Abstract

We introduce and experimentally validate a computational imaging technique that employs confocal scanning and coherent detection in the Fourier domain. We show how this method may be used to tomographically reconstruct attenuation, aberration, and even occlusion. We also show how these image parameters may be combined with the conventional confocal image reconstruction of the object reflectivity. We demonstrate the method experimentally by imaging a sample consisting of an occlusion above a mirror of varying reflectivity.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. G. N. Vishnyakov, G. G Levin, V. L. Minaev, V. V. Pickalov, and A. V. Likhachev, “Tomographic interference microscopy of living cells,” Microscopy Anal. 18, 15–17 (2004).
  15. N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Synthetic aperture tomographic phase microscopy for 3D imaging of live cells in translational motion,” Opt. Express 16, 16240–16246 (2008).
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2008

2004

G. N. Vishnyakov, G. G Levin, V. L. Minaev, V. V. Pickalov, and A. V. Likhachev, “Tomographic interference microscopy of living cells,” Microscopy Anal. 18, 15–17 (2004).

2003

2002

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef]

2001

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

2000

S. W. Paddock, “Principles and practices of laser scanning confocal microscopy,” Mol. Biotechnol. 16, 127–149 (2000).
[CrossRef]

1996

S. Kikuchi, K. Sonobe, and N. Ohyama, “Three-dimensional microscopic computed tomography based on generalized Radon transform for optical imaging systems,” Opt. Commun. 123, 725–733 (1996).
[CrossRef]

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41, 369–382 (1996).
[CrossRef]

1995

1990

1986

J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Probl. 2, 161–183 (1986).
[CrossRef]

Ahlgren, U.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef]

Badizadegan, K.

Baldock, R.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef]

Beuthan, J.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41, 369–382 (1996).
[CrossRef]

Boas, D. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Boppart, S. A.

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Buzug, T. M.

T. M. Buzug, Computed Tomography: From Photon Statistics to Modern Cone-Beam CT (Springer, 2008).

Carney, P. S.

Chalmond, B.

O. Renaud, J. Viña, Y. Yu, C. Machu, A. Trouvé, H. Van der Voort, B. Chalmond, and S. L. Shorte, “High-resolution 3-D imaging of living cells in suspension using confocal axial tomography,” Biotechnol. J. 3, 53–62 (2008).
[CrossRef]

Choi, W.

Dasari, R. R.

Davidson, D.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef]

Deans, S. R.

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, 1983).

Devaney, J.

J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Probl. 2, 161–183 (1986).
[CrossRef]

DiMarzio, C. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Feld, M. S.

Gaudette, R. J.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical Interferometry, 2nd ed. (Elsevier, 2003).

Hecksher-Sorensen, J.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef]

Helfmann, J.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41, 369–382 (1996).
[CrossRef]

Herrig, M.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41, 369–382 (1996).
[CrossRef]

Hill, B.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef]

Kawata, S.

Kikuchi, S.

S. Kikuchi, K. Sonobe, and N. Ohyama, “Three-dimensional microscopic computed tomography based on generalized Radon transform for optical imaging systems,” Opt. Commun. 123, 725–733 (1996).
[CrossRef]

Kilmer, M.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Kuroiwa, Y.

Levin, G. G

G. N. Vishnyakov, G. G Levin, V. L. Minaev, V. V. Pickalov, and A. V. Likhachev, “Tomographic interference microscopy of living cells,” Microscopy Anal. 18, 15–17 (2004).

Likhachev, A. V.

G. N. Vishnyakov, G. G Levin, V. L. Minaev, V. V. Pickalov, and A. V. Likhachev, “Tomographic interference microscopy of living cells,” Microscopy Anal. 18, 15–17 (2004).

Lue, N.

Machu, C.

O. Renaud, J. Viña, Y. Yu, C. Machu, A. Trouvé, H. Van der Voort, B. Chalmond, and S. L. Shorte, “High-resolution 3-D imaging of living cells in suspension using confocal axial tomography,” Biotechnol. J. 3, 53–62 (2008).
[CrossRef]

Marks, D. L.

Miller, E. L.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Minaev, V. L.

G. N. Vishnyakov, G. G Levin, V. L. Minaev, V. V. Pickalov, and A. V. Likhachev, “Tomographic interference microscopy of living cells,” Microscopy Anal. 18, 15–17 (2004).

Minami, S.

Minet, O.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41, 369–382 (1996).
[CrossRef]

Muller, G.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41, 369–382 (1996).
[CrossRef]

Nakamura, O.

Noda, T.

Ogino, K.

Ohyama, N.

S. Kikuchi, K. Sonobe, and N. Ohyama, “Three-dimensional microscopic computed tomography based on generalized Radon transform for optical imaging systems,” Opt. Commun. 123, 725–733 (1996).
[CrossRef]

Ooki, H.

Paddock, S. W.

S. W. Paddock, “Principles and practices of laser scanning confocal microscopy,” Mol. Biotechnol. 16, 127–149 (2000).
[CrossRef]

Perry, P.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef]

Pickalov, V. V.

G. N. Vishnyakov, G. G Levin, V. L. Minaev, V. V. Pickalov, and A. V. Likhachev, “Tomographic interference microscopy of living cells,” Microscopy Anal. 18, 15–17 (2004).

Popescu, G.

Renaud, O.

O. Renaud, J. Viña, Y. Yu, C. Machu, A. Trouvé, H. Van der Voort, B. Chalmond, and S. L. Shorte, “High-resolution 3-D imaging of living cells in suspension using confocal axial tomography,” Biotechnol. J. 3, 53–62 (2008).
[CrossRef]

Reynolds, J. J.

Ross, A.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef]

Schlachter, S. C.

Sharpe, J.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef]

Shorte, S. L.

O. Renaud, J. Viña, Y. Yu, C. Machu, A. Trouvé, H. Van der Voort, B. Chalmond, and S. L. Shorte, “High-resolution 3-D imaging of living cells in suspension using confocal axial tomography,” Biotechnol. J. 3, 53–62 (2008).
[CrossRef]

Singer, W.

Sonobe, K.

S. Kikuchi, K. Sonobe, and N. Ohyama, “Three-dimensional microscopic computed tomography based on generalized Radon transform for optical imaging systems,” Opt. Commun. 123, 725–733 (1996).
[CrossRef]

Stamnes, J. J.

Trouvé, A.

O. Renaud, J. Viña, Y. Yu, C. Machu, A. Trouvé, H. Van der Voort, B. Chalmond, and S. L. Shorte, “High-resolution 3-D imaging of living cells in suspension using confocal axial tomography,” Biotechnol. J. 3, 53–62 (2008).
[CrossRef]

Van der Voort, H.

O. Renaud, J. Viña, Y. Yu, C. Machu, A. Trouvé, H. Van der Voort, B. Chalmond, and S. L. Shorte, “High-resolution 3-D imaging of living cells in suspension using confocal axial tomography,” Biotechnol. J. 3, 53–62 (2008).
[CrossRef]

Viña, J.

O. Renaud, J. Viña, Y. Yu, C. Machu, A. Trouvé, H. Van der Voort, B. Chalmond, and S. L. Shorte, “High-resolution 3-D imaging of living cells in suspension using confocal axial tomography,” Biotechnol. J. 3, 53–62 (2008).
[CrossRef]

Vishnyakov, G. N.

G. N. Vishnyakov, G. G Levin, V. L. Minaev, V. V. Pickalov, and A. V. Likhachev, “Tomographic interference microscopy of living cells,” Microscopy Anal. 18, 15–17 (2004).

Wedberg, T. C.

Yu, Y.

O. Renaud, J. Viña, Y. Yu, C. Machu, A. Trouvé, H. Van der Voort, B. Chalmond, and S. L. Shorte, “High-resolution 3-D imaging of living cells in suspension using confocal axial tomography,” Biotechnol. J. 3, 53–62 (2008).
[CrossRef]

Zhang, Q.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Zysk, A. M.

Appl. Opt.

Biotechnol. J.

O. Renaud, J. Viña, Y. Yu, C. Machu, A. Trouvé, H. Van der Voort, B. Chalmond, and S. L. Shorte, “High-resolution 3-D imaging of living cells in suspension using confocal axial tomography,” Biotechnol. J. 3, 53–62 (2008).
[CrossRef]

IEEE Signal Process. Mag.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Inverse Probl.

J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Probl. 2, 161–183 (1986).
[CrossRef]

J. Opt. Soc. Am. A

Microscopy Anal.

G. N. Vishnyakov, G. G Levin, V. L. Minaev, V. V. Pickalov, and A. V. Likhachev, “Tomographic interference microscopy of living cells,” Microscopy Anal. 18, 15–17 (2004).

Mol. Biotechnol.

S. W. Paddock, “Principles and practices of laser scanning confocal microscopy,” Mol. Biotechnol. 16, 127–149 (2000).
[CrossRef]

Opt. Commun.

S. Kikuchi, K. Sonobe, and N. Ohyama, “Three-dimensional microscopic computed tomography based on generalized Radon transform for optical imaging systems,” Opt. Commun. 123, 725–733 (1996).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41, 369–382 (1996).
[CrossRef]

Science

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef]

Other

P. Hariharan, Optical Interferometry, 2nd ed. (Elsevier, 2003).

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, 1983).

T. M. Buzug, Computed Tomography: From Photon Statistics to Modern Cone-Beam CT (Springer, 2008).

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Figures (13)

Fig. 1
Fig. 1

(a) Computational imaging system versus (b) conventional scanning confocal system. The dashed lines on the sample represent the scanning paths of the focal point as the sample is moved on a translation stage.

Fig. 2
Fig. 2

Geometry of locations of a virtual detector pixel and its physical relationship to the point source, which is assumed to be fixed relative to the detector pixels.

Fig. 3
Fig. 3

Definition of the sample as a complex attenuation function η ( r ) , which includes the point-source amplitudes in the focal plane of the microscope objective.

Fig. 4
Fig. 4

Schematic diagram describing the detector pixels and the focal point locations at three different steps in a one-dimensional confocal scan of a two-dimensional sample. This example shows four pixels of the photodetector array and three scanning points of the object.

Fig. 5
Fig. 5

(a) Matrix representation of the complex data from all pixels over all steps in the scanning process for the example of Fig. 4 for a four-pixel, three-step scan. (b) Rays corresponding to the ( n = 2 ) column of the slant-stack data.

Fig. 6
Fig. 6

Rays corresponding to the ( n = 2 ) column of the slant-stack data with sheared coordinates to obtain vertical projection.

Fig. 7
Fig. 7

Description of a sample-on-mirror system.

Fig. 8
Fig. 8

Schematic diagram of a spatial heterodyne system for detection of the complex amplitude of the signal from the object.

Fig. 9
Fig. 9

Description of the measured sample: (a) three-dimensional view and (b) cross-sectional view.

Fig. 10
Fig. 10

Amplitude of slant stack for the sample of Fig. 9: (a) raw and (b) corrected for deterministic variation.

Fig. 11
Fig. 11

Inverse Radon transform of slant-stack data.

Fig. 12
Fig. 12

Ray between focal point and detector pixel in 3D.

Fig. 13
Fig. 13

Locations of discrete samples in k space on the k x k z plane.

Equations (35)

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

u ( r s , r ) = A 1 | r r s | exp { j [ k | r r s | ] } ,
u ( r s , r p ) = a ( r s , r p ) A 1 | r p r s | exp { j [ k | r p r s | + Δ ϕ ( r s , r p ) ] } ,
u ( r s , r p ) = exp { μ ( r s , r p ) } ,
μ ( r s , r p ) = j [ k | r p r s | + Δ ϕ ( r s , r p ) ] ln a ( r s , r p ) ln A + ln | r p r s | .
μ ( r s , r p ) = μ 0 ( r s , r p ) + μ t ( r s , r p ) ,
μ 0 ( r s , r p ) = j k | r p r s | + ln | r p r s | ,
μ t ( r s , r p ) = j Δ ϕ ( r s , r p ) ln a ( r s , r p ) ln A .
Δ ϕ ( r s , r p ) = r s r p k Δ n ( r ) d s ,
a ( r s , r p ) = exp { r s r p α ( r ) d s } .
μ t ( r s , r p ) = j r s r p k Δ n ( r ) d s + r s r p α ( r ) d s ln A .
r s r p δ ( r r s ) d s = 1 ,
ln A = ( ln A ) r s r p δ ( r r s ) d s .
μ t ( r s , r p ) = r s r p η A ( r , r s ) d s ,
η A ( r , r s ) = j k Δ n ( r ) + α ( r ) δ ( r r s ) ln A .
u ( r s , r p ) = u 0 ( r s , r p ) exp { r s r p η A ( r , r s ) d s } ,
η ( r ) = j k Δ n ( r ) + α ( r ) m = 0 M δ ( r r s ( m ) ) ln A ( m ) ,
r s ( m ) = r s ( 0 ) + m Δ x ,
r p ( m , n ) = r p ( 0 ) + m Δ x + n Δ x ,
u m , n = u 0 ; m , n exp { r s ( 0 ) + m Δ x r p ( 0 ) + m Δ x + n Δ x η ( r ) d s } .
p 0 ( x ) = η ( x , z ) d z .
p θ ( x ) = η ( x z tan θ , z ) d z .
u m , n = ( u 0 ) m , n exp { p θ ( n ) ( m Δ x ) } ,
θ ( n ) = tan 1 ( z p ( 0 ) z s ( 0 ) x p ( 0 ) x s ( 0 ) + n Δ x ) , r s ( 0 ) = ( x s ( 0 ) , z s ( 0 ) ) , r p ( 0 ) = ( x p ( 0 ) , z p ( 0 ) ) .
( x , y , z ) ( x z tan θ x z , y z tan θ y z , z ) ,
x = Ax ,
A θ x z , θ z x ; θ y z , θ z y = ( 1 0 tan θ z x 0 1 tan θ z y tan θ x z tan θ y z 1 ) ,
F ( k ) = F T { f ( x ) } , F ( A θ z x , 0 ; θ z y , 0 k ) = F T { f ( A 0 , θ z x ; 0 , θ z y x ) } .
p 0 ( x , y ) = f ( x , y , z ) d z , P 0 ( k x , k y ) = p 0 ( x , y ) e j [ x k x + y k y ] d x d y , = F ( k x , k y , 0 ) .
g ( x ) = f ( A 0 , θ z x ; 0 , θ z y x ) , = f ( x z tan θ z x , y z tan θ z x , z ) , G ( k ) = F ( A θ z x , 0 ; θ z y , 0 k ) , = F ( k x , k y , k z + k x tan θ z x + k y tan θ z y ) .
p θ ( x , y ) = g ( x , y , z ) d z , P θ ( k x , k y ) = G ( k x , k y , 0 ) , = F ( k x , k y , 0 + k x tan θ z x + k y tan θ z y ) ,
( k x , k y , k z ) = ( ( N Δ ) 1 s , ( N Δ ) 1 t , ( N Δ ) 1 s tan θ z x + ( N Δ ) 1 t tan θ z y ) .
Δ k x Δ k y Δ k z = [ ( N Δ ) 1 ] [ ( N Δ ) 1 ] [ ( N Δ ) 1 s tan Δ θ + ( N Δ ) 1 t tan Δ θ ] , = ( N Δ x ) 3 tan Δ θ ( s + t ) ,
Δ k x Δ k y Δ k z = [ ( N Δ ) 1 ] [ ( N Δ ) 1 ] [ ( N Δ ) 1 s tan Δ θ ( m x ) + ( N Δ ) 1 t tan Δ θ ( m y ) ] ,
Δ k x Δ k y Δ k z = ( N Δ x ) 3 tan Δ θ ( s + t ) .
H ( k ) | k x + k y | .

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