Abstract

Light sheet microscopy allows rapid imaging of three-dimensional fluorescent samples, using illumination and detection axes that are orthogonal. For imaging large samples, this often forces the objective to be tilted relative to the sample’s surface; for samples that are not precisely matched to the immersion medium index, this tilt introduces aberrations. Here we calculate the nature of these aberrations for a simple tissue model, and show that a low-dimensional parametrization of these aberrations facilitates online correction via a deformable mirror without introduction of beads or other fiducial markers. We use this approach to demonstrate improved image quality in living tissue.

© 2013 OSA

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References

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  1. J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt.10, 44014 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef]
  4. P. A. Santi, “Light sheet fluorescence microscopy: a review,” J. Histochem. Cytochem.59, 129–138 (2011).
    [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,” Neuron57, 661–672 (2008).
    [CrossRef] [PubMed]
  6. D. Turaga and T. E. Holy, “Organization of vomeronasal sensory coding revealed by fast volumetric calcium imaging,” J. Neurosci.32, 1612–1621 (2012).
    [CrossRef] [PubMed]
  7. C. Bourgenot, C. D. Saunter, J. M. Taylor, J. M. Girkin, and G. D. Love, “3d adaptive optics in a light sheet microscope,” Opt. Express20, 13252–13261 (2012).
    [CrossRef] [PubMed]
  8. R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
    [CrossRef] [PubMed]
  9. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing, 3rd ed. (Cambridge University PressCambridge, 2007).
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    [CrossRef] [PubMed]
  11. M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980), 6th ed.
  12. J. L. F. de Meijere and C. H. F. Velzel, “Linear ray-propagation models in geometrical optics,” J. Opt. Soc. Am. A4, 2162–2165 (1987).
    [CrossRef]
  13. D. Turaga and T. E. Holy, “Image-based calibration of a deformable mirror in wide-field microscopy,” Appl. Opt.49, 2030–2040 (2010).
    [CrossRef] [PubMed]
  14. J. He, L. Ma, S. Kim, J. Nakai, and C. Yu, “Encoding gender and individual information in the mouse vomeronasal organ,” Science320, 535–538 (2008).
    [CrossRef] [PubMed]

2012 (3)

D. Turaga and T. E. Holy, “Organization of vomeronasal sensory coding revealed by fast volumetric calcium imaging,” J. Neurosci.32, 1612–1621 (2012).
[CrossRef] [PubMed]

C. Bourgenot, C. D. Saunter, J. M. Taylor, J. M. Girkin, and G. D. Love, “3d adaptive optics in a light sheet microscope,” Opt. Express20, 13252–13261 (2012).
[CrossRef] [PubMed]

R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
[CrossRef] [PubMed]

2011 (1)

P. A. Santi, “Light sheet fluorescence microscopy: a review,” J. Histochem. Cytochem.59, 129–138 (2011).
[CrossRef] [PubMed]

2010 (1)

2008 (3)

J. He, L. Ma, S. Kim, J. Nakai, and C. Yu, “Encoding gender and individual information in the mouse vomeronasal organ,” Science320, 535–538 (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,” Neuron57, 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]

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, 44014 (2005).
[CrossRef] [PubMed]

1991 (1)

1987 (1)

Andilla, J.

R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
[CrossRef] [PubMed]

Awwal, A.

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

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980), 6th ed.

Bourgenot, C.

de Meijere, J. L. F.

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, 44014 (2005).
[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, 44014 (2005).
[CrossRef] [PubMed]

Ducommun, B.

R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing, 3rd ed. (Cambridge University PressCambridge, 2007).

Frongia, C.

R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
[CrossRef] [PubMed]

Girkin, J. M.

Gu, M.

He, J.

J. He, L. Ma, S. Kim, J. Nakai, and C. Yu, “Encoding gender and individual information in the mouse vomeronasal organ,” Science320, 535–538 (2008).
[CrossRef] [PubMed]

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,” Neuron57, 661–672 (2008).
[CrossRef] [PubMed]

Holy, T. E.

D. Turaga and T. E. Holy, “Organization of vomeronasal sensory coding revealed by fast volumetric calcium imaging,” J. Neurosci.32, 1612–1621 (2012).
[CrossRef] [PubMed]

D. Turaga and T. E. Holy, “Image-based calibration of a deformable mirror in wide-field microscopy,” Appl. Opt.49, 2030–2040 (2010).
[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]

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,” Neuron57, 661–672 (2008).
[CrossRef] [PubMed]

Jorand, R.

R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
[CrossRef] [PubMed]

Kim, S.

J. He, L. Ma, S. Kim, J. Nakai, and C. Yu, “Encoding gender and individual information in the mouse vomeronasal organ,” Science320, 535–538 (2008).
[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, 44014 (2005).
[CrossRef] [PubMed]

Le Corre, G.

R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
[CrossRef] [PubMed]

Lin, J. E.

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

Lobjois, V.

R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
[CrossRef] [PubMed]

Lorenzo, C.

R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
[CrossRef] [PubMed]

Love, G. D.

Ma, L.

J. He, L. Ma, S. Kim, J. Nakai, and C. Yu, “Encoding gender and individual information in the mouse vomeronasal organ,” Science320, 535–538 (2008).
[CrossRef] [PubMed]

Maandhui, A.

R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
[CrossRef] [PubMed]

Nakai, J.

J. He, L. Ma, S. Kim, J. Nakai, and C. Yu, “Encoding gender and individual information in the mouse vomeronasal organ,” Science320, 535–538 (2008).
[CrossRef] [PubMed]

Porter, J.

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

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing, 3rd ed. (Cambridge University PressCambridge, 2007).

Queener, H. M.

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

Santi, P. A.

P. A. Santi, “Light sheet fluorescence microscopy: a review,” J. Histochem. Cytochem.59, 129–138 (2011).
[CrossRef] [PubMed]

Saunter, C. D.

Sheppard, C. J.

Taylor, J. M.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing, 3rd ed. (Cambridge University PressCambridge, 2007).

Thorn, K.

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

Turaga, D.

D. Turaga and T. E. Holy, “Organization of vomeronasal sensory coding revealed by fast volumetric calcium imaging,” J. Neurosci.32, 1612–1621 (2012).
[CrossRef] [PubMed]

D. Turaga and T. E. Holy, “Image-based calibration of a deformable mirror in wide-field microscopy,” Appl. Opt.49, 2030–2040 (2010).
[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,” Neuron57, 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]

Velzel, C. H. F.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing, 3rd ed. (Cambridge University PressCambridge, 2007).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980), 6th ed.

Yu, C.

J. He, L. Ma, S. Kim, J. Nakai, and C. Yu, “Encoding gender and individual information in the mouse vomeronasal organ,” Science320, 535–538 (2008).
[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, 44014 (2005).
[CrossRef] [PubMed]

J. Histochem. Cytochem. (1)

P. A. Santi, “Light sheet fluorescence microscopy: a review,” J. Histochem. Cytochem.59, 129–138 (2011).
[CrossRef] [PubMed]

J. Neurosci. (1)

D. Turaga and T. E. Holy, “Organization of vomeronasal sensory coding revealed by fast volumetric calcium imaging,” J. Neurosci.32, 1612–1621 (2012).
[CrossRef] [PubMed]

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

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,” Neuron57, 661–672 (2008).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

PloS One (1)

R. Jorand, G. Le Corre, J. Andilla, A. Maandhui, C. Frongia, V. Lobjois, B. Ducommun, and C. Lorenzo, “Deep and clear optical imaging of thick inhomogeneous samples,” PloS One7, e35795 (2012).
[CrossRef] [PubMed]

Science (1)

J. He, L. Ma, S. Kim, J. Nakai, and C. Yu, “Encoding gender and individual information in the mouse vomeronasal organ,” Science320, 535–538 (2008).
[CrossRef] [PubMed]

Other (3)

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980), 6th ed.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: The Art of Scientific Computing, 3rd ed. (Cambridge University PressCambridge, 2007).

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

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Figures (4)

Fig. 1
Fig. 1

Geometry of light-sheet imaging for extended samples. The sample is modeled as a flat interface, with the light sheet (cyan) entering at an angle. Emitted fluorescence from sample point x0 (green ray) is shown, propagating in the direction ê. The tissue normal is at an angle α relative to the optic axis . The sample has refractive index ns and the immersion fluid ni.

Fig. 2
Fig. 2

Back pupil correction, Eq. (15), for a = 0.37, a tilt angle α = 30°, and β = c 2 0, Eq. (19). The colorbar is scaled in relative units (left) and in μm of wavefront aberration (right) for the specific case of ε = 0.04 and dz = 100μm.

Fig. 3
Fig. 3

Magnitude of aberration coefficients, Eqs. (2130), as a function of the tilt angle α. The coefficients are displayed in units of A = εdz (left) and in μm of wavefront aberration (right) for the same parameters used in Fig. 2.

Fig. 4
Fig. 4

Aberration correction in OCPI microscopy. (a) A 0.2 μm bead in PDMS, dz = 80μm. (b) The same bead after aberration correction. (c) Neurons of the vomeronasal organ in a mouse expressing GCaMP2, dz = 50μm. (d) The same field as (c) after correction.

Equations (38)

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s ( e ^ ) = c x 0 n ^ e ^ n ^ .
| x x 0 | + ε s ( e ^ ) | x ( x 0 + Δ x ) | + C
ε s ( e ^ ) C e ^ Δ x .
s = d cos θ cos α + sin θ sin α
d ( 1 θ 2 / 2 ) cos α + θ sin α
d cos α [ 1 θ tan α + 1 2 θ 2 ( 1 + 2 tan 2 α ) ]
Δ y = ε d z tan α , Δ z = ε d z ( 1 + 2 tan 2 α ) .
s = d cos θ cos α
d cos α [ 1 + 1 2 θ 2 ] .
Δ x = 0 , Δ z = ε d z .
Δ z ¯ = ε d z ( 1 + tan 2 α ) .
Φ ( v , u ) = ε d cos α 1 ( a v u ) 2 + sin α ( a v y u y )
= ε d z 1 ( a v u ) 2 + tan α ( a v y u y )
Φ ( v , u ) = A 1 ( a v u ) 2 + t ( a v y u y ) .
1 2 Φ ( v , 0 ) = A [ 1 1 a 2 v 2 + t a v y c 0 2 2 c 1 1 v y β ( 2 v 2 1 ) ] .
c 0 0 = 1 8 ( a 4 t 4 + 2 a 4 t 2 + 2 a 2 t 2 + a 4 + 2 a 2 + 8 ) ;
c 1 1 = a t ( 3 a 2 t 2 + 4 a 2 + 6 ) 3 ;
c 1 1 = 0 ;
c 2 0 / 3 = a 2 ( t 2 + 1 ) ( 3 a 2 t 2 + 3 a 2 + 4 ) 16 ;
c 2 2 / 6 = 0 ;
c 2 2 / 6 = a 2 t 2 ( 6 a 2 t 2 + 9 a 2 + 8 ) 16 ;
c 3 1 / 8 = a 3 t ( 3 t 2 + 4 ) 12 ;
c 3 1 / 8 = 0 ;
c 3 3 / 8 = a 3 t 3 4 ;
c 3 3 / 8 = 0 ;
c 4 0 / 5 = a 4 ( t 2 + 1 ) 2 16 ;
c 4 2 / 10 = 0 ;
c 4 2 / 10 = a 4 t 2 ( 2 t 2 + 3 ) 16 ;
c 4 4 / 10 = 0 ;
c 4 4 / 10 = a 4 t 4 8 .
ζ ( x 0 , x 1 ) = inf C S [ C ] ,
S [ C ] = d s L = d s n ( x ( s ) ) | x ˙ ( s ) | .
ζ tot ( x 0 , x 1 ) = inf C S tot = inf C ( S n + S ε ) ,
S tot [ C + δ C ] = S n [ C + δ C ] + S ε [ C + δ C ]
S n [ C ] + 1 2 S n [ C ] δ C 2 + S ε [ C ] + S ε [ C ] δ C + 1 2 S ε [ C ] δ C 2 .
L tot ( C + δ C ) L tot ( C ) + b δ C + a δ C 2 .
L tot ( C + δ C ) L tot ( C ) b 2 2 a .
ζ tot = S n [ C ] + S ε [ C ] .

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