Abstract

In this paper we analyze the capability of adaptive lenses to replace mechanical axial scanning in confocal microscopy. The adaptive approach promises to achieve high scan rates in a rather simple implementation. This may open up new applications in biomedical imaging or surface analysis in micro- and nanoelectronics, where currently the axial scan rates and the flexibility at the scan process are the limiting factors. The results show that fast and adaptive axial scanning is possible using electrically tunable lenses but the performance degrades during the scan. This is due to defocus and spherical aberrations introduced to the system by tuning of the adaptive lens. These detune the observation plane away from the best focus which strongly deteriorates the axial resolution by a factor of ~2.4. Introducing balancing aberrations allows addressing these influences. The presented approach is based on the employment of a second adaptive lens, located in the detection path. It enables shifting the observation plane back to the best focus position and thus creating axial scans with homogeneous axial resolution. We present simulated and experimental proof-of-principle results.

© 2014 Optical Society of America

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2014 (1)

2013 (3)

2012 (1)

2011 (3)

2010 (3)

K. S. Lee, P. Vanderwall, J. P. Rolland, “Two-photon microscopy with dynamic focusing objective using a liquid lens,” Proc. SPIE 7569, 756923 (2010).
[CrossRef]

B. F. Grewe, D. Langer, H. Kasper, B. M. Kampa, F. Helmchen, “High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision,” Nat. Methods 7(5), 399–405 (2010).
[CrossRef] [PubMed]

S. Murali, P. Meemon, K.-S. Lee, W. P. Kuhn, K. P. Thompson, J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (2010).
[CrossRef] [PubMed]

2009 (3)

2008 (1)

2007 (3)

W. Amir, R. Carriles, E. E. Hoover, T. A. Planchon, C. G. Durfee, J. A. Squier, “Simultaneous imaging of multiple focal planes using a two-photon scanning microscope,” Opt. Lett. 32(12), 1731–1733 (2007).
[CrossRef] [PubMed]

W. Göbel, F. Helmchen, “New angles on neuronal dendrites in vivo,” J. Neurophysiol. 98(6), 3770–3779 (2007).
[CrossRef] [PubMed]

R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, O. G. Schmidt, “„Triggered polarization entangled photon pairs from a single quantum dot up to 30 K,” New J. Phys. 9(9), 315 (2007).
[CrossRef]

2006 (1)

B. Wang, M. Ye, S. Sato, “Liquid crystal lens with focal length variable from negative to positive values,” Photonics Technol. Lett. IEEE 18(1), 79–81 (2006).
[CrossRef]

2005 (3)

2004 (1)

2003 (2)

2002 (1)

M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

2001 (1)

L. J. Allen, M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

2000 (3)

O. Albert, L. Sherman, G. Mourou, T. B. Norris, G. Vdovin, “Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy,” Opt. Lett. 25(1), 52–54 (2000).
[CrossRef] [PubMed]

B. Berge, J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000).
[CrossRef]

G. Udupa, M. Singaperumal, R. S. Sirohi, M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000).
[CrossRef]

1999 (1)

1998 (2)

1996 (1)

R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59(3), 427–471 (1996).
[CrossRef]

1994 (1)

1993 (1)

D. A. Lange, H. M. Jennings, S. P. Shah, “Analysis of surface roughness using confocal microscopy,” J. Mater. Sci. 28(14), 3879–3884 (1993).
[CrossRef]

1991 (5)

A. E. Dixon, S. Damaskinos, M. R. Atkinson, “Transmission and double-reflection scanning stage confocal microscope,” Scanning 13(4), 299–306 (1991).
[CrossRef]

J. Benschop, G. van Rosmalen, “Confocal compact scanning optical microscope based on compact disc technology,” Appl. Opt. 30(10), 1179–1184 (1991).
[CrossRef] [PubMed]

C. J. R. Sheppard, M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30(25), 3563–3568 (1991).
[CrossRef] [PubMed]

G. Martial, “Strehl ratio and aberration balancing,” J. Opt. Soc. Am. A 8(1), 164–170 (1991).
[CrossRef]

C. J. R. Sheppard, C. J. Cogswell, “Effects of aberrating layers and tube length of confocal imaging properties,” Optik (Stuttg.) 87, 34–38 (1991).

1988 (1)

M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10(4), 128–138 (1988).
[CrossRef]

1987 (2)

J. G. White, W. B. Amos, “Confocal microscopy comes of age,” Nature 328(6126), 183–184 (1987).
[CrossRef]

J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105(1), 41–48 (1987).
[CrossRef] [PubMed]

1984 (1)

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta (Lond.) 31(6), 723–727 (1984).
[CrossRef]

1978 (1)

C. Cremer, T. Cremer, “Considerations on a laser-scanning-microscope with high resolution and depth of field,” Microsc. Acta 81(1), 31–44 (1978).
[PubMed]

1977 (1)

1968 (1)

Albert, O.

Allen, L. J.

L. J. Allen, M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

Amir, W.

Amos, W. B.

J. G. White, W. B. Amos, “Confocal microscopy comes of age,” Nature 328(6126), 183–184 (1987).
[CrossRef]

J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105(1), 41–48 (1987).
[CrossRef] [PubMed]

Anderson, R. R.

Andrés, P.

Arnold, C. B.

Atkinson, M. R.

A. E. Dixon, S. Damaskinos, M. R. Atkinson, “Transmission and double-reflection scanning stage confocal microscope,” Scanning 13(4), 299–306 (1991).
[CrossRef]

Benschop, J.

Berge, B.

B. Berge, J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000).
[CrossRef]

Booth, M. J.

M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Bouma, B. E.

Brain, K.

Büttner, L.

J. König, K. Tschulik, L. Büttner, M. Uhlemann, J. Czarske, “Analysis of the Electrolyte Convection inside the concentration boundary layer during structured electrodeposition of Copper in high magnetic gradient fields,” Anal. Chem. 85(6), 3087–3094 (2013).
[CrossRef] [PubMed]

L. Büttner, C. Leithold, J. Czarske, “Interferometric velocity measurements through a fluctuating Gas-Liquid interface employing Adaptive Optics,” Opt. Express 21(25), 30653–30663 (2013).
[CrossRef] [PubMed]

Carriles, R.

Cheng, S.

Cheng, Y.-S. L.

Chun, B. S.

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

Cogswell, C. J.

C. J. R. Sheppard, C. J. Cogswell, “Effects of aberrating layers and tube length of confocal imaging properties,” Optik (Stuttg.) 87, 34–38 (1991).

Cremer, C.

C. Cremer, T. Cremer, “Considerations on a laser-scanning-microscope with high resolution and depth of field,” Microsc. Acta 81(1), 31–44 (1978).
[PubMed]

Cremer, T.

C. Cremer, T. Cremer, “Considerations on a laser-scanning-microscope with high resolution and depth of field,” Microsc. Acta 81(1), 31–44 (1978).
[PubMed]

Cuenca, R.

Czarske, J.

Damaskinos, S.

A. E. Dixon, S. Damaskinos, M. R. Atkinson, “Transmission and double-reflection scanning stage confocal microscope,” Scanning 13(4), 299–306 (1991).
[CrossRef]

Dixon, A. E.

A. E. Dixon, S. Damaskinos, M. R. Atkinson, “Transmission and double-reflection scanning stage confocal microscope,” Scanning 13(4), 299–306 (1991).
[CrossRef]

Draheim, J.

Dunbar, L. A.

Durfee, C. G.

Egger, M. D. A. V. I. D.

Fahrbach, F. O.

Fordham, M.

J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105(1), 41–48 (1987).
[CrossRef] [PubMed]

Galambos, R. O. B. E. R. T.

Göbel, W.

W. Göbel, F. Helmchen, “New angles on neuronal dendrites in vivo,” J. Neurophysiol. 98(6), 3770–3779 (2007).
[CrossRef] [PubMed]

Grewe, B. F.

B. F. Grewe, D. Langer, H. Kasper, B. M. Kampa, F. Helmchen, “High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision,” Nat. Methods 7(5), 399–405 (2010).
[CrossRef] [PubMed]

Gu, M.

Günther, P.

Gweon, D.

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

Hadravsky, M.

Hafenbrak, R.

R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, O. G. Schmidt, “„Triggered polarization entangled photon pairs from a single quantum dot up to 30 K,” New J. Phys. 9(9), 315 (2007).
[CrossRef]

Hamilton, D. K.

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta (Lond.) 31(6), 723–727 (1984).
[CrossRef]

Hashimoto, K.

Helmchen, F.

F. O. Fahrbach, F. F. Voigt, B. Schmid, F. Helmchen, J. Huisken, “Rapid 3D light-sheet microscopy with a tunable lens,” Opt. Express 21(18), 21010–21026 (2013).
[CrossRef] [PubMed]

B. F. Grewe, D. Langer, H. Kasper, B. M. Kampa, F. Helmchen, “High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision,” Nat. Methods 7(5), 399–405 (2010).
[CrossRef] [PubMed]

W. Göbel, F. Helmchen, “New angles on neuronal dendrites in vivo,” J. Neurophysiol. 98(6), 3770–3779 (2007).
[CrossRef] [PubMed]

Hendricks, B. H. W.

B. H. W. Hendricks, S. Kuiper, M. A. J. Van As, C. A. Renders, T. W. Tukker, “Electrowetting-based variable-focus lens for miniature systems,” Opt. Rev. 12(3), 255–259 (2005).
[CrossRef]

Hoover, E. E.

Hua, H.

Huisken, J.

Ishikawa, M.

Jabbour, J. M.

Jennings, H. M.

D. A. Lange, H. M. Jennings, S. P. Shah, “Analysis of surface roughness using confocal microscopy,” J. Mater. Sci. 28(14), 3879–3884 (1993).
[CrossRef]

Jillella, P.

Jo, J. A.

Juskaitis, R.

M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Kamberger, R.

Kampa, B. M.

B. F. Grewe, D. Langer, H. Kasper, B. M. Kampa, F. Helmchen, “High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision,” Nat. Methods 7(5), 399–405 (2010).
[CrossRef] [PubMed]

Kang, D. K.

Kasper, H.

B. F. Grewe, D. Langer, H. Kasper, B. M. Kampa, F. Helmchen, “High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision,” Nat. Methods 7(5), 399–405 (2010).
[CrossRef] [PubMed]

Kim, K.

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

König, J.

J. König, K. Tschulik, L. Büttner, M. Uhlemann, J. Czarske, “Analysis of the Electrolyte Convection inside the concentration boundary layer during structured electrodeposition of Copper in high magnetic gradient fields,” Anal. Chem. 85(6), 3087–3094 (2013).
[CrossRef] [PubMed]

Kothiyal, M. P.

G. Udupa, M. Singaperumal, R. S. Sirohi, M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000).
[CrossRef]

Kowalczyk, M.

Kuhn, W. P.

Kuiper, S.

B. H. W. Hendricks, S. Kuiper, M. A. J. Van As, C. A. Renders, T. W. Tukker, “Electrowetting-based variable-focus lens for miniature systems,” Opt. Rev. 12(3), 255–259 (2005).
[CrossRef]

Kuschmierz, R.

Lange, D. A.

D. A. Lange, H. M. Jennings, S. P. Shah, “Analysis of surface roughness using confocal microscopy,” J. Mater. Sci. 28(14), 3879–3884 (1993).
[CrossRef]

Langer, D.

B. F. Grewe, D. Langer, H. Kasper, B. M. Kampa, F. Helmchen, “High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision,” Nat. Methods 7(5), 399–405 (2010).
[CrossRef] [PubMed]

Lee, J. N.

J. N. Lee, C. Park, G. M. Whitesides, “Solvent compatibility of poly(dimethylsiloxane)-based microfluidic devices,” Anal. Chem. 75(23), 6544–6554 (2003).
[CrossRef] [PubMed]

Lee, K. S.

K. S. Lee, P. Vanderwall, J. P. Rolland, “Two-photon microscopy with dynamic focusing objective using a liquid lens,” Proc. SPIE 7569, 756923 (2010).
[CrossRef]

Lee, K.-S.

Leithold, C.

Liu, S.

Mac Raighne, A.

Mahajan, V. N.

Maitland, K. C.

Makita, S.

Malik, B. H.

Martial, G.

Martínez-Corral, M.

McCabe, E. M.

McLeod, E.

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B. H. W. Hendricks, S. Kuiper, M. A. J. Van As, C. A. Renders, T. W. Tukker, “Electrowetting-based variable-focus lens for miniature systems,” Opt. Rev. 12(3), 255–259 (2005).
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G. Udupa, M. Singaperumal, R. S. Sirohi, M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000).
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R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, O. G. Schmidt, “„Triggered polarization entangled photon pairs from a single quantum dot up to 30 K,” New J. Phys. 9(9), 315 (2007).
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B. H. W. Hendricks, S. Kuiper, M. A. J. Van As, C. A. Renders, T. W. Tukker, “Electrowetting-based variable-focus lens for miniature systems,” Opt. Rev. 12(3), 255–259 (2005).
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[CrossRef] [PubMed]

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Yang, L.

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B. Wang, M. Ye, S. Sato, “Liquid crystal lens with focal length variable from negative to positive values,” Photonics Technol. Lett. IEEE 18(1), 79–81 (2006).
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Anal. Chem. (2)

J. König, K. Tschulik, L. Büttner, M. Uhlemann, J. Czarske, “Analysis of the Electrolyte Convection inside the concentration boundary layer during structured electrodeposition of Copper in high magnetic gradient fields,” Anal. Chem. 85(6), 3087–3094 (2013).
[CrossRef] [PubMed]

J. N. Lee, C. Park, G. M. Whitesides, “Solvent compatibility of poly(dimethylsiloxane)-based microfluidic devices,” Anal. Chem. 75(23), 6544–6554 (2003).
[CrossRef] [PubMed]

Appl. Opt. (7)

Biomed. Opt. Express (2)

Eur. Phys. J. E (1)

B. Berge, J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000).
[CrossRef]

J. Cell Biol. (1)

J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105(1), 41–48 (1987).
[CrossRef] [PubMed]

J. Mater. Sci. (1)

D. A. Lange, H. M. Jennings, S. P. Shah, “Analysis of surface roughness using confocal microscopy,” J. Mater. Sci. 28(14), 3879–3884 (1993).
[CrossRef]

J. Microsc. (1)

T. Wilson, “Resolution and optical sectioning in the confocal microscope,” J. Microsc. 244(2), 113–121 (2011).
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W. Göbel, F. Helmchen, “New angles on neuronal dendrites in vivo,” J. Neurophysiol. 98(6), 3770–3779 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Meas. Sci. Technol. (1)

G. Udupa, M. Singaperumal, R. S. Sirohi, M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000).
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Nat. Methods (1)

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Nature (1)

J. G. White, W. B. Amos, “Confocal microscopy comes of age,” Nature 328(6126), 183–184 (1987).
[CrossRef]

New J. Phys. (1)

R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, O. G. Schmidt, “„Triggered polarization entangled photon pairs from a single quantum dot up to 30 K,” New J. Phys. 9(9), 315 (2007).
[CrossRef]

Opt. Acta (Lond.) (1)

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta (Lond.) 31(6), 723–727 (1984).
[CrossRef]

Opt. Commun. (1)

L. J. Allen, M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

Opt. Express (6)

Opt. Lett. (7)

Opt. Rev. (1)

B. H. W. Hendricks, S. Kuiper, M. A. J. Van As, C. A. Renders, T. W. Tukker, “Electrowetting-based variable-focus lens for miniature systems,” Opt. Rev. 12(3), 255–259 (2005).
[CrossRef]

Optik (Stuttg.) (1)

C. J. R. Sheppard, C. J. Cogswell, “Effects of aberrating layers and tube length of confocal imaging properties,” Optik (Stuttg.) 87, 34–38 (1991).

Photonics Technol. Lett. IEEE (1)

B. Wang, M. Ye, S. Sato, “Liquid crystal lens with focal length variable from negative to positive values,” Photonics Technol. Lett. IEEE 18(1), 79–81 (2006).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

M. J. Booth, M. A. A. Neil, R. Juskaitis, T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Proc. SPIE (1)

K. S. Lee, P. Vanderwall, J. P. Rolland, “Two-photon microscopy with dynamic focusing objective using a liquid lens,” Proc. SPIE 7569, 756923 (2010).
[CrossRef]

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B. S. Chun, K. Kim, D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum. 80(7), 073706 (2009).
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A. E. Dixon, S. Damaskinos, M. R. Atkinson, “Transmission and double-reflection scanning stage confocal microscope,” Scanning 13(4), 299–306 (1991).
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J. Draheim, T. Burger, and R. Kamberger, “Closed-loop pressure control of an adaptive single chamber membrane lens with integrated actuation,” in International Conference on Optical MEMS and Nanophotonics, 47–48 (2011).
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J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd-Edition (Springer Science + Business Media, 2006).

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Figures (12)

Fig. 1
Fig. 1

Cross-section view of the device design in a) unactuated and b) actuated state. c) Schematic bimorph actuator configuration. d) Sketch of the assembly procedure with integrated filling and bonding and photographs of the components.

Fig. 2
Fig. 2

a) Stack of line-scans across the profiles obtained with the triangulation sensor. The curvature was used to calculate the refractive power at each voltage. b) Refractive power as a function of rising voltage. For UAL = 40 V the focal length is about f = 150 mm. At UAL = 0 V the membrane has a pre-deflection induced by fabrication tolerances.

Fig. 3
Fig. 3

Confocal microscope employing adaptive lenses (CAL) in the illumination and the detection path.

Fig. 4
Fig. 4

a) Block diagram of the setup. b) Test-chart.

Fig. 5
Fig. 5

a) The experimentally measured A-scans show that the focus is tuned with the driving voltage of the lens UAL1. b) The shift of the peak position of the experimentally measured and simulated A-scans agree very well. The tuning range amounts to about 380 µm. c) The FWHM increases, which means that the axial resolution decreases with voltage. d) The peak intensity also decreases with voltage. The behavior can be explained by aberrations introduced to the system by the adaptive lens.

Fig. 6
Fig. 6

The stage is positioned at z = 0. There the sample is out of focus. Using UAL1 allows shifting the focus to the depth of the sample. Further increasing the voltage shifts the focus too far and the sample is out of focus again. At UAL1 = 10 V the 500 nm element of the sample is resolved as can be expected for a pinhole with 0.6 AU [43].

Fig. 7
Fig. 7

Scheme of the simulated aberrated focal volume.

Fig. 8
Fig. 8

a) Zernike polynomial expansion for the simulated wave fronts reaching the pinhole. Initially the spherical aberrations are balanced. But they increase with increasing voltage as the system gets detuned from the CoC. b) The detuning of observation plane is determined by comparison of the peak position of the A-scans and the position with balanced aberrations, which corresponds to the CoC.

Fig. 9
Fig. 9

a) Experimentally measured A-scans as a function of UAL2. The confocal plane (green dots) scans the z-axis and shifts across the focal volume (orange dots). b) Peak position of the A-scans in dependency of UAL2. At large detuning, the A-scans appear to have two peaks, corresponding to both focal and confocal planes. c) and d) The confocal peak shifts across the focal peak. At UAL2 = 0 V both planes perfectly overlap leading to the highest intensity and smallest FWHM. At higher voltages the confocal peak passed the focal volume.

Fig. 10
Fig. 10

Simulated detuning of the initially aligned setup. a) and b) Increasing U A L 2 shifts the observation plane away of the CoC. This consequently increases the influence of the aberrations.

Fig. 11
Fig. 11

a) The shift between the CoC and the peak of the A-scan shows that at higher voltages UAL1, the shift becomes zero for higher negative voltages UAL2. b) The Zernike coefficient for defocus increases with UAL1. At c20 = 0 the spherical aberrations are balanced. c) Balancing the system minimizes the FWHM. d) The re-tuning is at the cost of tuning range which is nearly halved.

Fig. 12
Fig. 12

a) The experimentally measured FWHM proves that driving UAL2 with negative voltage allows retuning the confocal plane to the CoC. b) Exemplary A-scans. Increasing the voltage from UAL1 = 0 V to UAL1 = 20 V at UAL2 = 0 V increases the FWHM by 20%. Applying UAL2 = −2 V re-tunes the setup and the FWHM decreases.

Equations (7)

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

Δ z = 0.67 λ n n 2 N A 2 1 + A U 2 4 µ m .
Δ r = k λ N A
P ( ρ , U A L 1 ) = exp ( j Φ A L ( ρ , U A L 1 ) ) .
Φ U A L 1 ( ρ ) = Σ n , f c n f Z n f .
Z 2 0 ( ρ ) = 2 ρ 2 1
Z 4 0 ( ρ ) = 6 ρ 4 6 ρ 2 + 1
Z 6 0 ( ρ ) = 20 ρ 6 30 ρ 4 + 12 ρ 2 1.

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