Abstract

Dynamic speckle illumination (DSI) microscopy is a widefield fluorescence imaging technique that provides depth discrimination. The technique relies on the illumination of a sample with a sequence of speckle patterns. We consider an image processing algorithm based on a differential intensity variance between consecutive images, and demonstrate that DSI sectioning strength depends on the dynamics of the speckle pattern. Translated speckle patterns confer greater sectioning strength than randomized speckle patterns because they retain out-of-focus correlations that lead to better background rejection. We present a theory valid for arbitrary point-spread-functions, which we corroborate with experimental results.

© 2006 Optical Society of America

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References

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  1. T. Wilson and C. Sheppard, Theory and practice of scanning optical microscopy, Academic Press, London (1984).
  2. G. Q. Xiao, T. R. Corle, and G. S. Kino, "Real-time confocal scanning optical microscope," Appl. Phys. Lett. 53, 716-718 (2000).
    [CrossRef]
  3. E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, and J. Hegarty, "Direct-view microscopy: Optical sectioning strength for finite-sized, multiple-pinhole arrays," J. Microscopy 184, 95-105 (1996)
    [CrossRef]
  4. T. Wilson, R. Juskaitis, M. A. A. Neil and M. Kozubek, "Confocal microscopy by aperture correlation," Opt. Lett. 21, 1879-1981 (1996).
    [CrossRef] [PubMed]
  5. R. Juskaitis, T. Wilson,M. A. A. Neil andM. Kozubek, "Efficient real-time confocal microscopy with white light sources," Nature 383, 804-806 (1996).
    [CrossRef] [PubMed]
  6. P. J. Verveer, G. S. Hanley, P. W. Verbeek, L.J. Van Vliet, and T. M. Jovin, "Theory of confocal fluorescence imaging in the programmable array microscope (PAM)," J. Microscopy 189, 192-198 (1998).
    [CrossRef]
  7. M. A. A. Neil and T. Wilson, "Method of obtaining optical sectioning by using structured light in a conventional microscope," Opt. Lett. 22, 1905-1907 (1997).
    [CrossRef]
  8. M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens and T. Wilson, "Wide-field optically sectioning fluorescence microscopy with laser illumination," J. Microscopy 197, 1 (2000).
    [CrossRef]
  9. C. Ventalon and J. Mertz, "Quasi-confocal fluorescence sectioning with dynamic speckle illumination," Opt. Lett. 30,3350-3352 (2005).
    [CrossRef]
  10. J. W. Goodman, Statistical Optics, Wiley, New-York (1985).
  11. P. A. Stokseth, "Properties of a defocused optical system," J. Opt. Soc. Am. 59, 1314-1321 (1969).
    [CrossRef]
  12. T. Yoshimura, "Statistical properties of dynamic speckles," J. Opt. Soc. Am. A 3, 1032-1054 (1986)
    [CrossRef]
  13. H. T. Yura, S. G. Hanson, R. S. Hansen, and B. Rose, "Three-dimensional speckle dynamics in paraxial optical systems," J. Opt. Soc. Am. A 16, 1402-1414 (1999)
    [CrossRef]

2005 (1)

2000 (2)

G. Q. Xiao, T. R. Corle, and G. S. Kino, "Real-time confocal scanning optical microscope," Appl. Phys. Lett. 53, 716-718 (2000).
[CrossRef]

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens and T. Wilson, "Wide-field optically sectioning fluorescence microscopy with laser illumination," J. Microscopy 197, 1 (2000).
[CrossRef]

1999 (1)

1998 (1)

P. J. Verveer, G. S. Hanley, P. W. Verbeek, L.J. Van Vliet, and T. M. Jovin, "Theory of confocal fluorescence imaging in the programmable array microscope (PAM)," J. Microscopy 189, 192-198 (1998).
[CrossRef]

1997 (1)

1996 (3)

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, and J. Hegarty, "Direct-view microscopy: Optical sectioning strength for finite-sized, multiple-pinhole arrays," J. Microscopy 184, 95-105 (1996)
[CrossRef]

T. Wilson, R. Juskaitis, M. A. A. Neil and M. Kozubek, "Confocal microscopy by aperture correlation," Opt. Lett. 21, 1879-1981 (1996).
[CrossRef] [PubMed]

R. Juskaitis, T. Wilson,M. A. A. Neil andM. Kozubek, "Efficient real-time confocal microscopy with white light sources," Nature 383, 804-806 (1996).
[CrossRef] [PubMed]

1986 (1)

1969 (1)

Bastiaens, P. I. H.

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens and T. Wilson, "Wide-field optically sectioning fluorescence microscopy with laser illumination," J. Microscopy 197, 1 (2000).
[CrossRef]

Corle, T. R.

G. Q. Xiao, T. R. Corle, and G. S. Kino, "Real-time confocal scanning optical microscope," Appl. Phys. Lett. 53, 716-718 (2000).
[CrossRef]

Fewer, D. T.

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, and J. Hegarty, "Direct-view microscopy: Optical sectioning strength for finite-sized, multiple-pinhole arrays," J. Microscopy 184, 95-105 (1996)
[CrossRef]

Hanley, G. S.

P. J. Verveer, G. S. Hanley, P. W. Verbeek, L.J. Van Vliet, and T. M. Jovin, "Theory of confocal fluorescence imaging in the programmable array microscope (PAM)," J. Microscopy 189, 192-198 (1998).
[CrossRef]

Hansen, R. S.

Hanson, S. G.

Hegarty, J.

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, and J. Hegarty, "Direct-view microscopy: Optical sectioning strength for finite-sized, multiple-pinhole arrays," J. Microscopy 184, 95-105 (1996)
[CrossRef]

Hewlett, S. J.

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, and J. Hegarty, "Direct-view microscopy: Optical sectioning strength for finite-sized, multiple-pinhole arrays," J. Microscopy 184, 95-105 (1996)
[CrossRef]

Jovin, T. M.

P. J. Verveer, G. S. Hanley, P. W. Verbeek, L.J. Van Vliet, and T. M. Jovin, "Theory of confocal fluorescence imaging in the programmable array microscope (PAM)," J. Microscopy 189, 192-198 (1998).
[CrossRef]

Juskaitis, R.

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens and T. Wilson, "Wide-field optically sectioning fluorescence microscopy with laser illumination," J. Microscopy 197, 1 (2000).
[CrossRef]

T. Wilson, R. Juskaitis, M. A. A. Neil and M. Kozubek, "Confocal microscopy by aperture correlation," Opt. Lett. 21, 1879-1981 (1996).
[CrossRef] [PubMed]

R. Juskaitis, T. Wilson,M. A. A. Neil andM. Kozubek, "Efficient real-time confocal microscopy with white light sources," Nature 383, 804-806 (1996).
[CrossRef] [PubMed]

Kino, G. S.

G. Q. Xiao, T. R. Corle, and G. S. Kino, "Real-time confocal scanning optical microscope," Appl. Phys. Lett. 53, 716-718 (2000).
[CrossRef]

Kozubek, M.

McCabe, E. M.

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, and J. Hegarty, "Direct-view microscopy: Optical sectioning strength for finite-sized, multiple-pinhole arrays," J. Microscopy 184, 95-105 (1996)
[CrossRef]

Mertz, J.

Neil, M. A. A.

Ottewill, A. C.

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, and J. Hegarty, "Direct-view microscopy: Optical sectioning strength for finite-sized, multiple-pinhole arrays," J. Microscopy 184, 95-105 (1996)
[CrossRef]

Rose, B.

Squire, A.

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens and T. Wilson, "Wide-field optically sectioning fluorescence microscopy with laser illumination," J. Microscopy 197, 1 (2000).
[CrossRef]

Stokseth, P. A.

Van Vliet, L.J.

P. J. Verveer, G. S. Hanley, P. W. Verbeek, L.J. Van Vliet, and T. M. Jovin, "Theory of confocal fluorescence imaging in the programmable array microscope (PAM)," J. Microscopy 189, 192-198 (1998).
[CrossRef]

Ventalon, C.

Verbeek, P. W.

P. J. Verveer, G. S. Hanley, P. W. Verbeek, L.J. Van Vliet, and T. M. Jovin, "Theory of confocal fluorescence imaging in the programmable array microscope (PAM)," J. Microscopy 189, 192-198 (1998).
[CrossRef]

Verveer, P. J.

P. J. Verveer, G. S. Hanley, P. W. Verbeek, L.J. Van Vliet, and T. M. Jovin, "Theory of confocal fluorescence imaging in the programmable array microscope (PAM)," J. Microscopy 189, 192-198 (1998).
[CrossRef]

Wilson, T.

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens and T. Wilson, "Wide-field optically sectioning fluorescence microscopy with laser illumination," J. Microscopy 197, 1 (2000).
[CrossRef]

M. A. A. Neil and T. Wilson, "Method of obtaining optical sectioning by using structured light in a conventional microscope," Opt. Lett. 22, 1905-1907 (1997).
[CrossRef]

R. Juskaitis, T. Wilson,M. A. A. Neil andM. Kozubek, "Efficient real-time confocal microscopy with white light sources," Nature 383, 804-806 (1996).
[CrossRef] [PubMed]

T. Wilson, R. Juskaitis, M. A. A. Neil and M. Kozubek, "Confocal microscopy by aperture correlation," Opt. Lett. 21, 1879-1981 (1996).
[CrossRef] [PubMed]

Xiao, G. Q.

G. Q. Xiao, T. R. Corle, and G. S. Kino, "Real-time confocal scanning optical microscope," Appl. Phys. Lett. 53, 716-718 (2000).
[CrossRef]

Yoshimura, T.

Yura, H. T.

Appl. Phys. Lett. (1)

G. Q. Xiao, T. R. Corle, and G. S. Kino, "Real-time confocal scanning optical microscope," Appl. Phys. Lett. 53, 716-718 (2000).
[CrossRef]

J. Microscopy (3)

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, and J. Hegarty, "Direct-view microscopy: Optical sectioning strength for finite-sized, multiple-pinhole arrays," J. Microscopy 184, 95-105 (1996)
[CrossRef]

P. J. Verveer, G. S. Hanley, P. W. Verbeek, L.J. Van Vliet, and T. M. Jovin, "Theory of confocal fluorescence imaging in the programmable array microscope (PAM)," J. Microscopy 189, 192-198 (1998).
[CrossRef]

M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens and T. Wilson, "Wide-field optically sectioning fluorescence microscopy with laser illumination," J. Microscopy 197, 1 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nature (1)

R. Juskaitis, T. Wilson,M. A. A. Neil andM. Kozubek, "Efficient real-time confocal microscopy with white light sources," Nature 383, 804-806 (1996).
[CrossRef] [PubMed]

Opt. Lett. (3)

Other (2)

J. W. Goodman, Statistical Optics, Wiley, New-York (1985).

T. Wilson and C. Sheppard, Theory and practice of scanning optical microscopy, Academic Press, London (1984).

Supplementary Material (2)

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Figures (6)

Fig. 1.
Fig. 1.

Schematic view of the laser speckle (blue ovals) inside the sample and the detection PSF (green lines) for an arbitrary CCD pixel. We define two regions delimited by the dashed vertical lines: the in-focus region corresponding to the signal S we want to measure, and the out-of-focus region corresponding to the background B we want to reject. Id is the recorded pixel intensity at each camera frame k.

Fig. 2.
Fig. 2.

Simple picture to evaluate the translation and random DSI signals produced by a uniform fluorescent plane located at defocus position zc . When the plane is in focus (a), PSFdet is narrow and the detected speckle pattern is completely renewed upon randomization (b) or translation (c). When the plane is out of focus (d), PSFdet is wide and the detected speckle pattern is completely renewed upon randomization (b) but only partially renewed upon translation (c). Δρs is the translation step size.

Fig. 3.
Fig. 3.

DSI sectioning strength for a circular aperture OTF (Eq. (19)). Panel (a): |OTF(k ,zc )|2 for zc Δk2/k = 0 (solid blue line), 10 (dashed red line) and 40 (dash-dotted green line). The dotted black line corresponds to the modulation factor [1 - cos(kx Δρs )] for a speckle translation in the x direction of step size Δρs = πk . Panel (b): Numerical evaluation of DT (Eq. (17)) for a uniform plane sample as a function of defocus zc , for Δρs = πk (bottom blue solid line), Δρs = 12πk (middle black solid line) and Δρs = 80πk (top green solid line), on a logarithmic scale. For Δρs = πk and Δρs = 80πk , the results are fitted by straight lines of slopes -2 and -3 respectively. For Δρs = 12πk there is a break between these slopes. Note: traces in panel (b) are normalized so that the random DSI signal is unity at zc = 0.

Fig. 4.
Fig. 4.

Experimental setup. A spatial light modulator (SLM) imparts a random phase mask on an argon laser beam. The SLM is imaged onto the back focal plane of the microscope objective, so as to create a widefield speckle illumination (the SLM is used in reflection but drawn here in transmission for simplicity). The fluorescent light emitted from the sample is imaged onto a CCD camera. The SLM is illuminated with a diverging beam so as to displace the SLM Fourier plane away form the objective focal plane. A translation of the SLM phase mask then results in a translation of the speckle pattern inside the sample (see text for details). The inset is a simplified schematic of the illumination geometry.

Fig. 5.
Fig. 5.

Experimental measurement of the DSI sectioning strength √D for a uniform fluorescent plane sample (thickness less than 1.5μm), for a translation step size Δρs of approximatively one speckle grain size (blue trace) and 30 speckle grain sizes (green trace). The red trace corresponds to speckle randomization. The objective used in this experiment has a numerical aperture of 0.65 (Olympus 40 × dry). Traces are shown in linear scale (a) and logarithmic scale (b), and are normalized such that the random DSI signal is unity at zc = 0. For a large Δρs , the sectioning trace is identical to that obtained with random DSI. In panel (b), the experimental traces are fitted with straight lines of slope -3/2 for small Δρs , and -1 for a large Δρs and random DSI.

Fig. 6.
Fig. 6.

Images of a fluorescent pollen grain obtained using an objective of numerical aperture 1.3 (Olympus 40 × oil). Panel (a): signal √DT obtained with translating speckle (one image from full z-stack - avi movie 2.27MB). Panel (b): signal √DR obtained with randomized speckle. Panel (c): widefield image (i.e. average of the raw images). Panel (d): 3D reconstruction from z-stack (using Image J - avi movie 1.75MB). 128 raw images (acquisition time 150 ms per image) were used for each sectioned DSI image. Images (a), (b) and (c) were calculated from the same set of raw images (see text for detail).

Equations (25)

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D = 1 2 N k = 1 N ( I d , k + 1 I d , k ) 2
I d = C A d N s n = 1 N s I s , n
D R = ( C A d I ¯ s ) 2 N s
Δ I d = C A d N s [ n = 1 Δ N s I s , n n = 1 Δ N s I s , n ]
D T = ( C A d I ¯ s ) 2 Δ N s N s 2
I d ( ρ d ) = PSF det ( ρ d ρ , z ) C ( ρ , z ) I s ( ρ , z ) d 2 ρ dz
I d ( ρ d ) = C PSF det ( ρ d ρ , z c ) I s ( ρ , z c ) d 2 ρ .
Δ I d ( ρ d ) = C PSF det ( ρ d ρ , z c ) I s ( ρ , z c ) d 2 ρ C PSF det ( ρ d ρ , z c ) I s ( ρ , Δ ρ s , z c ) d 2 ρ
Δ I d ( ρ d ) = C [ PSF det ( ρ d ρ , z c ) PSF det ( ρ d ρ + Δ ρ s , z c ) ] I s ( ρ , z c ) d 2 ρ .
D T ( ρ d ) = C 2 2 [ PSF det ( ρ d ρ , z c ) PSF det ( ρ d ρ + Δρ s , z c ) ]
[ PSF det ( ρ d ρ , z c ) PSF det ( ρ d ρ + Δ ρ s , z c ) ]
I s ( ρ , z c ) I s ( ρ , z c ) d 2 ρ d 2 ρ ¯
I s ( ρ , z ) I s ( ρ , z ) ¯ = I s ¯ 2 [ 1 + PSF ill ( Δ ρ , 0 ) ]
R det ( Δ ρ , z c ) = PSF det ( ρ d ρ , z c ) PSF det ( ρ d ρ + Δ ρ , z c ) d 2 ρ
D T ( ρ d ) = I s ¯ 2 C 2 [ R det ( Δ ρ , z c ) 1 2 R det ( Δ ρ + Δ ρ s , z c ) 1 2 R det ( Δ ρ Δ ρ s , z c ) ] PSF ill ( Δ ρ , 0 ) d 2 Δ ρ
D T ( ρ d ) = I s ¯ 2 C 2 A s [ R det ( 0 , z c ) 1 2 R det ( Δ ρ s , z c ) 1 2 R det ( Δ ρ s , z c ) ]
Area [ PSF det ] = [ PSF det ( ρ , z c ) d 2 ρ ] 2 PSF det 2 ( ρ , z c ) d 2 ρ = A d 2 R det ( 0 , z c ) ,
OTF det ( k , z ) = 1 A d PSF det ( ρ , z ) e i ρ k d 2 ρ
R det ( Δ ρ , z c ) = 1 ( 2 π ) 2 A d 2 OTF det ( k , z c ) 2 e i Δ ρ k d 2 k
D T ( ρ d ) = I s ¯ 2 C 2 A s ( 2 π ) 2 A d 2 OTF det ( k , z c ) 2 [ 1 cos ( Δ ρ s k ) ] d 2 k
D R ( ρ d ) = I s ¯ 2 C 2 A s ( 2 π ) 2 A d 2 OTF det ( k , z c ) 2 d 2 k .
OTF det ( k , z ) = g ( k Δ k ) 2 J 1 ( z k k ( Δ k 1 2 k ) ) z k k ( Δ k 1 2 k )
g ( k Δ k ) = 1 0.69 ( k Δ k ) + 0.076 ( k Δ k ) 2 + 0.043 ( k Δ k ) 3 .
D T ( ρ d ) = 2 A 2 3 + 2 ζ c 2 [ 1 e 2 Δ ρ s 2 w 0 2 ( 3 + 2 ζ c 2 ) ]
D T = 1 2 N k = 1 N 2 ( I d , 2 k + 1 I d , 2 k ) 2 and D R = 1 2 N k = 1 N 2 ( I d , 2 k I d , 2 k 1 ) 2

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