” Meas. Sci. Rev. 12(6), 302–308 (2012).
[Crossref]

Xie, S.

S. Xie, X. Zhang, S. Chen, and C. Zhu, “Hybrid neural network models of transducers,” Meas. Sci. Technol. 22(10), 105201 (2011).
[Crossref]

Xu, Z.

Yang, J.

Yang, W.

C. Chen, W. Yang, J. Wang, W. Lu, X. Liu, and X. Jiang, “Accurate and efficient height extraction in chromatic confocal microscopy using corrected fitting of the differential signal,” Precis. Eng. 56, 447–454 (2019).
[Crossref]

Yao, Q. H.

W. J. Xiang, Z. X. Zhou, D. Y. Ge, Q. Y. Zhang, and Q. H. Yao, “Camera calibration by hybrid Hopfield network and self-adaptive genetic algorithm,” Meas. Sci. Rev. 12(6), 302–308 (2012).
[Crossref]

Ye, R.

Q. Yu, K. Zhang, R. Zhou, C. Cui, F. Cheng, S. Fu, and R. Ye, “Calibration of a chromatic confocal microscope for measuring a colored specimen,” IEEE Photonics J. 10(6), 1–9 (2018).
[Crossref]

Q. Yu, K. Zhang, C. Cui, R. Zhou, F. Cheng, R. Ye, and Y. Zhang, “Method of thickness measurement for transparent specimens with chromatic confocal microscopy,” Appl. Opt. 57(33), 9722–9728 (2018).
[Crossref]

Yin, S.

You, X.

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

J. Liu, Y. Wang, K. Gu, X. You, M. Zhang, M. Li, and J. Tan, “Measuring profile of large hybrid aspherical diffractive infrared elements using confocal profilometer,” Meas. Sci. Technol. 27(12), 125011 (2016).
[Crossref]

Yu, Q.

Q. Yu, K. Zhang, R. Zhou, C. Cui, F. Cheng, S. Fu, and R. Ye, “Calibration of a chromatic confocal microscope for measuring a colored specimen,” IEEE Photonics J. 10(6), 1–9 (2018).
[Crossref]

Q. Yu, K. Zhang, C. Cui, R. Zhou, F. Cheng, R. Ye, and Y. Zhang, “Method of thickness measurement for transparent specimens with chromatic confocal microscopy,” Appl. Opt. 57(33), 9722–9728 (2018).
[Crossref]

Yuan, X.

H. Nouira, N. E. Hayek, X. Yuan, and N. Anwer, “Characterization of the main error sources of chromatic confocal probes for dimensional measurement,” Meas. Sci. Technol. 25(4), 044011 (2014).
[Crossref]

Zhang, C.

C. Chen, J. Wang, C. Zhang, W. Lu, X. Liu, Z. Lei, and X. Jiang, “Influence of optical aberrations on the peak extraction in confocal microscopy,” Opt. Commun. 449, 24–32 (2019).
[Crossref]

C. Zhang, Y. Niu, H. Zhang, and J. Lu, “Optimized star sensors laboratory calibration method using a regularization neural network,” Appl. Opt. 57(5), 1067–1074 (2018).
[Crossref]

Zhang, H.

C. Zhang, Y. Niu, H. Zhang, and J. Lu, “Optimized star sensors laboratory calibration method using a regularization neural network,” Appl. Opt. 57(5), 1067–1074 (2018).
[Crossref]

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

Zhang, K.

Q. Yu, K. Zhang, R. Zhou, C. Cui, F. Cheng, S. Fu, and R. Ye, “Calibration of a chromatic confocal microscope for measuring a colored specimen,” IEEE Photonics J. 10(6), 1–9 (2018).
[Crossref]

Q. Yu, K. Zhang, C. Cui, R. Zhou, F. Cheng, R. Ye, and Y. Zhang, “Method of thickness measurement for transparent specimens with chromatic confocal microscopy,” Appl. Opt. 57(33), 9722–9728 (2018).
[Crossref]

Zhang, M.

J. Liu, Y. Wang, K. Gu, X. You, M. Zhang, M. Li, and J. Tan, “Measuring profile of large hybrid aspherical diffractive infrared elements using confocal profilometer,” Meas. Sci. Technol. 27(12), 125011 (2016).
[Crossref]

Zhang, Q. Y.

W. J. Xiang, Z. X. Zhou, D. Y. Ge, Q. Y. Zhang, and Q. H. Yao, “Camera calibration by hybrid Hopfield network and self-adaptive genetic algorithm,” Meas. Sci. Rev. 12(6), 302–308 (2012).
[Crossref]

Zhang, X.

S. Xie, X. Zhang, S. Chen, and C. Zhu, “Hybrid neural network models of transducers,” Meas. Sci. Technol. 22(10), 105201 (2011).
[Crossref]

Zhang, Y.

Zhao, H.

Zhao, W.

Zheng, T.

C. Liu, Y. Liu, T. Zheng, J. Tan, and J. Liu, “Monte Carlo based analysis of confocal peak extraction uncertainty,” Meas. Sci. Technol. 28(10), 105016 (2017).
[Crossref]

Zhou, J.

X. Chen, Y. Chen, K. Gupta, J. Zhou, and H. Najjaran, “SliceNet: A proficient model for real-time 3D shape-based recognition,” Neurocomputing 316, 144–155 (2018).
[Crossref]

Zhou, Q.

Zhou, R.

Q. Yu, K. Zhang, C. Cui, R. Zhou, F. Cheng, R. Ye, and Y. Zhang, “Method of thickness measurement for transparent specimens with chromatic confocal microscopy,” Appl. Opt. 57(33), 9722–9728 (2018).
[Crossref]

Q. Yu, K. Zhang, R. Zhou, C. Cui, F. Cheng, S. Fu, and R. Ye, “Calibration of a chromatic confocal microscope for measuring a colored specimen,” IEEE Photonics J. 10(6), 1–9 (2018).
[Crossref]

Zhou, Z. X.

W. J. Xiang, Z. X. Zhou, D. Y. Ge, Q. Y. Zhang, and Q. H. Yao, “Camera calibration by hybrid Hopfield network and self-adaptive genetic algorithm,” Meas. Sci. Rev. 12(6), 302–308 (2012).
[Crossref]

Zhu, C.

S. Xie, X. Zhang, S. Chen, and C. Zhu, “Hybrid neural network models of transducers,” Meas. Sci. Technol. 22(10), 105201 (2011).
[Crossref]

Zhu, H.

Zhu, L.

Zhuo, G.

G. Zhuo, C. Hsu, Y. Wang, and M. Chan, “Chromatic confocal microscopy to rapidly reveal nanoscale surface/interface topography by position-sensitive detection,” Appl. Phys. Lett. 113(8), 083106 (2018).
[Crossref]

Adv. Opt. Technol. (1)

M. Hillenbrand, B. Mitschunas, C. Wenzel, A. Grewe, X. Ma, P. Feßer, M. Bichra, and S. Sinzinger, “Hybrid hyperchromats for chromatic confocal sensor systems,” Adv. Opt. Technol. 1(3), 187 (2012).
[Crossref]

Appl. Opt. (15)

P. N. Robb and R. I. Mercado, “Calculation of refractive indices using Buchdahl’s chromatic coordinate,” Appl. Opt. 22(8), 1198–1215 (1983).
[Crossref]

B. Tatian, “Fitting Refractive-Index Data With The Sellmeier Dispersion Formula,” Appl. Opt. 23(24), 4477–4485 (1984).
[Crossref]

S.L. Dobson, P. Sun, and Y. Fainman, “Diffractive lenses for chromatic confocal imaging,” Appl. Opt. 36(20), 4744–4748 (1997).
[Crossref]

P. C. Lin, P. Sun, L. Zhu, and Y. Fainman, “Single-shot depth-section imaging through chromatic slit-scan confocal microscopy,” Appl. Opt. 37(28), 6764–6770 (1998).
[Crossref]

S. Cha, P. C. Lin, L. Zhu, P. Sun, and Y. Fainman, “Nontranslational three-dimensional profilometry by chromatic confocal microscopy with dynamically configurable micromirror scanning,” Appl. Opt. 39(16), 2605–2613 (2000).
[Crossref]

A. K. Ruprecht, T. F. Wiesendanger, and H. J. Tiziani, “Signal evaluation for high-speed confocal measurements,” Appl. Opt. 41(35), 7410–7415 (2002).
[Crossref]

M. J. Baker, J. T. Xi, and J. F. Chicharo, “Neural Network digital fringe calibration technique for structured light profilometers,” Appl. Opt. 46(8), 1233–1243 (2007).
[Crossref]

D. N. Fuller, A. L. Kellner, and J. H. Price, “Exploiting chromatic aberration for image-based microscope autofocus,” Appl. Opt. 50(25), 4967–4976 (2011).
[Crossref]

J. Yang, L. Qiu, W. Zhao, R. Shao, and Z. Li, “Measuring the lens focal length by laser reflection-confocal technology,” Appl. Opt. 52(16), 3812–3817 (2013).
[Crossref]

M. Rayer and D. Mansfield, “Chromatic confocal microscopy using staircase diffractive surface,” Appl. Opt. 53(23), 5123–5130 (2014).
[Crossref]

M. Hillenbrand, B. Mitschunas, F. Brill, A. Grewe, and S. Sinzinger, “Spectral characteristics of chromatic confocal imaging systems,” Appl. Opt. 53(32), 7634–7642 (2014).
[Crossref]

M. Rahlves, B. Roth, and E. Reithmeier, “Confocal signal evaluation algorithms for surface metrology: uncertainty and numerical efficiency,” Appl. Opt. 56(21), 5920–5926 (2017).
[Crossref]

C. Zhang, Y. Niu, H. Zhang, and J. Lu, “Optimized star sensors laboratory calibration method using a regularization neural network,” Appl. Opt. 57(5), 1067–1074 (2018).
[Crossref]

C. Chen, J. Wang, X. J. Liu, W. L. Lu, H. Zhu, and X. Q. Jiang, “Influence of sample surface height for evaluation of peak extraction algorithms in confocal microscopy,” Appl. Opt. 57(22), 6516–6526 (2018).
[Crossref]

Q. Yu, K. Zhang, C. Cui, R. Zhou, F. Cheng, R. Ye, and Y. Zhang, “Method of thickness measurement for transparent specimens with chromatic confocal microscopy,” Appl. Opt. 57(33), 9722–9728 (2018).
[Crossref]

Appl. Phys. Lett. (1)

G. Zhuo, C. Hsu, Y. Wang, and M. Chan, “Chromatic confocal microscopy to rapidly reveal nanoscale surface/interface topography by position-sensitive detection,” Appl. Phys. Lett. 113(8), 083106 (2018).
[Crossref]

Biomed. Opt. Express (1)

Bull. Mater. Sci. (1)

B.V.R. Tata and B. Raj, “Confocal laser scanning microscopy: Applications in material science and technology,” Bull. Mater. Sci. 21(4), 263–278 (1998).
[Crossref]

IEEE Photonics J. (1)

Q. Yu, K. Zhang, R. Zhou, C. Cui, F. Cheng, S. Fu, and R. Ye, “Calibration of a chromatic confocal microscope for measuring a colored specimen,” IEEE Photonics J. 10(6), 1–9 (2018).
[Crossref]

IEEE Trans. Neural Netw. (1)

S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2(2), 302–309 (1991).
[Crossref]

IEEE Trans. Neural Netw. Learning Syst. (1)

F. A. Tobar, S. Y. Kung, and D. P. Mandic, “Multikernel least mean square algorithm,” IEEE Trans. Neural Netw. Learning Syst. 25(2), 265–277 (2014).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

J. Garzón, T. Gharbi, and J. Meneses, “Real-time determination of the optical thickness and topography of tissues by chromatic confocal microscopy,” J. Opt. A: Pure Appl. Opt. 10(10), 104028 (2008).
[Crossref]

J. R. Stat. Soc. Series C (1)

J. A. Hartigan and M. A. Wong, “Algorithm AS 136: A K-means clustering algorithm,” J. R. Stat. Soc. Series C 28(1), 100–108 (1979).
[Crossref]

Meas. Sci. Rev. (1)

W. J. Xiang, Z. X. Zhou, D. Y. Ge, Q. Y. Zhang, and Q. H. Yao, “Camera calibration by hybrid Hopfield network and self-adaptive genetic algorithm,” Meas. Sci. Rev. 12(6), 302–308 (2012).
[Crossref]

Meas. Sci. Technol. (5)

S. Xie, X. Zhang, S. Chen, and C. Zhu, “Hybrid neural network models of transducers,” Meas. Sci. Technol. 22(10), 105201 (2011).
[Crossref]

C. Liu, Y. Liu, T. Zheng, J. Tan, and J. Liu, “Monte Carlo based analysis of confocal peak extraction uncertainty,” Meas. Sci. Technol. 28(10), 105016 (2017).
[Crossref]

H. Nouira, N. E. Hayek, X. Yuan, and N. Anwer, “Characterization of the main error sources of chromatic confocal probes for dimensional measurement,” Meas. Sci. Technol. 25(4), 044011 (2014).
[Crossref]

J. Chesna, B. Wiedmaier, J. Wang, A. Samara, R. Leach, T. Her, and S. Smith, “Aerial wetting contact angle measurement using confocal microscopy,” Meas. Sci. Technol. 27(12), 125202 (2016).
[Crossref]

J. Liu, Y. Wang, K. Gu, X. You, M. Zhang, M. Li, and J. Tan, “Measuring profile of large hybrid aspherical diffractive infrared elements using confocal profilometer,” Meas. Sci. Technol. 27(12), 125011 (2016).
[Crossref]

Nanoscale (1)

L. Li, J. Liu, Y. Liu, C. Liu, H. Zhang, X. You, K. Gu, Y. Wang, and J Tan, “A promising solution to the limits of microscopes for smooth surfaces: fluorophore-aided scattering microscopy,” Nanoscale 10(20), 9484–9488 (2018).
[Crossref]

Neural Networks (1)

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks 2(5), 359–366 (1989).
[Crossref]

Neurocomputing (2)

X. Chen, Y. Chen, K. Gupta, J. Zhou, and H. Najjaran, “SliceNet: A proficient model for real-time 3D shape-based recognition,” Neurocomputing 316, 144–155 (2018).
[Crossref]

D. Manrique, J. Rios, and A. Rodriguez-Paton, “Evolutionary system for automatically constructing and adapting radial basis function networks,” Neurocomputing 69(16-18), 2268–2283 (2006).
[Crossref]

Opt. Commun. (1)

C. Chen, J. Wang, C. Zhang, W. Lu, X. Liu, Z. Lei, and X. Jiang, “Influence of optical aberrations on the peak extraction in confocal microscopy,” Opt. Commun. 449, 24–32 (2019).
[Crossref]

Opt. Eng. (1)

L. Chen, Y. Chang, and H. Li, “Full-field chromatic confocal surface profilometry employing digital micromirror device correspondence for minimizing lateral cross talks,” Opt. Eng. 51(8), 081507 (2012).
[Crossref]

Opt. Express (9)

J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Opt. Express 20(23), 26027–26036 (2012).
[Crossref]

K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic Confocal Microscopy using supercontinuum light,” Opt. Express 12(10), 2096–2101 (2004).
[Crossref]

H. Zhao, S. Shi, H. Jiang, Y. Zhang, and Z. Xu, “Calibration of AOTF-based 3D measurement system using multiplane model based on phase fringe and BP neural network,” Opt. Express 25(9), 10413–10433 (2017).
[Crossref]

C. Chen, J. Wang, R. Leach, W. Lu, X. Liu, and X. Jiang, “Corrected parabolic fitting for height extraction in confocal microscopy,” Opt. Express 27(3), 3682–3697 (2019).
[Crossref]

B. Jiao, X. Li, Q. Zhou, K. Ni, and X. Wang, “Improved chromatic confocal displacement-sensor based on a spatial-bandpass-filter and an X-shaped fiber-coupler,” Opt. Express 27(8), 10961–10973 (2019).
[Crossref]

D. Luo and M. W. Kudenov, “Neural network calibration of a snapshot birefringent Fourier transform spectrometer with periodic phase errors,” Opt. Express 24(10), 11266 (2016).
[Crossref]

L. Fan, W. Li, A. Dahlback, J. J. Stamnes, S. Stamnes, and K. Stamnes, “New neural-network-based method to infer total ozone column amounts and cloud effects from multi-channel, moderate bandwidth filter instruments,” Opt. Express 22(16), 19595–19609 (2014).
[Crossref]

L. Qiu, D. Liu, W. Zhao, H. Cui, and Z. Sheng, “Real-time laser differential confocal microscopy without sample reflectivity effects,” Opt. Express 22(18), 21626–21640 (2014).
[Crossref]

C.L. Li and J. Sasián, “Adaptive dispersion formula for index interpolation and chromatic aberration correction,” Opt. Express 22(1), 1193–1202 (2014).
[Crossref]

Opt. Laser Technol. (4)

D. Duque and J. Garzon, “Effects of both diffractive element and fiber optic based detector in a chromatic confocal system,” Opt. Laser Technol. 50, 182–189 (2013).
[Crossref]

D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol. 44(4), 788–793 (2012).
[Crossref]

X. Chen, T. Nakamura, Y. Shimizu, C. Chen, Y. Chen, H. Matsukuma, and W. Gao, “A chromatic confocal probe with a mode-locked femtosecond laser source,” Opt. Laser Technol. 103, 359–366 (2018).
[Crossref]

U. Minoni, G. Manili, S. Bettoni, E. Varrenti, D. Modotto, and C. De Angelis, “Chromatic confocal setup for displacement measurement using a supercontinuum light source,” Opt. Laser Technol. 49, 91–94 (2013).
[Crossref]

Opt. Lett. (4)

Optik (1)

J. Novak and A. Miks, “Hyperchromats with linear dependence of longitudinal chromatic aberration on wavelength,” Optik 116(4), 165–168 (2005).
[Crossref]

Precis. Eng. (1)

C. Chen, W. Yang, J. Wang, W. Lu, X. Liu, and X. Jiang, “Accurate and efficient height extraction in chromatic confocal microscopy using corrected fitting of the differential signal,” Precis. Eng. 56, 447–454 (2019).
[Crossref]

Proc. SPIE (3)

M. Grunwald, P. Laube, M. Schall, G. Umlauf, and M.O. Franz, “Radiometric calibration of digital cameras using neural networks,” Proc. SPIE 10395, 1039505 (2017).
[Crossref]

A. Ruprecht, K. Koerner, T. Wiesendanger, H. Tiziani, and W. Osten, “Chromatic confocal detection for high-speed microtopography measurements,” Proc. SPIE 5302, 53–60 (2004).
[Crossref]

D. Claus, G. Pedrini, T. Boettcher, M. Taphanel, W. Osten, and R. Hibst, “Development of a realistic wave propagation-based chromatic confocal microscopy model,” Proc. SPIE 10677, 106770X (2018).
[Crossref]

Rev. Sci. Instrum. (2)

K. Ang, Z. Fang, and A. Tay, “Note: Real-time three-dimensional topography measurement of microfluidic devices with pillar structures using confocal microscope,” Rev. Sci. Instrum. 85(2), 026108 (2014).
[Crossref]

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum. 80(7), 073706 (2009).
[Crossref]

Science (1)

S. T. Roweis and S. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290(5500), 2323–2326 (2000).
[Crossref]

Wiley Interdiscip. Rev. Comput. Stat. (1)

H. Abdi and L. J. Williams, “Principal component analysis,” Wiley Interdiscip. Rev. Comput. Stat. 2(4), 433–459 (2010).
[Crossref]

Other (11)

I. T. Jolliffe, Principle Component Analysis (Springer, 1986).

R. K. Leach, Fundamental Principles of Engineering Nanometrology (Elsevier, 2014).

Schott glass catalog (2011), http://www.us.schott.com .

D.W. Sesko, “Intensity compensation for interchangeable chromatic point sensor components,” U.S.patent US7, 876, 456 B2 (Jan. 25, 2011).

R.K. Leach, Optical Measurement of Surface Topography (Springer, 2011).

M. Gu, Principles of three-dimensional imaging in confocal microscopes (World Scientific, 1996).

J. B. Pawley, Handbook of biological confocal microscopy (Springer, 2006).

I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, Deep learning (MIT press, Cambridge, 2016).

J. Liu and J. Tan, Confocal Microscopy (Morgan & Claypool, 2016).

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems (McGraw-Hill, New York, 1990).

M. J. L. Orr, "Introduction to radial basis function networks," University of Edinburgh, Edinburgh, Scotland, 1996.

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Figures (12)

Fig. 1.
Fig. 1. Schema of the CCM characterization procedure.
Fig. 2.
Fig. 2. Structure of the hybrid RBFN.
Fig. 3.
Fig. 3. Refractive index fitting error of Buchdahl’s dispersion formula against wavelength.
Fig. 4.
Fig. 4. Accuracy of chromatic dispersion model for a hyperchromatic objective lens with multi-lenses (a) Displacement-wavelength relationships for the ray tracing data and the chromatic dispersion model and (b) Variation of the residual errors from the chromatic dispersion model with the wavelength
Fig. 5.
Fig. 5. The topological structure of an RBFN.
Fig. 6.
Fig. 6. Spectral ARSs at different axial positions.
Fig. 7.
Fig. 7. Illustrations of the training/validation and testing data sets.
Fig. 8.
Fig. 8. Network training performance of different peak extraction algorithms.
Fig. 9.
Fig. 9. Network training performance of different displacement-wavelength fitting models.
Fig. 10.
Fig. 10. The individual and summing proportion of the data variance in the PCA.
Fig. 11.
Fig. 11. Network training performance with and without PCA based dimensionality reduction.
Fig. 12.
Fig. 12. Measurement results with different calibration models. (a) Systematic errors at different PZT displacements and (b) Standard deviations at different PZT displacements.

Equations (8)

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N ( λ ) = N 0 + ν 1 ω + ν 2 ω 2 + + ν q ω q ,
ω = λ / λ 1000 1000 0.5876 1 + 2.5 ( λ / λ 1000 1000 0.5876 ) ,
f ( λ ) = 1 N ( λ ) 1 r 1 r 2 r 2 r 1 ,
f ( λ ) = f n o m ( n n o m 1 ) N ( λ ) 1 = C n o m N ( λ ) 1 ,
f ( λ ) C n o m N 0 1 [ 1 1 N 0 1 ( ν 1 ω + ν 2 ω 2 + + ν q ω q ) ] ,
φ ( X ) = i = 1 N h w i exp ( | | X k i | | 2 2 σ i 2 ) ,
R M S E = 1 N t t = 1 N t ( Y t d e s Y t n e t ) 2 ,
{ z 1 = α 11 x 1 + α 12 x 2 + . . . + α 1 n x n z 2 = α 21 x 1 + α 22 x 2 + . . . + α 2 n x n . . . z l = α l 1 x 1 + α l 1 x 2 + . . . + α ln x n ,

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