Abstract

Oblique back-illumination microscopy (OBM) provides high resolution, sub-surface phase-gradient images from arbitrarily thick samples. We present an image formation theory for OBM and demonstrate that OBM lends itself to volumetric imaging because of its capacity for optical sectioning. In particular, OBM can provide extended depth of field (EDOF) images from single exposures, by rapidly scanning the focal plane with an electrically tunable lens. These EDOF images can be further enhanced by deconvolution. We corroborate our theory with experimental volumetric images obtained from transparent bead samples and mouse cortical brain slices.

© 2014 Optical Society of America

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References

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2013 (2)

T. N. Ford, J. Mertz, “Video-rate imaging of microcirculation with single-exposure oblique back-illumination microscopy,” J. Biomed. Opt. 18, 0066007 (2013).
[CrossRef]

F. O. Fahrbach, F. F. Voigt, B. Schmid, F. Helmchen, J. Huisken, “Rapid 3D light-sheet microscopy with a tunable lens,” Opt. Express 21, 21010–21026 (2013).
[CrossRef] [PubMed]

2012 (1)

T. N. Ford, K. K. Chu, J. Mertz, “Phase-gradient microscopy in thick tissue with oblique back-illumination,” Nat. Methods 9, 1195–1197 (2012).
[CrossRef] [PubMed]

2011 (1)

2009 (1)

2008 (1)

2007 (1)

2006 (1)

2000 (1)

M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete, K. Larkin, “Using the Hilbert transform for 3D visualization of differential interference contrast microscope images,” J. Micro. 199, 79–84 (2000).
[CrossRef]

1991 (1)

1985 (1)

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–768 (1985).
[CrossRef] [PubMed]

1976 (1)

1975 (1)

1972 (1)

G. Häusler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

1969 (1)

1964 (1)

Arnison, M. R.

M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete, K. Larkin, “Using the Hilbert transform for 3D visualization of differential interference contrast microscope images,” J. Micro. 199, 79–84 (2000).
[CrossRef]

Booth, M. J.

Botcherby, E. J.

Carter, W.

Chu, K. K.

T. N. Ford, K. K. Chu, J. Mertz, “Phase-gradient microscopy in thick tissue with oblique back-illumination,” Nat. Methods 9, 1195–1197 (2012).
[CrossRef] [PubMed]

R. Yi, K. K. Chu, J. Mertz, “Graded-field microscopy with white light,” Opt. Express 14, 5191–5200 (2006).
[CrossRef] [PubMed]

Cogswell, C. J.

M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete, K. Larkin, “Using the Hilbert transform for 3D visualization of differential interference contrast microscope images,” J. Micro. 199, 79–84 (2000).
[CrossRef]

Fahrbach, F. O.

Fekete, P. W.

M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete, K. Larkin, “Using the Hilbert transform for 3D visualization of differential interference contrast microscope images,” J. Micro. 199, 79–84 (2000).
[CrossRef]

Ford, T. N.

T. N. Ford, J. Mertz, “Video-rate imaging of microcirculation with single-exposure oblique back-illumination microscopy,” J. Biomed. Opt. 18, 0066007 (2013).
[CrossRef]

T. N. Ford, K. K. Chu, J. Mertz, “Phase-gradient microscopy in thick tissue with oblique back-illumination,” Nat. Methods 9, 1195–1197 (2012).
[CrossRef] [PubMed]

Gu, M.

Häusler, G.

G. Häusler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

Heintzmann, R.

C. Ventalon, R. Heintzmann, J. Mertz, “Dynamic speckle illumination microscopy with wavelet prefiltering,” Opt. Lett. 32, 1417–1419 (2007).
[CrossRef] [PubMed]

K. Wicker, R. Heintzmann, “Fluorescence microscopy with extended depth of field” in Nanoscopy and Multidimensional Optical Fluorescence Microscopy, Alberto Diaspro, ed. (Chapman and Hall, 2010), pp. 4-1–4-16.

Helmchen, F.

Hua, H.

Huisken, J.

Juskaitis, R.

Kachar, B.

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–768 (1985).
[CrossRef] [PubMed]

Kuthirummal, S.

H. Nagahara, S. Kuthirummal, C. Zhou, S. Nayar, “Flexible depth of field photography,” in Computer Vision ECCV 2008, D. Forsyth, P. Torr, A. Zisserman, eds. (SpringerBerlin Heidelberg, 2008), pp. 60–73.
[CrossRef]

Larkin, K.

M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete, K. Larkin, “Using the Hilbert transform for 3D visualization of differential interference contrast microscope images,” J. Micro. 199, 79–84 (2000).
[CrossRef]

Liu, S.

McCutchen, C. W.

Mehta, S. B.

Mertz, J.

T. N. Ford, J. Mertz, “Video-rate imaging of microcirculation with single-exposure oblique back-illumination microscopy,” J. Biomed. Opt. 18, 0066007 (2013).
[CrossRef]

T. N. Ford, K. K. Chu, J. Mertz, “Phase-gradient microscopy in thick tissue with oblique back-illumination,” Nat. Methods 9, 1195–1197 (2012).
[CrossRef] [PubMed]

C. Ventalon, R. Heintzmann, J. Mertz, “Dynamic speckle illumination microscopy with wavelet prefiltering,” Opt. Lett. 32, 1417–1419 (2007).
[CrossRef] [PubMed]

R. Yi, K. K. Chu, J. Mertz, “Graded-field microscopy with white light,” Opt. Express 14, 5191–5200 (2006).
[CrossRef] [PubMed]

J. Mertz, Introduction to Optical Microscopy (Roberts & Company, 2010).

Nagahara, H.

H. Nagahara, S. Kuthirummal, C. Zhou, S. Nayar, “Flexible depth of field photography,” in Computer Vision ECCV 2008, D. Forsyth, P. Torr, A. Zisserman, eds. (SpringerBerlin Heidelberg, 2008), pp. 60–73.
[CrossRef]

Nayar, S.

H. Nagahara, S. Kuthirummal, C. Zhou, S. Nayar, “Flexible depth of field photography,” in Computer Vision ECCV 2008, D. Forsyth, P. Torr, A. Zisserman, eds. (SpringerBerlin Heidelberg, 2008), pp. 60–73.
[CrossRef]

Schmid, B.

Sheppard, C. J. R.

Smith, N. I.

M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete, K. Larkin, “Using the Hilbert transform for 3D visualization of differential interference contrast microscope images,” J. Micro. 199, 79–84 (2000).
[CrossRef]

Stewart, W. C.

Stokseth, P. A.

Ventalon, C.

Voigt, F. F.

Wicker, K.

K. Wicker, R. Heintzmann, “Fluorescence microscopy with extended depth of field” in Nanoscopy and Multidimensional Optical Fluorescence Microscopy, Alberto Diaspro, ed. (Chapman and Hall, 2010), pp. 4-1–4-16.

Wilson, T.

Wolf, E.

Yi, R.

Zhou, C.

H. Nagahara, S. Kuthirummal, C. Zhou, S. Nayar, “Flexible depth of field photography,” in Computer Vision ECCV 2008, D. Forsyth, P. Torr, A. Zisserman, eds. (SpringerBerlin Heidelberg, 2008), pp. 60–73.
[CrossRef]

J. Biomed. Opt. (1)

T. N. Ford, J. Mertz, “Video-rate imaging of microcirculation with single-exposure oblique back-illumination microscopy,” J. Biomed. Opt. 18, 0066007 (2013).
[CrossRef]

J. Micro. (1)

M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete, K. Larkin, “Using the Hilbert transform for 3D visualization of differential interference contrast microscope images,” J. Micro. 199, 79–84 (2000).
[CrossRef]

J. Opt. Soc. Am. (4)

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

Nat. Methods (1)

T. N. Ford, K. K. Chu, J. Mertz, “Phase-gradient microscopy in thick tissue with oblique back-illumination,” Nat. Methods 9, 1195–1197 (2012).
[CrossRef] [PubMed]

Opt. Commun. (1)

G. Häusler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Science (1)

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–768 (1985).
[CrossRef] [PubMed]

Other (3)

J. Mertz, Introduction to Optical Microscopy (Roberts & Company, 2010).

K. Wicker, R. Heintzmann, “Fluorescence microscopy with extended depth of field” in Nanoscopy and Multidimensional Optical Fluorescence Microscopy, Alberto Diaspro, ed. (Chapman and Hall, 2010), pp. 4-1–4-16.

H. Nagahara, S. Kuthirummal, C. Zhou, S. Nayar, “Flexible depth of field photography,” in Computer Vision ECCV 2008, D. Forsyth, P. Torr, A. Zisserman, eds. (SpringerBerlin Heidelberg, 2008), pp. 60–73.
[CrossRef]

Supplementary Material (5)

» Media 1: AVI (3034 KB)     
» Media 2: AVI (907 KB)     
» Media 3: AVI (1696 KB)     
» Media 4: AVI (1708 KB)     
» Media 5: AVI (4255 KB)     

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Figures (5)

Fig. 1
Fig. 1

(Color online) OBM with a tunable lens relay system. A focal plane in the sample (horizontal dashed line) is imaged to an intermediate plane (vertical dashed line) and reimaged to a camera. The tunable lens of focal length fv is in an aperture plane, enabling a rapid tuning of the focal plane depth without moving the sample. Alternating LED light is launched into the sample via two off-axis fibers (only a single fiber is shown active).

Fig. 2
Fig. 2

OBM phase-gradient images of mouse pyramidal neurons demonstrating optical sectioning. The frames are selected from a z-stack obtained by scanning the tunable lens ( Media 1). The images were taken at equal intervals along a span of 42 μm (displayed here at intervals of 4.7 μm) at increasing depths from top-left to bottom-right. The field of view for each image is 67×96 μm. The total exposure time per frame was 20 ms (10 ms per active LED).

Fig. 3
Fig. 3

EDOF images of polystyrene (2 μm) and glass (3–10 μm) beads embedded in agarose gel. Panel a is a standard OBM phase-gradient image. Panels b,c are EDOF phase-gradient images acquired in single exposures by scanning the focal plane over ranges 25 μm and 100 μm respectively. Panels d,e are the same EDOF images, but deblurred according to Eq. (18). The field of view for all panels is 63×63 μm.

Fig. 4
Fig. 4

Integrated intensity projections from a phase-gradient z-stack of beads in agarose gel (same sample as in Fig. 3). Panel b is a projection along the z-direction. Panels a,c are projections from ± 10° tilt directions (animation in Media 2). Panels d–f are the same as the top row, but deblurred according to Eg. 18 (animation in Media 3). The projections are generated from a 63×63×82 μm3 volume.

Fig. 5
Fig. 5

Integrated intensity projections from a phase-gradient z-stack of pyramidal neurons in a mouse brain slice (same sample as in Fig. 2). Panel b is a projection along the z-direction. Panels a,c are projections from ± 10° tilt directions (animation in Media 4). Panels d–f are the same as the top row, but deblurred according to Eqn. (18) (animation in Media 5). The projections are generated from a 67×96×42 μm3 volume.

Equations (18)

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I ± ( ρ 1 ) = I s CSF ( ρ 1 ρ 0 ) CSF * ( ρ 1 ρ 0 ) t ( ρ 0 ) t * ( ρ 0 ) μ ± ( ρ 0 ρ 0 ) d 2 ρ 0 d 2 ρ 0
μ ± ( ρ ) = μ L ( ρ ) exp ( ± i 2 π x κ sin θ t )
I ± ( ρ 1 ) = I s CSF ( ρ 1 ρ 0 c + 1 2 ρ 0 d ) CSF * ( ρ 1 ρ 0 c 1 2 ρ 0 d ) × T ( ρ 0 c , ρ 0 d ) μ ± ( ρ 0 d ) d 2 ρ 0 d d 2 ρ 0 c ,
T ( ρ 0 c , ρ 0 d ) | t ( ρ 0 c ) | 2 ( 1 + i ρ 0 d ϕ ( ρ 0 c ) ) ,
PSF ( ρ 1 ρ 0 c ) CSF ( ρ 1 ρ 0 c + 1 2 ρ 0 d ) CSF * ( ρ 1 ρ 0 c 1 2 ρ 0 d ) ,
Σ I ( ρ 1 ) I Σ PSF ( ρ 1 ρ 0 c ) | t ( ρ 0 c ) | 2 d ρ 0 c ,
Δ I ( ρ 1 ) I Δ PSF ( ρ 1 ρ 0 c ) | t ( ρ 0 c ) | 2 x ϕ ( ρ 0 c ) d 2 ρ 0 c ,
I Σ = 2 π I s μ L ( ρ 0 d ) d 2 ρ 0 d ,
I Δ = 4 π κ sin θ t I s x 2 μ L ( ρ 0 d ) d 2 ρ 0 d .
Δ I ( ρ 1 ) = I Δ PSF ( ρ 1 ρ 0 , z 0 ) x ϕ ( ρ 0 , z 0 ) d 2 ρ 0 d z 0 ,
Δ I ˜ ( κ ) = I Δ OTF ( κ ; z 0 ) κ x ϕ ˜ ( κ ; z 0 ) d z 0 ,
z v = 1 M 2 f r 2 f v n s
PSF EDOF ( ρ , z ) = D / 2 D / 2 PSF ( ρ , z + z v ) d z v ,
OTF EDOF ( κ ; z ) = D / 2 D / 2 OTF ( κ ; z + z v ) d z v
OTF ( κ ; 0 ) D / 2 D / 2 jinc ( π ( z + z v ) κ κ Δ κ [ 1 κ Δ κ ] ) d z v
OTF EDOF ( κ ) 4 κ π Δ κ 1 κ ,
Δ I ˜ EDOF ( κ ) κ x κ ϕ ˜ ( κ ; z 0 ) d z 0 .
F ( κ ) = { 1 D 4 κ π Δ κ 2 κ < 1 D 4 κ π Δ κ κ Δ κ 1 D 4 κ π Δ κ < κ < Δ κ 1 κ > Δ κ

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