Abstract

Optical aberrations limit resolution in biological tissues, and their influence is particularly large for promising techniques such as light-sheet microscopy. In principle, image quality might be improved by adaptive optics (AO), in which aberrations are corrected by using a deformable mirror (DM). To implement AO in microscopy, one requires a method to measure wavefront aberrations, but the most commonly used methods have limitations for samples lacking point-source emitters. Here we implement an image-based wavefront-sensing technique, a variant of generalized phase-diverse imaging called multiframe blind deconvolution, and exploit it to calibrate a DM in a light-sheet microscope. We describe two methods of parameterizing the influence of the DM on aberrations: a traditional Zernike expansion requiring 1040 parameters, and a direct physical model of the DM requiring just 8 or 110 parameters. By randomizing voltages on all actuators, we show that the Zernike expansion successfully predicts wavefronts to an accuracy of approximately 30nm (rms) even for large aberrations. We thus show that image-based wavefront sensing, which requires no additional optical equipment, allows a simple but powerful method to calibrate a deformable optical element in a microscope setting.

© 2010 Optical Society of America

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References

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  1. J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).
    [CrossRef]
  2. J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
    [CrossRef]
  3. M. J. Booth, “Adaptive optics in microscopy,” Philos. Transact. R. Soc. A. 365, 2829-2843 (2007).
    [CrossRef]
  4. D. Turaga and T. E. Holy, “Miniaturization and defocus correction for objective-coupled planar illumination microscopy,” Opt. Lett. 33, 2302-2304 (2008).
    [CrossRef] [PubMed]
  5. T. F. Holekamp, D. Turaga, and T. E. Holy, “Fast three-dimensional fluorescence imaging of activity in neural populations by objective-coupled planar illumination microscopy,” Neuron 57, 661-672 (2008).
    [CrossRef] [PubMed]
  6. E. Fuchs, J. S. Jaffe, R. A. Long, and F. Azam, “Thin laser light sheet microscope for microbial oceanography,” Opt. Express 10, 145-154 (2002).
    [PubMed]
  7. J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodth, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305, 1007-1009 (2004).
    [CrossRef] [PubMed]
  8. H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
    [CrossRef] [PubMed]
  9. R. K. Tyson, Introduction to Adaptive Optics (SPIE Press, 2000).
    [CrossRef]
  10. J. Porter, H. Queener, J. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science (Wiley-Interscience, 2006).
    [CrossRef]
  11. L. A. Poyneer, “Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,” Appl. Opt. 42, 5807-5815(2003).
    [CrossRef] [PubMed]
  12. M. Feierabend, M. Ruckel, and W. Denk, “Coherence-gated wave-front sensing in strongly scattering samples,” Opt. Lett. 29, 2255-2257 (2004).
    [CrossRef] [PubMed]
  13. B. Hermann, E. J. Fernandez, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, “Adaptive-optics ultrahigh-resolution optical coherence tomography,” Opt. Lett. 29, 2142-2144 (2004).
    [CrossRef] [PubMed]
  14. M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788-5792 (2002).
    [CrossRef] [PubMed]
  15. D. Debarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34, 2495-2497 (2009).
    [CrossRef] [PubMed]
  16. B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microscopy 216, 32-48 (2004).
    [CrossRef]
  17. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829-832 (1982).
  18. R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072-1085 (1992).
    [CrossRef]
  19. M. G. Lofdahl, G. B. Scharmer, and W. Wei, “Calibration of a deformable mirror and Strehl ratio measurements by use of phase diversity,” Appl. Opt. 39, 94-103 (2000).
    [CrossRef]
  20. T. J. Schulz, “Multi-frame blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064-1073 (1993).
    [CrossRef]
  21. E. J. Fernandez, L. Vabre, B. Hermann, A. Unterhuber, B. Povazay, and W. Drexler, “Adaptive optics with a magnetic deformable mirror: applications in the human eye,” Opt. Express 14, 8900-8917 (2006).
    [CrossRef] [PubMed]
  22. M. Born and E. Wolf, Principles of Optics (Pergamon, , 1986).
  23. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207-211 (1976).
    [CrossRef]
  24. Y. A. Melnikov, “Influence functions of a point force for Kirchhoff plates with rigid inclusions,” J. Mec. 20, 249-256 (2004).

2009 (1)

2008 (2)

D. Turaga and T. E. Holy, “Miniaturization and defocus correction for objective-coupled planar illumination microscopy,” Opt. Lett. 33, 2302-2304 (2008).
[CrossRef] [PubMed]

T. F. Holekamp, D. Turaga, and T. E. Holy, “Fast three-dimensional fluorescence imaging of activity in neural populations by objective-coupled planar illumination microscopy,” Neuron 57, 661-672 (2008).
[CrossRef] [PubMed]

2007 (2)

M. J. Booth, “Adaptive optics in microscopy,” Philos. Transact. R. Soc. A. 365, 2829-2843 (2007).
[CrossRef]

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (1)

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

2004 (5)

M. Feierabend, M. Ruckel, and W. Denk, “Coherence-gated wave-front sensing in strongly scattering samples,” Opt. Lett. 29, 2255-2257 (2004).
[CrossRef] [PubMed]

B. Hermann, E. J. Fernandez, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, “Adaptive-optics ultrahigh-resolution optical coherence tomography,” Opt. Lett. 29, 2142-2144 (2004).
[CrossRef] [PubMed]

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microscopy 216, 32-48 (2004).
[CrossRef]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodth, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305, 1007-1009 (2004).
[CrossRef] [PubMed]

Y. A. Melnikov, “Influence functions of a point force for Kirchhoff plates with rigid inclusions,” J. Mec. 20, 249-256 (2004).

2003 (1)

2002 (2)

M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788-5792 (2002).
[CrossRef] [PubMed]

E. Fuchs, J. S. Jaffe, R. A. Long, and F. Azam, “Thin laser light sheet microscope for microbial oceanography,” Opt. Express 10, 145-154 (2002).
[PubMed]

2000 (1)

1993 (1)

1992 (1)

1982 (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829-832 (1982).

1976 (1)

Agard, D. A.

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microscopy 216, 32-48 (2004).
[CrossRef]

Artal, P.

Awwal, A.

J. Porter, H. Queener, J. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science (Wiley-Interscience, 2006).
[CrossRef]

Azam, F.

Becker, K.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Booth, M. J.

D. Debarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34, 2495-2497 (2009).
[CrossRef] [PubMed]

M. J. Booth, “Adaptive optics in microscopy,” Philos. Transact. R. Soc. A. 365, 2829-2843 (2007).
[CrossRef]

M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788-5792 (2002).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, , 1986).

Botcherby, E. J.

Debarre, D.

Decraemer, W. F.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

Deininger, K.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Del Bene, F.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodth, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305, 1007-1009 (2004).
[CrossRef] [PubMed]

Denk, W.

Deussing, J. M.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Dirckx, J. J. J.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

Dodt, H.-U.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Drexler, W.

Eder, M.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Feierabend, M.

Fercher, A. F.

Fernandez, E. J.

Fienup, J. R.

Fuchs, E.

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829-832 (1982).

Gustafsson, M. G. L.

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microscopy 216, 32-48 (2004).
[CrossRef]

Hanser, B. M.

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microscopy 216, 32-48 (2004).
[CrossRef]

Hermann, B.

Holekamp, T. F.

T. F. Holekamp, D. Turaga, and T. E. Holy, “Fast three-dimensional fluorescence imaging of activity in neural populations by objective-coupled planar illumination microscopy,” Neuron 57, 661-672 (2008).
[CrossRef] [PubMed]

Holy, T. E.

D. Turaga and T. E. Holy, “Miniaturization and defocus correction for objective-coupled planar illumination microscopy,” Opt. Lett. 33, 2302-2304 (2008).
[CrossRef] [PubMed]

T. F. Holekamp, D. Turaga, and T. E. Holy, “Fast three-dimensional fluorescence imaging of activity in neural populations by objective-coupled planar illumination microscopy,” Neuron 57, 661-672 (2008).
[CrossRef] [PubMed]

Huisken, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodth, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305, 1007-1009 (2004).
[CrossRef] [PubMed]

Jaffe, J. S.

Jährling, N.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Juškaitis, R.

M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788-5792 (2002).
[CrossRef] [PubMed]

Kuypers, L. C.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

Leischner, U.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Lin, J.

J. Porter, H. Queener, J. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science (Wiley-Interscience, 2006).
[CrossRef]

Lofdahl, M. G.

Long, R. A.

Mauch, C. P.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Melnikov, Y. A.

Y. A. Melnikov, “Influence functions of a point force for Kirchhoff plates with rigid inclusions,” J. Mec. 20, 249-256 (2004).

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788-5792 (2002).
[CrossRef] [PubMed]

Noll, R. J.

Pawley, J. B.

J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).
[CrossRef]

Paxman, R. G.

Porter, J.

J. Porter, H. Queener, J. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science (Wiley-Interscience, 2006).
[CrossRef]

Povazay, B.

Poyneer, L. A.

Prieto, P. M.

Queener, H.

J. Porter, H. Queener, J. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science (Wiley-Interscience, 2006).
[CrossRef]

Ruckel, M.

Sattmann, H.

Scharmer, G. B.

Schierloh, A.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Schulz, T. J.

Sedat, J. W.

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microscopy 216, 32-48 (2004).
[CrossRef]

Srinivas, S.

Stelzer, E. H. K.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodth, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305, 1007-1009 (2004).
[CrossRef] [PubMed]

Swoger, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodth, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305, 1007-1009 (2004).
[CrossRef] [PubMed]

Thorn, K.

J. Porter, H. Queener, J. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science (Wiley-Interscience, 2006).
[CrossRef]

Turaga, D.

T. F. Holekamp, D. Turaga, and T. E. Holy, “Fast three-dimensional fluorescence imaging of activity in neural populations by objective-coupled planar illumination microscopy,” Neuron 57, 661-672 (2008).
[CrossRef] [PubMed]

D. Turaga and T. E. Holy, “Miniaturization and defocus correction for objective-coupled planar illumination microscopy,” Opt. Lett. 33, 2302-2304 (2008).
[CrossRef] [PubMed]

Tyson, R. K.

R. K. Tyson, Introduction to Adaptive Optics (SPIE Press, 2000).
[CrossRef]

Unterhuber, A.

Vabre, L.

Watanabe, T.

Wei, W.

Wilson, T.

D. Debarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34, 2495-2497 (2009).
[CrossRef] [PubMed]

M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788-5792 (2002).
[CrossRef] [PubMed]

Wittbrodth, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodth, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305, 1007-1009 (2004).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, , 1986).

Zieglgänsberger, W.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Biomed. Opt. (1)

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

J. Mec. (1)

Y. A. Melnikov, “Influence functions of a point force for Kirchhoff plates with rigid inclusions,” J. Mec. 20, 249-256 (2004).

J. Microscopy (1)

B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microscopy 216, 32-48 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nat. Methods (1)

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4, 331-336 (2007).
[CrossRef] [PubMed]

Neuron (1)

T. F. Holekamp, D. Turaga, and T. E. Holy, “Fast three-dimensional fluorescence imaging of activity in neural populations by objective-coupled planar illumination microscopy,” Neuron 57, 661-672 (2008).
[CrossRef] [PubMed]

Opt. Eng. (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829-832 (1982).

Opt. Express (2)

Opt. Lett. (4)

Philos. Transact. R. Soc. A. (1)

M. J. Booth, “Adaptive optics in microscopy,” Philos. Transact. R. Soc. A. 365, 2829-2843 (2007).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

M. J. Booth, M. A. A. Neil, R. Juškaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. USA 99, 5788-5792 (2002).
[CrossRef] [PubMed]

Science (1)

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodth, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305, 1007-1009 (2004).
[CrossRef] [PubMed]

Other (4)

R. K. Tyson, Introduction to Adaptive Optics (SPIE Press, 2000).
[CrossRef]

J. Porter, H. Queener, J. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science (Wiley-Interscience, 2006).
[CrossRef]

J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Pergamon, , 1986).

Supplementary Material (4)

» Media 1: MOV (2766 KB)     
» Media 2: MOV (2774 KB)     
» Media 3: MOV (2831 KB)     
» Media 4: MOV (904 KB)     

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Figures (15)

Fig. 1
Fig. 1

AO-OCPI schematic: (a) Experimental setup for AO-OCPI microscope. A DM is placed behind the back aperture of the objective. The light reflected off the DM is imaged onto a camera. (b), (c) Schematic of wavefront aberration when the DM is flat and when one actuator on the DM is moved.

Fig. 2
Fig. 2

Mirao 52-d. (a) Schematic image of the Mirao 52-d DM. The 52 actuators encompass a pupil of diameter 15 mm . The numbering of the actuators presented here is used in rest of the paper. (b) The mirror is made of a sheet of mirror with voltage-controlled magnetic actuators on the back surface of the mirror.

Fig. 3
Fig. 3

Images of a 0.2 μm bead obtained after applying from 0.09 to 0.1 V to actuator 22 [see Fig. 2a for the location of the actuator]. Each image is 64 × 64 pixels, with 1   pixel = 0.29 μm × 0.29 μm . (All consequent bead images have the same dimensions). Media 1 shows images obtained from moving each of the 52 actuators.

Fig. 4
Fig. 4

Measured (top) and calculated (bottom) images of a bead when different voltages are applied to actuator 22. The calculated images were obtained from the calculated estimate of ϕ using Gaussian parameterization.

Fig. 5
Fig. 5

Actuator 22 calibration using a Zernike parameterization. (a) Each of the 20 Zernike coefficients varies nearly linearly with voltage. The slope of the relationship is plotted as a phase plot in (b). (b) The single-hump peak of the phase plot depicts the movement of the actuator at the location of the peak (colorbar units are radians per volt).

Fig. 6
Fig. 6

Measured (top) and calculated (bottom) images of a bead when different voltages are applied to actuator 22. The calculated images were obtained from the Zernike parameterization. Media 2 shows corresponding images obtained for all actuators.

Fig. 7
Fig. 7

Phase plots obtained for all 52 actuators, using Zernike parameterization. Each of the phase plots is scaled independently to demonstrate the underlying differences.

Fig. 8
Fig. 8

DM flat. (a) Magnitude of Zernike coefficients for each of the actuators at zero applied voltage obtained from optimization of each actuator independently; note the consistency of the fitting result. The first two Zernike coefficients contribute to overall tip and tilt of the PSF and are not shown in this figure. (b) Phase present at zero applied voltage (colorbar units are radians).

Fig. 9
Fig. 9

Phase plot obtained for all 52 actuators, using the 8-parameter biharmonic parameterization. Each of the phase plots is scaled independently to demonstrate the underlying differences.

Fig. 10
Fig. 10

Values of m i obtained for each of the actuators after a 110 parameter biharmonic parameterization of ϕ (colorbar units are radians per volt).

Fig. 11
Fig. 11

Measured (top) and calculated (middle, bottom) images of a bead when different voltages are applied to actuator 22. The calculated images were obtained by using a biharmonic parameterization with 8 (middle) and 110 (bottom) parameters. Media 4 shows corresponding images obtained for all actuators.

Fig. 12
Fig. 12

Comparison of fitting errors: (a) fitting error between experimental and calculated images using different ϕ parameterizations, for actuator 22. The different parameterizations are Gaussian (G), from second- to eighth-order Zernike parameters, biharmonic parameterization using 8 parameters (B8), and biharmonic parameterization using 110 parameters (B110). (b) Total fitting error between the experimental and calculated images for all actuators.

Fig. 13
Fig. 13

A random set of voltages are applied to the DM to produce the acquired image. The Zernike-parameterization-based calibration of the DM is used to calculate the predicted phase produced by the set of random voltages (colorbar units are radians). The predicted phase is then used to create the predicted image. The agreement between the acquired and predicted images demonstrates the accuracy of the calibration of the DM. Media 3 shows images obtained from using the 50 sets of random voltages.

Fig. 14
Fig. 14

Sets of random voltages were applied to the DM to obtain the experimental (Exp.) images. Zernike-based calibration of the DM was used without ( Calc . ) and with (Calc.+) offset correction to obtain the calculated images for the given set of random voltages. Each column represents images obtained from a different set of random voltages.

Fig. 15
Fig. 15

(a) Predicted phase from calibration data (colorbar units are radians). (b) Optimized phase calculated by using PDI on the unaberrated and aberrated images shown in Fig. 13. (c) Difference in the two phases. Note that the colormap has been rescaled to show fine detail. (d) Zernike coefficients for predicted (a) and optimized (b) phases. (e) The rms error (in nanometers) between the two phases for all 50 sets of random voltages tested. The red × represents the rms error obtained for the example shown in (d).

Equations (22)

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s k ( x ) = | h k ( x ) | 2 ,
h k ( x ) = FT 1 [ H k ( u ) ] = d u e 2 π ι u · x H 0 ( u ) e ι ϕ k ( u ) ,
E [ f , { ϕ k } ] = k = 1 K d u | D k ( u ) F ( u ) S k ( u ) | 2 ,
F = k = 1 K D k S k / l = 1 K | S l | 2 ,
E [ { ϕ k } ] = d u | k D k ( u ) S k ( u ) | 2 l | S l ( u ) | 2 d u k | D k ( u ) | 2 .
δ E δ ϕ k ( u ) = 4 Im [ k = 1 K H k ( u ) ( Z k * H k ) ( u ) ] ,
Z k = [ l | S l | 2 ( j D j S j ) D k | j D j S j | 2 S k ] / ( l | S l | 2 ) 2 .
p = k d u ϕ k ( u ) p δ δ ϕ k ( u ) .
ϕ ( u ) = A e ( u u 0 ) 2 / 2 σ 2 ,
ϕ k A = e ( u u 0 ) 2 / 2 σ 2 ,
u 0 ϕ k = A ( u u 0 ) σ 2 e ( u u 0 ) 2 / 2 σ 2 ,
ϕ k σ = A ( u u 0 ) 2 σ 3 e ( u u 0 ) 2 / 2 σ 2 .
ϕ k = j = 1 J α j Z j ,
ϕ k α j = Z j .
ϕ k ( u ) = ψ k ( A u + ξ 0 ) ,
A = ( a 1 a 2 a 2 a 3 ) .
ψ k ( ξ ) = i ( m i v k i + ζ i ) b i ( ξ ) ,
E membrane [ b ] d ξ ( 2 b ) 2 ,
( 2 ) 2 b = 0 .
b ( ξ ˜ | c ˜ ) = 1 R 2 | ξ ˜ c ˜ | 2 log ( R 2 | ξ ˜ c ˜ | 2 | R 2 c ˜ ξ ˜ | 2 ) + 1 R 4 ( R 2 | ξ ˜ | 2 ) ( R 2 | c ˜ | 2 ) ,
ϕ k ( u ) = ψ k ( A u + ξ 0 ) + α ( 2 u 2 1 ) ,
v 0 = M + Z 0 ,

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