Abstract

We present a new optimization concept for 3D multiphoton fluorescence microscopy by finding the optimal excitation beam giving rise to the smallest possible light-emitting volume or the highest possible signal to noise ratio (SNR).

© 2013 Optical Society of America

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  1. W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
    [CrossRef]
  2. Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
    [CrossRef]
  3. S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, Science 275, 530 (1997).
    [CrossRef]
  4. D. Yelin and Y. Silberberg, Opt. Express 5, 169 (1999).
    [CrossRef]
  5. D. A. Parthenopoulos and P. M. Rentzepis, Science 245, 843 (1989).
    [CrossRef]
  6. B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
    [CrossRef]
  7. W. Haske, V. W. Chen, J. M. Hales, W. Dong, S. Barlow, S. R. Marder, and J. W. Perry, Opt. Express 15, 3426 (2007).
    [CrossRef]
  8. T. R. M. Sales, Phys. Rev. Lett. 81, 3844 (1998).
    [CrossRef]
  9. M. Gu, Opt. Lett. 21, 988 (1996).
    [CrossRef]
  10. J. Squier and M. Muller, Rev. Sci. Inst. 72, 2855 (2001).
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    [CrossRef]
  14. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
    [CrossRef]
  15. S. W. Hell and J. Wichmann, Opt. Lett. 19, 780 (1994).
    [CrossRef]
  16. R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, Nat. Methods 5, 539 (2008).
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2011 (2)

2010 (1)

2008 (1)

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, Nat. Methods 5, 539 (2008).

2007 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

2001 (1)

J. Squier and M. Muller, Rev. Sci. Inst. 72, 2855 (2001).

2000 (1)

1999 (2)

D. Yelin and Y. Silberberg, Opt. Express 5, 169 (1999).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

1998 (2)

T. R. M. Sales, Phys. Rev. Lett. 81, 3844 (1998).
[CrossRef]

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
[CrossRef]

1997 (2)

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, Science 275, 530 (1997).
[CrossRef]

1996 (1)

1994 (1)

1990 (1)

W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
[CrossRef]

1989 (1)

D. A. Parthenopoulos and P. M. Rentzepis, Science 245, 843 (1989).
[CrossRef]

1986 (1)

1835 (1)

G. B. Airy, Trans. Cambridge Philos. Soc. 5, 283 (1835).

Airy, G. B.

G. B. Airy, Trans. Cambridge Philos. Soc. 5, 283 (1835).

Ananthavel, S. P.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Barad, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

Barlow, S.

W. Haske, V. W. Chen, J. M. Hales, W. Dong, S. Barlow, S. R. Marder, and J. W. Perry, Opt. Express 15, 3426 (2007).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Brown, T.

Chen, V. W.

Chen, Z.

Christodoulides, D.

Christodoulides, D. N.

Christodoul-ides, D. N.

Cumpston, B. H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Denk, W.

W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
[CrossRef]

Dong, W.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Dyer, D. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Efremidis, N. K.

Egner, A.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, Nat. Methods 5, 539 (2008).

Ehrlich, J. E.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Eisenberg, H.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

Engelhardt, J.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, Nat. Methods 5, 539 (2008).

Erskine, L. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Gammaitoni, L.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
[CrossRef]

Gu, M.

Hales, J. M.

Hänggi, P.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
[CrossRef]

Haske, W.

Heikal, A. A.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Hell, S. W.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, Nat. Methods 5, 539 (2008).

S. W. Hell and J. Wichmann, Opt. Lett. 19, 780 (1994).
[CrossRef]

Horowitz, M.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

Jakobs, S.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, Nat. Methods 5, 539 (2008).

Jung, P.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
[CrossRef]

Kuebler, S. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Mahajan, V. N.

Maiti, S.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, Science 275, 530 (1997).
[CrossRef]

Marchesoni, F.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
[CrossRef]

Marder, S. R.

W. Haske, V. W. Chen, J. M. Hales, W. Dong, S. Barlow, S. R. Marder, and J. W. Perry, Opt. Express 15, 3426 (2007).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

McCord-Maughon, D.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Mills, M. S.

Muller, M.

J. Squier and M. Muller, Rev. Sci. Inst. 72, 2855 (2001).

Papazoglou, D. G.

Parthenopoulos, D. A.

D. A. Parthenopoulos and P. M. Rentzepis, Science 245, 843 (1989).
[CrossRef]

Perry, J. W.

W. Haske, V. W. Chen, J. M. Hales, W. Dong, S. Barlow, S. R. Marder, and J. W. Perry, Opt. Express 15, 3426 (2007).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Prakash, J.

Qin, J.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Rentzepis, P. M.

D. A. Parthenopoulos and P. M. Rentzepis, Science 245, 843 (1989).
[CrossRef]

Röckel, H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Rumi, M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Sales, T. R. M.

T. R. M. Sales, Phys. Rev. Lett. 81, 3844 (1998).
[CrossRef]

Sandy Lee, I.-Y.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Schmidt, R.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, Nat. Methods 5, 539 (2008).

Shear, J. B.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, Science 275, 530 (1997).
[CrossRef]

Silberberg, Y.

D. Yelin and Y. Silberberg, Opt. Express 5, 169 (1999).
[CrossRef]

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

Squier, J.

J. Squier and M. Muller, Rev. Sci. Inst. 72, 2855 (2001).

Strickler, J.

W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
[CrossRef]

Tzortzakis, S.

Webb, W.

W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
[CrossRef]

Webb, W. W.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, Science 275, 530 (1997).
[CrossRef]

Wichmann, J.

Williams, R. M.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, Science 275, 530 (1997).
[CrossRef]

Wu, X.-L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Wurm, C. A.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, Nat. Methods 5, 539 (2008).

Yelin, D.

Youngworth, K.

Zhang, P.

Zhang, Z.

Zipfel, W. R.

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, Science 275, 530 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nat. Methods (1)

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, Nat. Methods 5, 539 (2008).

Nature (1)

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. Sandy Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, Nature 398, 51 (1999).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. Lett. (2)

T. R. M. Sales, Phys. Rev. Lett. 81, 3844 (1998).
[CrossRef]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Rev. Mod. Phys. (1)

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
[CrossRef]

Rev. Sci. Inst. (1)

J. Squier and M. Muller, Rev. Sci. Inst. 72, 2855 (2001).

Science (3)

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, Science 275, 530 (1997).
[CrossRef]

D. A. Parthenopoulos and P. M. Rentzepis, Science 245, 843 (1989).
[CrossRef]

W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
[CrossRef]

Trans. Cambridge Philos. Soc. (1)

G. B. Airy, Trans. Cambridge Philos. Soc. 5, 283 (1835).

Other (1)

https://www.researchgate.net/publication/256120919_Supplementary_material_for_the_paper_Optimizing_3D_multiphoton_fluorescence_microscopy?ev=srch_pub .

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Figures (2)

Fig. 1.
Fig. 1.

Demonstration of SNR optimizations for n=2 and NA=1. (a) and (b) Amplitudes of the MFM spot of an optimal Gaussian beam and the optimized beam found by our algorithm, respectively. The beams are normalized to have the same “signal” strength, meaning that the numerator of Eq. (1) is the same. Note that the side lobes of the optimized beam are smaller, mainly along the z axis. The blue ellipses mark the edge of the FOM window, with diameters of 2×1.5 wavelengths. The maximum fluorescence intensity outside the window (marked by dashed arrows) is reduced by 54%. The figures present the normalized intensity, and the axes are measured in units of the optical wavelength. The axes are z (vertical) and x (horizontal). (c) Comparison between the on-axis MFM side lobes of the optimal Gaussian beam (blue), the beam of equal angular distribution (black), and our optimized solution (red). The plots are normalized to have the same maximum peak amplitude. The maximum fluorescence intensity outside the window (marked by dashed arrows) is reduced by a factor of 200!

Fig. 2.
Fig. 2.

Demonstration of the procedure for minimizing the illumination volume, for n=3 and NA=1. (a) and (b) Amplitudes of the MFM spot of an optimal Gaussian beam and the optimized beam found by our algorithm, respectively. The beams are normalized so that the numerator of Eq. (1) is the same. The two subfigures have the same color scale to emphasize that the optimized illumination spot is smaller and more intense. The volumes are calculated as S3/2 and measured in wavelengths. (c) Several iterations in the optimization process, showing the angular k-space distribution w(kθ) in subsequent steps in the algorithm (plotting every 2nd step until the procedure converges). The initial distribution is uniform (red line), with later steps having a steeper curve around the right boundary of π/2. (d) The difference between amplitude of the initial condition (uniform angular k-space distribution) and amplitude of the optimal spot. Positive (bright) values are where the optimized beam has smaller amplitude, plotted in % of the maximum amplitudes, and in the same length scales of the two left subfigures. This highlights pros and cons of the optimized solution: the width of the optimized beam is narrower mostly along the z axis, but the peak intensity is slightly smaller and it contains side-lobes.

Equations (3)

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

S=f(x,y,z)|E(x,y,z)|2ndV|E(x,y,z)|2ndV.
E(r,z)=0π/2w(kθ)eikzcos(kθ)J0(krsin(kθ))sin(kθ)dkθ.
Δw(kθ)=E|E|2n2J0(krsin(kθ))eikzcos(kθ)(f(r,z)S)rdrdz.

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