Abstract

This article presents a new robust, precise, high-frequency focal-distance-modulated confocal point sensor for probing in coordinate measuring systems (CMSs). While maintaining the known advantages of the confocal measurement principle, the sensor represents an innovative combination of a fiber-coupled confocal illumination and detection with a tuneable, acoustically driven gradient-index fluid lens for modulation of the focus distance and a novel signal processing utilizing a lock-in amplifier. The new arrangement is able to achieve an approximately linear characteristic curve for the optimized feedback control of the CMS in scanning sample mode. This article emphasizes the optical application and the signal processing of the setup.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. E. Uhlmann, B. Mullany, D. Biermann, K. P. Rajurkar, T. Hausotte, and E. Brinksmeier, “Process chains for high-precision components with micro-scale features,” CIRP Ann. 65, 549–572 (2016).
    [Crossref]
  2. F. G. Balzer, U. Gerhardt, T. Hausotte, K. Albrecht, E. Manske, and G. Jäger, “Application of a novel fibre-coupled confocal sensor in a nanopositioning and nanomeasuring machine,” in 12th Euspen International Conference (2012).
  3. “Part 602: nominal characteristics of non-contact (confocal chromatic probe) instruments,” .
  4. Tag Optics Inc., “The physics behind TAG optics’ technology and the mechanism of action of using sound to shape light” (2013).
  5. M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
    [Crossref]
  6. C. Cremer and T. Cremer, “Considerations on a laser-scanning-microscope with high resolution and depth of field,” Microsc. Acta 81, 31–44 (1978).
  7. G. Tosello, H. Haitjema, R. K. Leach, D. Quagliotti, S. Gasparin, and H. N. Hansen, “An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments,” CIRP Ann. 65, 529–532 (2016).
    [Crossref]
  8. N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
    [Crossref]
  9. A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. 33, 2146–2148 (2008).
    [Crossref]
  10. M. Duocastella, G. Vicidomini, and A. Diaspro, “Simultaneous multiplane confocal microscopy using acoustic tunable lenses,” Opt. Express 22, 019293 (2014).
    [Crossref]
  11. N. Olivier, A. Mermillod-Blondin, C. B. Arnold, and E. Beaurepaire, “Two-photon microscopy with simultaneous standard and extended depth of field using a tunable acoustic gradient-index lens,” Opt. Lett. 34, 1684–1686 (2009).
    [Crossref]
  12. T. Tsai, E. McLeod, and C. B. Arnold, “Generating Bessel beams with a tunable acoustic gradient index of refraction lens,” Proc. SPIE 6326, 63261F (2006).
    [Crossref]
  13. C. Sheppard and A. Choudhury, “Image formation in scanning microscope,” Opt. Acta. 24, 1051–1073 (1977).
    [Crossref]
  14. T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).
  15. P. Török and L. Mule’stagno, “Application of scanning optical microscopy in materials science to detect bulk microdefects in semiconductors,” J. Microsc. 188, 1–16 (1997).
  16. T. Hausotte, B. Percle, and G. Jäger, “Advanced three-dimensional scan methods in the nanopositioning and nanomeasuring machine,” Meas. Sci. Technol. 20, 084004 (2009).
    [Crossref]
  17. M. Gu, C. J. R. Sheppard, and X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. 8, 1755–1761 (1991).
    [Crossref]

2016 (2)

E. Uhlmann, B. Mullany, D. Biermann, K. P. Rajurkar, T. Hausotte, and E. Brinksmeier, “Process chains for high-precision components with micro-scale features,” CIRP Ann. 65, 549–572 (2016).
[Crossref]

G. Tosello, H. Haitjema, R. K. Leach, D. Quagliotti, S. Gasparin, and H. N. Hansen, “An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments,” CIRP Ann. 65, 529–532 (2016).
[Crossref]

2014 (2)

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

M. Duocastella, G. Vicidomini, and A. Diaspro, “Simultaneous multiplane confocal microscopy using acoustic tunable lenses,” Opt. Express 22, 019293 (2014).
[Crossref]

2009 (2)

N. Olivier, A. Mermillod-Blondin, C. B. Arnold, and E. Beaurepaire, “Two-photon microscopy with simultaneous standard and extended depth of field using a tunable acoustic gradient-index lens,” Opt. Lett. 34, 1684–1686 (2009).
[Crossref]

T. Hausotte, B. Percle, and G. Jäger, “Advanced three-dimensional scan methods in the nanopositioning and nanomeasuring machine,” Meas. Sci. Technol. 20, 084004 (2009).
[Crossref]

2008 (1)

2006 (1)

T. Tsai, E. McLeod, and C. B. Arnold, “Generating Bessel beams with a tunable acoustic gradient index of refraction lens,” Proc. SPIE 6326, 63261F (2006).
[Crossref]

1997 (1)

P. Török and L. Mule’stagno, “Application of scanning optical microscopy in materials science to detect bulk microdefects in semiconductors,” J. Microsc. 188, 1–16 (1997).

1991 (1)

M. Gu, C. J. R. Sheppard, and X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. 8, 1755–1761 (1991).
[Crossref]

1988 (1)

M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
[Crossref]

1978 (1)

C. Cremer and T. Cremer, “Considerations on a laser-scanning-microscope with high resolution and depth of field,” Microsc. Acta 81, 31–44 (1978).

1977 (1)

C. Sheppard and A. Choudhury, “Image formation in scanning microscope,” Opt. Acta. 24, 1051–1073 (1977).
[Crossref]

Albrecht, K.

F. G. Balzer, U. Gerhardt, T. Hausotte, K. Albrecht, E. Manske, and G. Jäger, “Application of a novel fibre-coupled confocal sensor in a nanopositioning and nanomeasuring machine,” in 12th Euspen International Conference (2012).

Arnold, C. B.

Balzer, F. G.

F. G. Balzer, U. Gerhardt, T. Hausotte, K. Albrecht, E. Manske, and G. Jäger, “Application of a novel fibre-coupled confocal sensor in a nanopositioning and nanomeasuring machine,” in 12th Euspen International Conference (2012).

Beaurepaire, E.

Biermann, D.

E. Uhlmann, B. Mullany, D. Biermann, K. P. Rajurkar, T. Hausotte, and E. Brinksmeier, “Process chains for high-precision components with micro-scale features,” CIRP Ann. 65, 549–572 (2016).
[Crossref]

Brinksmeier, E.

E. Uhlmann, B. Mullany, D. Biermann, K. P. Rajurkar, T. Hausotte, and E. Brinksmeier, “Process chains for high-precision components with micro-scale features,” CIRP Ann. 65, 549–572 (2016).
[Crossref]

Choudhury, A.

C. Sheppard and A. Choudhury, “Image formation in scanning microscope,” Opt. Acta. 24, 1051–1073 (1977).
[Crossref]

Cremer, C.

C. Cremer and T. Cremer, “Considerations on a laser-scanning-microscope with high resolution and depth of field,” Microsc. Acta 81, 31–44 (1978).

Cremer, T.

C. Cremer and T. Cremer, “Considerations on a laser-scanning-microscope with high resolution and depth of field,” Microsc. Acta 81, 31–44 (1978).

Czarske, J. W.

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

Diaspro, A.

M. Duocastella, G. Vicidomini, and A. Diaspro, “Simultaneous multiplane confocal microscopy using acoustic tunable lenses,” Opt. Express 22, 019293 (2014).
[Crossref]

Duocastella, M.

M. Duocastella, G. Vicidomini, and A. Diaspro, “Simultaneous multiplane confocal microscopy using acoustic tunable lenses,” Opt. Express 22, 019293 (2014).
[Crossref]

Finkeldey, M.

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

Fischer, A.

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

Gan, X.

M. Gu, C. J. R. Sheppard, and X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. 8, 1755–1761 (1991).
[Crossref]

Gasparin, S.

G. Tosello, H. Haitjema, R. K. Leach, D. Quagliotti, S. Gasparin, and H. N. Hansen, “An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments,” CIRP Ann. 65, 529–532 (2016).
[Crossref]

Gerhardt, N. C. M.

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

Gerhardt, U.

F. G. Balzer, U. Gerhardt, T. Hausotte, K. Albrecht, E. Manske, and G. Jäger, “Application of a novel fibre-coupled confocal sensor in a nanopositioning and nanomeasuring machine,” in 12th Euspen International Conference (2012).

Gu, M.

M. Gu, C. J. R. Sheppard, and X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. 8, 1755–1761 (1991).
[Crossref]

Haitjema, H.

G. Tosello, H. Haitjema, R. K. Leach, D. Quagliotti, S. Gasparin, and H. N. Hansen, “An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments,” CIRP Ann. 65, 529–532 (2016).
[Crossref]

Hansen, H. N.

G. Tosello, H. Haitjema, R. K. Leach, D. Quagliotti, S. Gasparin, and H. N. Hansen, “An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments,” CIRP Ann. 65, 529–532 (2016).
[Crossref]

Hausotte, T.

E. Uhlmann, B. Mullany, D. Biermann, K. P. Rajurkar, T. Hausotte, and E. Brinksmeier, “Process chains for high-precision components with micro-scale features,” CIRP Ann. 65, 549–572 (2016).
[Crossref]

T. Hausotte, B. Percle, and G. Jäger, “Advanced three-dimensional scan methods in the nanopositioning and nanomeasuring machine,” Meas. Sci. Technol. 20, 084004 (2009).
[Crossref]

F. G. Balzer, U. Gerhardt, T. Hausotte, K. Albrecht, E. Manske, and G. Jäger, “Application of a novel fibre-coupled confocal sensor in a nanopositioning and nanomeasuring machine,” in 12th Euspen International Conference (2012).

Hofmann, R.

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

Jäger, G.

T. Hausotte, B. Percle, and G. Jäger, “Advanced three-dimensional scan methods in the nanopositioning and nanomeasuring machine,” Meas. Sci. Technol. 20, 084004 (2009).
[Crossref]

F. G. Balzer, U. Gerhardt, T. Hausotte, K. Albrecht, E. Manske, and G. Jäger, “Application of a novel fibre-coupled confocal sensor in a nanopositioning and nanomeasuring machine,” in 12th Euspen International Conference (2012).

Koukourakis, N.

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

Leach, R. K.

G. Tosello, H. Haitjema, R. K. Leach, D. Quagliotti, S. Gasparin, and H. N. Hansen, “An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments,” CIRP Ann. 65, 529–532 (2016).
[Crossref]

Leithold, C.

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

Manske, E.

F. G. Balzer, U. Gerhardt, T. Hausotte, K. Albrecht, E. Manske, and G. Jäger, “Application of a novel fibre-coupled confocal sensor in a nanopositioning and nanomeasuring machine,” in 12th Euspen International Conference (2012).

McLeod, E.

A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. 33, 2146–2148 (2008).
[Crossref]

T. Tsai, E. McLeod, and C. B. Arnold, “Generating Bessel beams with a tunable acoustic gradient index of refraction lens,” Proc. SPIE 6326, 63261F (2006).
[Crossref]

Mermillod-Blondin, A.

Minsky, M.

M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
[Crossref]

Mule’stagno, L.

P. Török and L. Mule’stagno, “Application of scanning optical microscopy in materials science to detect bulk microdefects in semiconductors,” J. Microsc. 188, 1–16 (1997).

Mullany, B.

E. Uhlmann, B. Mullany, D. Biermann, K. P. Rajurkar, T. Hausotte, and E. Brinksmeier, “Process chains for high-precision components with micro-scale features,” CIRP Ann. 65, 549–572 (2016).
[Crossref]

Olivier, N.

Percle, B.

T. Hausotte, B. Percle, and G. Jäger, “Advanced three-dimensional scan methods in the nanopositioning and nanomeasuring machine,” Meas. Sci. Technol. 20, 084004 (2009).
[Crossref]

Quagliotti, D.

G. Tosello, H. Haitjema, R. K. Leach, D. Quagliotti, S. Gasparin, and H. N. Hansen, “An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments,” CIRP Ann. 65, 529–532 (2016).
[Crossref]

Rajurkar, K. P.

E. Uhlmann, B. Mullany, D. Biermann, K. P. Rajurkar, T. Hausotte, and E. Brinksmeier, “Process chains for high-precision components with micro-scale features,” CIRP Ann. 65, 549–572 (2016).
[Crossref]

Sheppard, C.

C. Sheppard and A. Choudhury, “Image formation in scanning microscope,” Opt. Acta. 24, 1051–1073 (1977).
[Crossref]

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Sheppard, C. J. R.

M. Gu, C. J. R. Sheppard, and X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. 8, 1755–1761 (1991).
[Crossref]

Stürmer, M.

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

Török, P.

P. Török and L. Mule’stagno, “Application of scanning optical microscopy in materials science to detect bulk microdefects in semiconductors,” J. Microsc. 188, 1–16 (1997).

Tosello, G.

G. Tosello, H. Haitjema, R. K. Leach, D. Quagliotti, S. Gasparin, and H. N. Hansen, “An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments,” CIRP Ann. 65, 529–532 (2016).
[Crossref]

Tsai, T.

T. Tsai, E. McLeod, and C. B. Arnold, “Generating Bessel beams with a tunable acoustic gradient index of refraction lens,” Proc. SPIE 6326, 63261F (2006).
[Crossref]

Uhlmann, E.

E. Uhlmann, B. Mullany, D. Biermann, K. P. Rajurkar, T. Hausotte, and E. Brinksmeier, “Process chains for high-precision components with micro-scale features,” CIRP Ann. 65, 549–572 (2016).
[Crossref]

Vicidomini, G.

M. Duocastella, G. Vicidomini, and A. Diaspro, “Simultaneous multiplane confocal microscopy using acoustic tunable lenses,” Opt. Express 22, 019293 (2014).
[Crossref]

Wallrabe, U.

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

Wilson, T.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

CIRP Ann. (2)

E. Uhlmann, B. Mullany, D. Biermann, K. P. Rajurkar, T. Hausotte, and E. Brinksmeier, “Process chains for high-precision components with micro-scale features,” CIRP Ann. 65, 549–572 (2016).
[Crossref]

G. Tosello, H. Haitjema, R. K. Leach, D. Quagliotti, S. Gasparin, and H. N. Hansen, “An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments,” CIRP Ann. 65, 529–532 (2016).
[Crossref]

J. Microsc. (1)

P. Török and L. Mule’stagno, “Application of scanning optical microscopy in materials science to detect bulk microdefects in semiconductors,” J. Microsc. 188, 1–16 (1997).

J. Opt. Soc. Am. (1)

M. Gu, C. J. R. Sheppard, and X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. 8, 1755–1761 (1991).
[Crossref]

Meas. Sci. Technol. (1)

T. Hausotte, B. Percle, and G. Jäger, “Advanced three-dimensional scan methods in the nanopositioning and nanomeasuring machine,” Meas. Sci. Technol. 20, 084004 (2009).
[Crossref]

Microsc. Acta (1)

C. Cremer and T. Cremer, “Considerations on a laser-scanning-microscope with high resolution and depth of field,” Microsc. Acta 81, 31–44 (1978).

Opt. Acta. (1)

C. Sheppard and A. Choudhury, “Image formation in scanning microscope,” Opt. Acta. 24, 1051–1073 (1977).
[Crossref]

Opt. Express (2)

M. Duocastella, G. Vicidomini, and A. Diaspro, “Simultaneous multiplane confocal microscopy using acoustic tunable lenses,” Opt. Express 22, 019293 (2014).
[Crossref]

N. Koukourakis, M. Finkeldey, M. Stürmer, C. Leithold, N. C. M. Gerhardt, R. Hofmann, U. Wallrabe, J. W. Czarske, and A. Fischer, “Axial scanning in confocal microscopy employing adaptive lenses (CAL),” Opt. Express 22, 006025 (2014).
[Crossref]

Opt. Lett. (2)

Proc. SPIE (1)

T. Tsai, E. McLeod, and C. B. Arnold, “Generating Bessel beams with a tunable acoustic gradient index of refraction lens,” Proc. SPIE 6326, 63261F (2006).
[Crossref]

Scanning (1)

M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
[Crossref]

Other (4)

F. G. Balzer, U. Gerhardt, T. Hausotte, K. Albrecht, E. Manske, and G. Jäger, “Application of a novel fibre-coupled confocal sensor in a nanopositioning and nanomeasuring machine,” in 12th Euspen International Conference (2012).

“Part 602: nominal characteristics of non-contact (confocal chromatic probe) instruments,” .

Tag Optics Inc., “The physics behind TAG optics’ technology and the mechanism of action of using sound to shape light” (2013).

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

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Figures (18)

Fig. 1.
Fig. 1. Optical setup: 1, laser; 2, photodetector; 3, y -fiber; 4, collimation lens; 5, TAG lens; 6, beam splitter; 7, microscope objective; 8, measured surface; 9, focus modulation range; 10, beam splitter; 11, tube lens; 12, image sensor; 13, white light source; 14, imaging system; 15, sensor head. Red solid and dashed lines: focus-modulated rays of the confocal sensor; green dashed lines: illumination rays of the observation system; blue dashed-dotted lines: camera rays of the observation system.
Fig. 2.
Fig. 2. Normalized intensity functions of 100 × objective with NA = 0.8 calculated and measured without modulation ( z stage stated relative to the focal plane of the objective).
Fig. 3.
Fig. 3. Distance z ( t ) from the sample to the focal plane of the lens combination (TAG lens plus objective) relative to the focal plane of the objective.
Fig. 4.
Fig. 4. Theoretical normalized intensity signal at an axial scanning speed of 0.04 m/s.
Fig. 5.
Fig. 5. Simulated signal processing using lock-in amplification on a plane mirror.
Fig. 6.
Fig. 6. Theoretical signal and signal processing at an axial scanning speed of 0.05 m/s.
Fig. 7.
Fig. 7. Simulated signal processing of a lock-in amplifier for a measured surface with an inhomogeneous index of reflection.
Fig. 8.
Fig. 8. Simulated signal processing of a lock-in amplifier on a plane mirror.
Fig. 9
Fig. 9 Optical setup: 1, laser; 2, photodetector; 3, y -fiber; 4, collimation lens; 5, TAG lens; 6, beam splitter; 7, 100 × microscope objective; 8, gold-coated plane mirror; 10, beam splitter; 11, tube lens; 12, image sensor; 13, white light source; 14, nano CMS NMM-1.
Fig. 10.
Fig. 10. Example of measured values with a 100 × objective NA = 0.8 and 45% TAG lens amplitude.
Fig. 11.
Fig. 11. Example of measured values with a 100 × objective NA = 0.8 and 25% TAG lens amplitude.
Fig. 12.
Fig. 12. Characteristic curves ( V out , 3 / V out , 2 ) of 25 measurements with a 100 × objective NA = 0.8 and 45% TAG lens amplitude.
Fig. 13.
Fig. 13. Characteristic curves ( V out , 3 / V out , 2 ) of 25 measurements with a 100 × objective NA = 0.8 and 25% TAG lens amplitude.
Fig. 14.
Fig. 14. Ranges of z position r z for 25 characteristic curves ( V out , 3 / V out , 2 ) (cf. Fig. 12) with a 100 × objective NA = 0.8 and 45% TAG lens amplitude.
Fig. 15.
Fig. 15. Ranges of z position r z of 25 characteristic curves ( V out , 3 / V out , 2 ) (cf. Fig. 13) with a 100 × objective NA = 0.8 and 25% TAG lens amplitude.
Fig. 16.
Fig. 16. Mean and ranges of residues of five repetitions of 25 characteristic curves with a 100 × objective NA = 0.8 .
Fig. 17.
Fig. 17. Ranges of z position r z of 500 characteristic curves ( V out , 3 / V out , 2 ) with a 100 × objective NA = 0.8 and 25% TAG lens amplitude.
Fig. 18.
Fig. 18. Correlation of temperature and zero-offset drift for 500 measurements over 19 h.

Tables (1)

Tables Icon

Table 1. Mean and Maximum Residues at Different TAG Lens Optical Power Settings for Five Repetitions of 25 Characteristic Curves

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

I ( u ) = { [ sin ( u / 2 ) ] / ( u / 2 ) } 2 ,
u = ( 8 π / λ ) · z · sin 2 ( α / 2 ) ,
α = arcsin ( NA ) .
z ( t ) = v stage · t A f · sin ( 2 π · t · f TAG ) .
V out , k ( t ) = V n T t n T t V in ( t ) · V ref , k ( t ) d t n N ,
V ref , k ( t ) = sin ( 2 π · t · f ref , k + ϕ ) ,
f ref , k = k · f TAG ,

Metrics