Abstract

Microscopic imaging at high spatial-temporal resolution over long time scales (minutes to hours) requires rapid and precise stabilization of the microscope focus. Conventional and commercial autofocus systems are largely based on piezoelectric stages or mechanical objective actuators. Objective to sample distance is either measured by image analysis approaches or by hardware modules measuring the intensity of reflected infrared light. We propose here a truly all-optical microscope autofocus taking advantage of an electrically tunable lens and a totally internally reflected infrared probe beam. We implement a feedback-loop based on the lateral position of a totally internally reflected infrared laser on a quadrant photodetector, as an indicator of the relative defocus. We show here how to treat the combined contributions due to mechanical defocus and deformation of the tunable lens. As a result, the sample can be kept in focus without any mechanical movement, at rates up to hundreds of Hertz. The device requires only reflective optics and can be implemented at a fraction of the cost required for a comparable piezo-based actuator.

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

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References

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  1. D. J. Stephens and V. J. Allan, “Light Microscopy Techniques for live cell imaging,” Science 300(5616), 82–87 (2003).
    [Crossref] [PubMed]
  2. J. H. Price and D. A. Gough, “Comparison of Phase-Contrast and Fluorescence Digital Autofocus for Scanning Microscopy,” Cytometry 16283–284 (1994).
    [Crossref] [PubMed]
  3. S. Li, X. Cui, and W. Huang, “High resolution autofocus for spatial temporal biomedical research,” Rev Sci Instrum 84(11), 114302 (2013).
    [Crossref] [PubMed]
  4. S. Yazdanfar, K. B. Kenny, K. Tasimi, A. D. Corwin, E. L. Dixon, and R. J. Filkins, “Simple and robust image-based autofocusing for digital microscopy,” Opt. Express 16(12), 8670–8677 (2008).
    [Crossref] [PubMed]
  5. Y. Liron, Y. Paran, N. G. Zatorsky, B. Geiger, and Z. Kam., “Laser autofocusing system for high-resolution cell biological imaging,” Journal of Microscopy 221(2), 145–151 (2006).
    [Crossref] [PubMed]
  6. A. Pertsinidis, Y. Zhang, and S. Chu., “Subnanometre single-molecule localization, registration and distance measurement,” Nature 466, 647–653 (2010).
    [Crossref] [PubMed]
  7. M. Blum, M. Bueeler, C. Graetzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
    [Crossref]
  8. B. F. Grewe, F. F. Voigt, M. van’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens,” Biomed. Opt. Express 8167, 2035–2046 (2011).
    [Crossref]
  9. S. Piazza, P. Bianchini, C. Sheppard, A. Diaspro, and M. Duocastella, “Enhanced volumetric imaging in 2-photon microscopy via acoustic lens beam shaping,” J. Biophotonics 10, e201700050 (2017).
    [Crossref]
  10. P. Annibale, A. Dvornikov, and E. Gratton., “Electrically tunable lens speeds up 3d orbital tracking,” Biomed Opt Express 6(6), 2181–2190 (2015).
    [Crossref] [PubMed]
  11. Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
    [Crossref] [PubMed]
  12. Optotune Data Sheet, “ http://www.optotune.com/products/focus-tunable-lenses ,” Optotune (2017)
  13. J. Xu, K.F. Therani, and P. Steinberg., “Multicolor 3D Super-resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy,” August 30 2011. ACS Nano 9, 2917–2925 (2015).
    [Crossref] [PubMed]
  14. L. Fuh, J. K. Chen, and P. W. Chen., “Characterization of electrically tunable liquid lens and adaptive optics for aberration correction,” Optika 126(24), 5456–5459 (2015).
    [Crossref]

2017 (1)

S. Piazza, P. Bianchini, C. Sheppard, A. Diaspro, and M. Duocastella, “Enhanced volumetric imaging in 2-photon microscopy via acoustic lens beam shaping,” J. Biophotonics 10, e201700050 (2017).
[Crossref]

2015 (4)

P. Annibale, A. Dvornikov, and E. Gratton., “Electrically tunable lens speeds up 3d orbital tracking,” Biomed Opt Express 6(6), 2181–2190 (2015).
[Crossref] [PubMed]

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

J. Xu, K.F. Therani, and P. Steinberg., “Multicolor 3D Super-resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy,” August 30 2011. ACS Nano 9, 2917–2925 (2015).
[Crossref] [PubMed]

L. Fuh, J. K. Chen, and P. W. Chen., “Characterization of electrically tunable liquid lens and adaptive optics for aberration correction,” Optika 126(24), 5456–5459 (2015).
[Crossref]

2013 (1)

S. Li, X. Cui, and W. Huang, “High resolution autofocus for spatial temporal biomedical research,” Rev Sci Instrum 84(11), 114302 (2013).
[Crossref] [PubMed]

2011 (2)

M. Blum, M. Bueeler, C. Graetzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

B. F. Grewe, F. F. Voigt, M. van’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens,” Biomed. Opt. Express 8167, 2035–2046 (2011).
[Crossref]

2010 (1)

A. Pertsinidis, Y. Zhang, and S. Chu., “Subnanometre single-molecule localization, registration and distance measurement,” Nature 466, 647–653 (2010).
[Crossref] [PubMed]

2008 (1)

2006 (1)

Y. Liron, Y. Paran, N. G. Zatorsky, B. Geiger, and Z. Kam., “Laser autofocusing system for high-resolution cell biological imaging,” Journal of Microscopy 221(2), 145–151 (2006).
[Crossref] [PubMed]

2003 (1)

D. J. Stephens and V. J. Allan, “Light Microscopy Techniques for live cell imaging,” Science 300(5616), 82–87 (2003).
[Crossref] [PubMed]

1994 (1)

J. H. Price and D. A. Gough, “Comparison of Phase-Contrast and Fluorescence Digital Autofocus for Scanning Microscopy,” Cytometry 16283–284 (1994).
[Crossref] [PubMed]

Allan, V. J.

D. J. Stephens and V. J. Allan, “Light Microscopy Techniques for live cell imaging,” Science 300(5616), 82–87 (2003).
[Crossref] [PubMed]

Annibale, P.

P. Annibale, A. Dvornikov, and E. Gratton., “Electrically tunable lens speeds up 3d orbital tracking,” Biomed Opt Express 6(6), 2181–2190 (2015).
[Crossref] [PubMed]

Aschwanden, M.

M. Blum, M. Bueeler, C. Graetzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

Bianchini, P.

S. Piazza, P. Bianchini, C. Sheppard, A. Diaspro, and M. Duocastella, “Enhanced volumetric imaging in 2-photon microscopy via acoustic lens beam shaping,” J. Biophotonics 10, e201700050 (2017).
[Crossref]

Blum, M.

M. Blum, M. Bueeler, C. Graetzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

Bueeler, M.

M. Blum, M. Bueeler, C. Graetzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

Cai, Y.

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

Chen, J. K.

L. Fuh, J. K. Chen, and P. W. Chen., “Characterization of electrically tunable liquid lens and adaptive optics for aberration correction,” Optika 126(24), 5456–5459 (2015).
[Crossref]

Chen., P. W.

L. Fuh, J. K. Chen, and P. W. Chen., “Characterization of electrically tunable liquid lens and adaptive optics for aberration correction,” Optika 126(24), 5456–5459 (2015).
[Crossref]

Chu., S.

A. Pertsinidis, Y. Zhang, and S. Chu., “Subnanometre single-molecule localization, registration and distance measurement,” Nature 466, 647–653 (2010).
[Crossref] [PubMed]

Corwin, A. D.

Cui, X.

S. Li, X. Cui, and W. Huang, “High resolution autofocus for spatial temporal biomedical research,” Rev Sci Instrum 84(11), 114302 (2013).
[Crossref] [PubMed]

Diaspro, A.

S. Piazza, P. Bianchini, C. Sheppard, A. Diaspro, and M. Duocastella, “Enhanced volumetric imaging in 2-photon microscopy via acoustic lens beam shaping,” J. Biophotonics 10, e201700050 (2017).
[Crossref]

Dixon, E. L.

Duocastella, M.

S. Piazza, P. Bianchini, C. Sheppard, A. Diaspro, and M. Duocastella, “Enhanced volumetric imaging in 2-photon microscopy via acoustic lens beam shaping,” J. Biophotonics 10, e201700050 (2017).
[Crossref]

Dvornikov, A.

P. Annibale, A. Dvornikov, and E. Gratton., “Electrically tunable lens speeds up 3d orbital tracking,” Biomed Opt Express 6(6), 2181–2190 (2015).
[Crossref] [PubMed]

Filkins, R. J.

Fuh, L.

L. Fuh, J. K. Chen, and P. W. Chen., “Characterization of electrically tunable liquid lens and adaptive optics for aberration correction,” Optika 126(24), 5456–5459 (2015).
[Crossref]

Geiger, B.

Y. Liron, Y. Paran, N. G. Zatorsky, B. Geiger, and Z. Kam., “Laser autofocusing system for high-resolution cell biological imaging,” Journal of Microscopy 221(2), 145–151 (2006).
[Crossref] [PubMed]

Gough, D. A.

J. H. Price and D. A. Gough, “Comparison of Phase-Contrast and Fluorescence Digital Autofocus for Scanning Microscopy,” Cytometry 16283–284 (1994).
[Crossref] [PubMed]

Graetzel, C.

M. Blum, M. Bueeler, C. Graetzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

Gratton., E.

P. Annibale, A. Dvornikov, and E. Gratton., “Electrically tunable lens speeds up 3d orbital tracking,” Biomed Opt Express 6(6), 2181–2190 (2015).
[Crossref] [PubMed]

Grewe, B. F.

B. F. Grewe, F. F. Voigt, M. van’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens,” Biomed. Opt. Express 8167, 2035–2046 (2011).
[Crossref]

Helmchen, F.

B. F. Grewe, F. F. Voigt, M. van’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens,” Biomed. Opt. Express 8167, 2035–2046 (2011).
[Crossref]

Huang, W.

S. Li, X. Cui, and W. Huang, “High resolution autofocus for spatial temporal biomedical research,” Rev Sci Instrum 84(11), 114302 (2013).
[Crossref] [PubMed]

Kam., Z.

Y. Liron, Y. Paran, N. G. Zatorsky, B. Geiger, and Z. Kam., “Laser autofocusing system for high-resolution cell biological imaging,” Journal of Microscopy 221(2), 145–151 (2006).
[Crossref] [PubMed]

Kenny, K. B.

Lei, M.

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

Li, H.

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

Li, S.

S. Li, X. Cui, and W. Huang, “High resolution autofocus for spatial temporal biomedical research,” Rev Sci Instrum 84(11), 114302 (2013).
[Crossref] [PubMed]

Liang, Y.

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

Liron, Y.

Y. Liron, Y. Paran, N. G. Zatorsky, B. Geiger, and Z. Kam., “Laser autofocusing system for high-resolution cell biological imaging,” Journal of Microscopy 221(2), 145–151 (2006).
[Crossref] [PubMed]

Paran, Y.

Y. Liron, Y. Paran, N. G. Zatorsky, B. Geiger, and Z. Kam., “Laser autofocusing system for high-resolution cell biological imaging,” Journal of Microscopy 221(2), 145–151 (2006).
[Crossref] [PubMed]

Pertsinidis, A.

A. Pertsinidis, Y. Zhang, and S. Chu., “Subnanometre single-molecule localization, registration and distance measurement,” Nature 466, 647–653 (2010).
[Crossref] [PubMed]

Piazza, S.

S. Piazza, P. Bianchini, C. Sheppard, A. Diaspro, and M. Duocastella, “Enhanced volumetric imaging in 2-photon microscopy via acoustic lens beam shaping,” J. Biophotonics 10, e201700050 (2017).
[Crossref]

Price, J. H.

J. H. Price and D. A. Gough, “Comparison of Phase-Contrast and Fluorescence Digital Autofocus for Scanning Microscopy,” Cytometry 16283–284 (1994).
[Crossref] [PubMed]

Sheppard, C.

S. Piazza, P. Bianchini, C. Sheppard, A. Diaspro, and M. Duocastella, “Enhanced volumetric imaging in 2-photon microscopy via acoustic lens beam shaping,” J. Biophotonics 10, e201700050 (2017).
[Crossref]

Steinberg., P.

J. Xu, K.F. Therani, and P. Steinberg., “Multicolor 3D Super-resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy,” August 30 2011. ACS Nano 9, 2917–2925 (2015).
[Crossref] [PubMed]

Stephens, D. J.

D. J. Stephens and V. J. Allan, “Light Microscopy Techniques for live cell imaging,” Science 300(5616), 82–87 (2003).
[Crossref] [PubMed]

Tasimi, K.

Therani, K.F.

J. Xu, K.F. Therani, and P. Steinberg., “Multicolor 3D Super-resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy,” August 30 2011. ACS Nano 9, 2917–2925 (2015).
[Crossref] [PubMed]

van’t Hoff, M.

B. F. Grewe, F. F. Voigt, M. van’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens,” Biomed. Opt. Express 8167, 2035–2046 (2011).
[Crossref]

Voigt, F. F.

B. F. Grewe, F. F. Voigt, M. van’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens,” Biomed. Opt. Express 8167, 2035–2046 (2011).
[Crossref]

Wang, Z.

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

Xiong., D.

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

Xu, J.

J. Xu, K.F. Therani, and P. Steinberg., “Multicolor 3D Super-resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy,” August 30 2011. ACS Nano 9, 2917–2925 (2015).
[Crossref] [PubMed]

Yang, X.

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

Yang, Y.

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

Yao, B.

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

Yazdanfar, S.

Zatorsky, N. G.

Y. Liron, Y. Paran, N. G. Zatorsky, B. Geiger, and Z. Kam., “Laser autofocusing system for high-resolution cell biological imaging,” Journal of Microscopy 221(2), 145–151 (2006).
[Crossref] [PubMed]

Zhang, Y.

A. Pertsinidis, Y. Zhang, and S. Chu., “Subnanometre single-molecule localization, registration and distance measurement,” Nature 466, 647–653 (2010).
[Crossref] [PubMed]

ACS Nano (1)

J. Xu, K.F. Therani, and P. Steinberg., “Multicolor 3D Super-resolution Imaging by Quantum Dot Stochastic Optical Reconstruction Microscopy,” August 30 2011. ACS Nano 9, 2917–2925 (2015).
[Crossref] [PubMed]

Biomed Opt Express (2)

P. Annibale, A. Dvornikov, and E. Gratton., “Electrically tunable lens speeds up 3d orbital tracking,” Biomed Opt Express 6(6), 2181–2190 (2015).
[Crossref] [PubMed]

Z. Wang, M. Lei, B. Yao, Y. Cai, Y. Liang, Y. Yang, X. Yang, H. Li, and D. Xiong., “Compact multi-band fluorescent microscope with an electrically tunable lens for autofocusing,” Biomed Opt Express 6(11), 4353–4364 (2015).
[Crossref] [PubMed]

Biomed. Opt. Express (1)

B. F. Grewe, F. F. Voigt, M. van’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens,” Biomed. Opt. Express 8167, 2035–2046 (2011).
[Crossref]

Cytometry (1)

J. H. Price and D. A. Gough, “Comparison of Phase-Contrast and Fluorescence Digital Autofocus for Scanning Microscopy,” Cytometry 16283–284 (1994).
[Crossref] [PubMed]

J. Biophotonics (1)

S. Piazza, P. Bianchini, C. Sheppard, A. Diaspro, and M. Duocastella, “Enhanced volumetric imaging in 2-photon microscopy via acoustic lens beam shaping,” J. Biophotonics 10, e201700050 (2017).
[Crossref]

Journal of Microscopy (1)

Y. Liron, Y. Paran, N. G. Zatorsky, B. Geiger, and Z. Kam., “Laser autofocusing system for high-resolution cell biological imaging,” Journal of Microscopy 221(2), 145–151 (2006).
[Crossref] [PubMed]

Nature (1)

A. Pertsinidis, Y. Zhang, and S. Chu., “Subnanometre single-molecule localization, registration and distance measurement,” Nature 466, 647–653 (2010).
[Crossref] [PubMed]

Opt. Express (1)

Optika (1)

L. Fuh, J. K. Chen, and P. W. Chen., “Characterization of electrically tunable liquid lens and adaptive optics for aberration correction,” Optika 126(24), 5456–5459 (2015).
[Crossref]

Proc. SPIE (1)

M. Blum, M. Bueeler, C. Graetzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” Proc. SPIE 8167, 81670W (2011).
[Crossref]

Rev Sci Instrum (1)

S. Li, X. Cui, and W. Huang, “High resolution autofocus for spatial temporal biomedical research,” Rev Sci Instrum 84(11), 114302 (2013).
[Crossref] [PubMed]

Science (1)

D. J. Stephens and V. J. Allan, “Light Microscopy Techniques for live cell imaging,” Science 300(5616), 82–87 (2003).
[Crossref] [PubMed]

Other (1)

Optotune Data Sheet, “ http://www.optotune.com/products/focus-tunable-lenses ,” Optotune (2017)

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Figures (5)

Fig. 1
Fig. 1 Experimental setup and working principle. a) Experimental setup: an IR laser diode beam enters the microscope through the pigtailed fiber, gets reflected by the mirrors, passes through the ETL (in black, below the objective) and the objective where it gets totally internally reflected (red dashed). The reflected beam gets deflected by mirrors onto the QPD (dark red). The conventional laser excitation of the inverted microscope follows the usual path, reflected by the dichroic mirror (blue dashed), while the fluorescence is transmitted to the detector (green dashed). Inset: exponential decay of the TIR field at the sample. b) Left: ETL illustrating different curvatures and focal points for two different currents. Right: schematics of the ETL with its physical dimension. c) Schematics of the independent effect of current application on the reflected IR beam and the focal position. The combined objective-ETL assembly is illustrated as a thin lens. The reflected IR laser (dark red lines) exits through the lens hitting the QPD in distinct positions depending on the relative physical objective to sample distance (position 1 to 2) and the current applied to the ETL (position 3). The focal position (shaded blue embodies a collimated excitation beam) changes upon application of a current.
Fig. 2
Fig. 2 Acquisition of calibration curves. a) QPD voltage in dependence of axial position for constant input currents to the lens. Inlay: Axial position vs ETL current. b) QPD voltage vs the ETL input current. The orange arrows indicate how the different QPD(V) vs current curves in the family relate to changes of the physical axial position of the sample relative to the objective. They shift to the right for increasing objective to sample separation, and move to the left upon reduction of this separation. c) QPD vs current at each in-focus position. d) Same as b. The red dots represent the in-focus points of each curve, i.e. the value for which the autofocus corrects.
Fig. 3
Fig. 3 Explanation of the working principle of the autofocus. d1 to d4 are distinct axial distances, indicating a family of QPD(V) vs current curves. Panels show how the state of the system (QPD(V), current) changes in response to an axial displacement from an in-focus condition d2 (Panel A) to a position d3. Panel (C) illustrates how, in order to bring back the QPD(V) to its original set-point, a current is applied. In Panel (D) the adaptive set-point changes along the in-focus dashed curve, while the system state moves along the d3 QPD(V)-current curve trying to reach the new set-point. The process iterates in small steps (Panel E) until the sample reaches again the in-focus condition where the set-point and system states overlap (Panel F).
Fig. 4
Fig. 4 Autofocus system. a) Magnified time course showing the QPD voltage following the QPD set-point voltage. It also shows the input current trace for the lens. b) Images of a bead which is held in focus over time. The lines indicate where the profiles shown in d were collected. Color code corresponds to colors in d. Below: traces of the QPD voltage and input current for the lens with enabled autofocus. c) Represents the same as in b without autofocusing. The images show a loss of focus over time (top). The current is held constant and the QPD voltage is changing as a result of the focal drift. d) Fitting of the bead profiles in b, taken at the beginning and at the end of imaging series. e) Fitting of the bead profiles in c, taken at the beginning and at the end of imaging series.
Fig. 5
Fig. 5 Traces and images of enabled autofocus. a) Top images show fluorescent beads before and after the jump. Below: Traces for the QPD voltage and the current for a low proportional PID value and a moving average of the current used to adjust the set-point. Current and QPD voltage recover slowly after manual displacement of objective of about 500 nm. b) Same as in a, with a proportional term and without the moving average. Graphs show a faster focus recovery. c) Same as in a and b, with optimized PID parameters allowing a faster convergence of the QPD to its set-point (proportional constant 0.25, integral constant 0.2 and differential constant 0.01). d) Hek293AD cells displaying labeled mitochondria, imaged over 30 minutes with enabled autofocus (left and middle), and then for another 30 minutes with disabled autofocus (right). Insets show edge detection in a sub-region of the cell, emphasizing the effect of defocus in the right image. On the right: traces of the current and QPD voltage over time as the cell is maintained in focus.

Equations (3)

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I ( z ) = I ( 0 ) e z d
d = λ 4 π ( n 1 2 sin 2 ( θ ) n 2 2 ) ( 1 2 )
QPD ( V ) = ( V top ( 1 ) + V top ( 2 ) ) ( V bottom ( 1 ) + V bottom ( 2 ) ) V Sum

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