Abstract

A method is presented for imaging single isolated cell nuclei in 3D, employing computed tomographic image reconstruction. The system uses a scanning objective lens to create an extended depth-of-field (DOF) image similar to a projection or shadowgram. A microfabricated inverted v-groove allows a microcapillary tube to be rotated with sub-micron precision, and refractive index matching within 0.02 both inside and outside the tube keeps optical distortion low. Cells or bare cell nuclei are injected into the tube and imaged in 250 angular increments from 0 to 180 degrees to collect 250 extended DOF images. After these images are further aligned, the filtered backprojection algorithm is applied to compute the 3D image. To estimate the cutoff spatial frequency in the projection image, a spatial frequency ratio function is calculated by comparing the extended depth-of-field image of a typical cell nucleus to the fixed focus image. To assess loss of resolution from fixed focus image to extended DOF image to 3D reconstructed image, the 10–90% rise distance is measured for a dyed microsphere. The resolution is found to be 0.9 µm for both extended DOF images and 3D reconstructed images. Surface and translucent volume renderings and cross-sectional slices of the 3D images are shown of a stained nucleus from fibroblast and cancer cell cultures with added color histogram mapping to highlight 3D chromatin structure.

© 2005 Optical Society of America

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2005 (2)

Y. Garini, B. J. Vermolen, and I. T. Young, “From micro to nano: recent advances in high-resolution microscopy,” Current Opinion in Biotechnology 16, 3–12 (2005)
[CrossRef] [PubMed]

J.D. Debes, T.J. Sebo, H.V. Heemers, B.R. Kipp, A.L. Haugen de, C.M. Lohse, and D.J. Tindall. “p300 modulates nuclear morphology in prostate cancer” Cancer Res. 65, 708–12 (2005)
[PubMed]

2004 (2)

D. Zink, A.H. Fischer, and J.A. Nickerson. “Nuclear structure in cancer cells” Nat Rev Cancer 4, 677–87 (2004)
[CrossRef] [PubMed]

L. Vergani, M. Grattarola, and C. Nicolini. “Modifications of chromatin structure and gene expression following induced alterations of cellular shape” Int J Biochem Cell Biol. 36(8), 1447–61 (2004)
[CrossRef]

2003 (1)

P. Matula, M. Kozubek, F. Staier, and M. Hausmann, “Precise 3D image alignment in micro-axial tomography,” J. Microscopy 209(2), 126–142 (2003)
[CrossRef]

2002 (3)

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] [PubMed]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microscopy 205, 165–176 (2002)
[CrossRef]

R. Heintzmann and C. Cremer, “Axial tomographic confocal fluorescence microscopy,” J. Microscopy 206(1), 7–23 (2002)
[CrossRef]

2000 (1)

G.S. Stein, M. Montecino, A.J. van Wijnen, J.L. Stein, and J.B. Lian. “Nuclear structure-gene expression interrelationships: implications for aberrant gene expression in cancer” Cancer Res. 60, 2067–76 (2000)
[PubMed]

1997 (1)

1996 (1)

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

1995 (1)

1994 (2)

E.H.K. Stelzer and S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111(5–6), 536–547 (1994)
[CrossRef]

S. Kikuchi, K. Sonobe, L. S. Sidharta, and N. Ohyama, “Three-dimensional computed tomography for optical microscopes,” Opt. Commun. 107: 432–444 (1994)
[CrossRef]

1992 (1)

J. Bradl, M. Hausmann, B. Schneider, B. Rinke, and C. Cremer, “A versatile 2D-tilting device for fluorescence microscopes,” J. Microscopy 176(3): 211–221 (1992)

1989 (1)

P.J. Shaw, D.A. Agard, Y. Hiraoko, and J.W. Sedat, “Tilted view reconstruction in optical microscopy, three-dimensional reconstruction of Drosophila melanogaster embryo nuclei,” Biophys. J. 55:101–110 (1989)
[CrossRef] [PubMed]

1987 (1)

S. Kawata, O. Nakamura, and S. Minami, “Optical microscope tomography. I. Support constraint,” J. Opt. Soc. Am. A,  4(1), 292–297 (1987)
[CrossRef]

1983 (1)

D. Wittekind, E.R. Reinhardt, V. Kretschmer, and E. Zipfel “Influence of staining on fast automated cell segmentation, feature extraction, and cell image analysis” Anal. Quant. Cytol. 5 (1), 55–60 (1983)
[PubMed]

1972 (1)

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

1949 (1)

M.L. Barr and E.G. Bertram, “A morphological distinction between neurons of the male and female, and the behavior of the nuclear satellite during accelerated nucleoprotein synthesis,” Nature 163, 676–677 (1949)
[CrossRef] [PubMed]

Agard, D.A.

P.J. Shaw, D.A. Agard, Y. Hiraoko, and J.W. Sedat, “Tilted view reconstruction in optical microscopy, three-dimensional reconstruction of Drosophila melanogaster embryo nuclei,” Biophys. J. 55:101–110 (1989)
[CrossRef] [PubMed]

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] [PubMed]

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] [PubMed]

Barr, M.L.

M.L. Barr and E.G. Bertram, “A morphological distinction between neurons of the male and female, and the behavior of the nuclear satellite during accelerated nucleoprotein synthesis,” Nature 163, 676–677 (1949)
[CrossRef] [PubMed]

Bertram, E.G.

M.L. Barr and E.G. Bertram, “A morphological distinction between neurons of the male and female, and the behavior of the nuclear satellite during accelerated nucleoprotein synthesis,” Nature 163, 676–677 (1949)
[CrossRef] [PubMed]

Bradburn, S.

Bradl, J.

J. Bradl, M. Hausmann, B. Schneider, B. Rinke, and C. Cremer, “A versatile 2D-tilting device for fluorescence microscopes,” J. Microscopy 176(3): 211–221 (1992)

Cathey, W.T.

Chamgoulov, R.O.

R.O. Chamgoulov, P.M. Lane, and C.E. MacAulay, “Optical computed-tomography microscope using digital spatial light modulation,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing, XI, J.-A. Conchello, C.J. Cogswell, and T. Wilson, eds., Proc. SPIE5324, 182–190 (2004)

Cremer, C.

R. Heintzmann and C. Cremer, “Axial tomographic confocal fluorescence microscopy,” J. Microscopy 206(1), 7–23 (2002)
[CrossRef]

J. Bradl, M. Hausmann, B. Schneider, B. Rinke, and C. Cremer, “A versatile 2D-tilting device for fluorescence microscopes,” J. Microscopy 176(3): 211–221 (1992)

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] [PubMed]

Debes, J.D.

J.D. Debes, T.J. Sebo, H.V. Heemers, B.R. Kipp, A.L. Haugen de, C.M. Lohse, and D.J. Tindall. “p300 modulates nuclear morphology in prostate cancer” Cancer Res. 65, 708–12 (2005)
[PubMed]

Dowski, E. R.

Fauver, M.

M. Fauver, E. J. Seibel, J.R. Rahn, F.W. Patten, and A.C. Nelson, “Micro optical tomography system,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing, XI, J.-A. Conchello, C.J. Cogswell, and T. Wilson, eds., Proc. SPIE5324, 171–181 (2004)

Fischer, A.H.

D. Zink, A.H. Fischer, and J.A. Nickerson. “Nuclear structure in cancer cells” Nat Rev Cancer 4, 677–87 (2004)
[CrossRef] [PubMed]

Garini, Y.

Y. Garini, B. J. Vermolen, and I. T. Young, “From micro to nano: recent advances in high-resolution microscopy,” Current Opinion in Biotechnology 16, 3–12 (2005)
[CrossRef] [PubMed]

Grattarola, M.

L. Vergani, M. Grattarola, and C. Nicolini. “Modifications of chromatin structure and gene expression following induced alterations of cellular shape” Int J Biochem Cell Biol. 36(8), 1447–61 (2004)
[CrossRef]

Haugen de, A.L.

J.D. Debes, T.J. Sebo, H.V. Heemers, B.R. Kipp, A.L. Haugen de, C.M. Lohse, and D.J. Tindall. “p300 modulates nuclear morphology in prostate cancer” Cancer Res. 65, 708–12 (2005)
[PubMed]

Häusler, G.

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

Hausmann, M.

P. Matula, M. Kozubek, F. Staier, and M. Hausmann, “Precise 3D image alignment in micro-axial tomography,” J. Microscopy 209(2), 126–142 (2003)
[CrossRef]

J. Bradl, M. Hausmann, B. Schneider, B. Rinke, and C. Cremer, “A versatile 2D-tilting device for fluorescence microscopes,” J. Microscopy 176(3): 211–221 (1992)

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] [PubMed]

Heemers, H.V.

J.D. Debes, T.J. Sebo, H.V. Heemers, B.R. Kipp, A.L. Haugen de, C.M. Lohse, and D.J. Tindall. “p300 modulates nuclear morphology in prostate cancer” Cancer Res. 65, 708–12 (2005)
[PubMed]

Heintzmann, R.

R. Heintzmann and C. Cremer, “Axial tomographic confocal fluorescence microscopy,” J. Microscopy 206(1), 7–23 (2002)
[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] [PubMed]

Hiraoko, Y.

P.J. Shaw, D.A. Agard, Y. Hiraoko, and J.W. Sedat, “Tilted view reconstruction in optical microscopy, three-dimensional reconstruction of Drosophila melanogaster embryo nuclei,” Biophys. J. 55:101–110 (1989)
[CrossRef] [PubMed]

Inoue, S.

S. Inoue and K. Spring, Video Microscopy: the fundamentals2nd Ed. (Plenum Press, New York, 1997)
[CrossRef]

Kak, A.C.

A.C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988)

Kawata, S.

S. Kawata, O. Nakamura, and S. Minami, “Optical microscope tomography. I. Support constraint,” J. Opt. Soc. Am. A,  4(1), 292–297 (1987)
[CrossRef]

Kazuo, S.

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

Kikuchi, S.

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

S. Kikuchi, K. Sonobe, L. S. Sidharta, and N. Ohyama, “Three-dimensional computed tomography for optical microscopes,” Opt. Commun. 107: 432–444 (1994)
[CrossRef]

Kipp, B.R.

J.D. Debes, T.J. Sebo, H.V. Heemers, B.R. Kipp, A.L. Haugen de, C.M. Lohse, and D.J. Tindall. “p300 modulates nuclear morphology in prostate cancer” Cancer Res. 65, 708–12 (2005)
[PubMed]

Kozubek, M.

P. Matula, M. Kozubek, F. Staier, and M. Hausmann, “Precise 3D image alignment in micro-axial tomography,” J. Microscopy 209(2), 126–142 (2003)
[CrossRef]

Kretschmer, V.

D. Wittekind, E.R. Reinhardt, V. Kretschmer, and E. Zipfel “Influence of staining on fast automated cell segmentation, feature extraction, and cell image analysis” Anal. Quant. Cytol. 5 (1), 55–60 (1983)
[PubMed]

Lane, P.M.

R.O. Chamgoulov, P.M. Lane, and C.E. MacAulay, “Optical computed-tomography microscope using digital spatial light modulation,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing, XI, J.-A. Conchello, C.J. Cogswell, and T. Wilson, eds., Proc. SPIE5324, 182–190 (2004)

Lauer, V.

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microscopy 205, 165–176 (2002)
[CrossRef]

Lian, J.B.

G.S. Stein, M. Montecino, A.J. van Wijnen, J.L. Stein, and J.B. Lian. “Nuclear structure-gene expression interrelationships: implications for aberrant gene expression in cancer” Cancer Res. 60, 2067–76 (2000)
[PubMed]

Lindek, S.

E.H.K. Stelzer and S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111(5–6), 536–547 (1994)
[CrossRef]

Lohse, C.M.

J.D. Debes, T.J. Sebo, H.V. Heemers, B.R. Kipp, A.L. Haugen de, C.M. Lohse, and D.J. Tindall. “p300 modulates nuclear morphology in prostate cancer” Cancer Res. 65, 708–12 (2005)
[PubMed]

MacAulay, C.E.

R.O. Chamgoulov, P.M. Lane, and C.E. MacAulay, “Optical computed-tomography microscope using digital spatial light modulation,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing, XI, J.-A. Conchello, C.J. Cogswell, and T. Wilson, eds., Proc. SPIE5324, 182–190 (2004)

Matula, P.

P. Matula, M. Kozubek, F. Staier, and M. Hausmann, “Precise 3D image alignment in micro-axial tomography,” J. Microscopy 209(2), 126–142 (2003)
[CrossRef]

Minami, S.

S. Kawata, O. Nakamura, and S. Minami, “Optical microscope tomography. I. Support constraint,” J. Opt. Soc. Am. A,  4(1), 292–297 (1987)
[CrossRef]

Montecino, M.

G.S. Stein, M. Montecino, A.J. van Wijnen, J.L. Stein, and J.B. Lian. “Nuclear structure-gene expression interrelationships: implications for aberrant gene expression in cancer” Cancer Res. 60, 2067–76 (2000)
[PubMed]

Nakamura, O.

S. Kawata, O. Nakamura, and S. Minami, “Optical microscope tomography. I. Support constraint,” J. Opt. Soc. Am. A,  4(1), 292–297 (1987)
[CrossRef]

Nelson, A.C.

M. Fauver, E. J. Seibel, J.R. Rahn, F.W. Patten, and A.C. Nelson, “Micro optical tomography system,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing, XI, J.-A. Conchello, C.J. Cogswell, and T. Wilson, eds., Proc. SPIE5324, 171–181 (2004)

Nickerson, J.A.

D. Zink, A.H. Fischer, and J.A. Nickerson. “Nuclear structure in cancer cells” Nat Rev Cancer 4, 677–87 (2004)
[CrossRef] [PubMed]

Nicolini, C.

L. Vergani, M. Grattarola, and C. Nicolini. “Modifications of chromatin structure and gene expression following induced alterations of cellular shape” Int J Biochem Cell Biol. 36(8), 1447–61 (2004)
[CrossRef]

Ohyama, N.

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

S. Kikuchi, K. Sonobe, L. S. Sidharta, and N. Ohyama, “Three-dimensional computed tomography for optical microscopes,” Opt. Commun. 107: 432–444 (1994)
[CrossRef]

Patten, F.W.

M. Fauver, E. J. Seibel, J.R. Rahn, F.W. Patten, and A.C. Nelson, “Micro optical tomography system,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing, XI, J.-A. Conchello, C.J. Cogswell, and T. Wilson, eds., Proc. SPIE5324, 171–181 (2004)

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] [PubMed]

Rahn, J.R.

M. Fauver, E. J. Seibel, J.R. Rahn, F.W. Patten, and A.C. Nelson, “Micro optical tomography system,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing, XI, J.-A. Conchello, C.J. Cogswell, and T. Wilson, eds., Proc. SPIE5324, 171–181 (2004)

Reinhardt, E.R.

D. Wittekind, E.R. Reinhardt, V. Kretschmer, and E. Zipfel “Influence of staining on fast automated cell segmentation, feature extraction, and cell image analysis” Anal. Quant. Cytol. 5 (1), 55–60 (1983)
[PubMed]

Rinke, B.

J. Bradl, M. Hausmann, B. Schneider, B. Rinke, and C. Cremer, “A versatile 2D-tilting device for fluorescence microscopes,” J. Microscopy 176(3): 211–221 (1992)

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] [PubMed]

Russ, J.C.

J.C. Russ, The Image Processing Handbook, 4th Ed. (RC Press, New York, 2002)

Schneider, B.

J. Bradl, M. Hausmann, B. Schneider, B. Rinke, and C. Cremer, “A versatile 2D-tilting device for fluorescence microscopes,” J. Microscopy 176(3): 211–221 (1992)

Sebo, T.J.

J.D. Debes, T.J. Sebo, H.V. Heemers, B.R. Kipp, A.L. Haugen de, C.M. Lohse, and D.J. Tindall. “p300 modulates nuclear morphology in prostate cancer” Cancer Res. 65, 708–12 (2005)
[PubMed]

Sedat, J.W.

P.J. Shaw, D.A. Agard, Y. Hiraoko, and J.W. Sedat, “Tilted view reconstruction in optical microscopy, three-dimensional reconstruction of Drosophila melanogaster embryo nuclei,” Biophys. J. 55:101–110 (1989)
[CrossRef] [PubMed]

Seibel, E. J.

M. Fauver, E. J. Seibel, J.R. Rahn, F.W. Patten, and A.C. Nelson, “Micro optical tomography system,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing, XI, J.-A. Conchello, C.J. Cogswell, and T. Wilson, eds., Proc. SPIE5324, 171–181 (2004)

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] [PubMed]

Shaw, P.J.

P.J. Shaw, D.A. Agard, Y. Hiraoko, and J.W. Sedat, “Tilted view reconstruction in optical microscopy, three-dimensional reconstruction of Drosophila melanogaster embryo nuclei,” Biophys. J. 55:101–110 (1989)
[CrossRef] [PubMed]

Sheppard, C.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic Press, London, 1984)

Sidharta, L. S.

S. Kikuchi, K. Sonobe, L. S. Sidharta, and N. Ohyama, “Three-dimensional computed tomography for optical microscopes,” Opt. Commun. 107: 432–444 (1994)
[CrossRef]

Slaney, M.

A.C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988)

Sonobe, K.

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G.S. Stein, M. Montecino, A.J. van Wijnen, J.L. Stein, and J.B. Lian. “Nuclear structure-gene expression interrelationships: implications for aberrant gene expression in cancer” Cancer Res. 60, 2067–76 (2000)
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G.S. Stein, M. Montecino, A.J. van Wijnen, J.L. Stein, and J.B. Lian. “Nuclear structure-gene expression interrelationships: implications for aberrant gene expression in cancer” Cancer Res. 60, 2067–76 (2000)
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Supplementary Material (6)

» Media 1: AVI (727 KB)     
» Media 2: AVI (1102 KB)     
» Media 3: AVI (1127 KB)     
» Media 4: AVI (545 KB)     
» Media 5: AVI (554 KB)     
» Media 6: AVI (471 KB)     

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Figures (13)

Fig. 1.
Fig. 1.

Schematic of optical projection tomography microscope (OPTM)

Fig. 2.
Fig. 2.

Comparison of standard slide mounting with microcapillary-based stage

Fig. 3.
Fig. 3.

Refractive index differences versus illumination wavelength for the microcapillary-based viewing stage

Fig. 4.
Fig. 4.

Extending depth of field for high NA objective to create a pseudoprojection

Fig. 5.
Fig. 5.

Example graph of 10–90% rise distance measurement

Fig. 6.
Fig. 6.

A lung cancer cell nucleus: the pseudoprojection (10 µm focal range, right) and the fixed-focal plane image (left) used for comparison

Fig. 7.
Fig. 7.

Profile of the radially symmetric SFRF obtained by comparing the pseudoprojection of a lung cancer nucleus to its fixed focal plane image. The solid line (blue) denotes a 10 µm scan range, the dashed line (yellow) a 20 µm scan range, and the dotted line (pink) a 40 µm scan range

Fig. 8.
Fig. 8.

Microsphere surface view (728 KB avi)

Fig. 9.
Fig. 9.

Normal lung fibroblast cell nucleus surface view (1.10 MB avi)

Fig. 10.
Fig. 10.

Normal lung fibroblast cell nucleus transparent view (1.13 MB avi)

Fig. 11.
Fig. 11.

Normal lung fibroblast cell nucleus slice view (546 KB avi)

Fig. 12.
Fig. 12.

A549 cancer cell nucleus surface view (554 KB avi)

Fig. 13.
Fig. 13.

A549 cancer cell nucleus slice view (472 KB avi)

Tables (1)

Tables Icon

Table 1. Diameter measurements and 10–90% rise distance for a single microsphere

Equations (2)

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

SFRF = < FT ( pseudoprojection ) > angle < FT ( fixed _ focus _ image ) > angle
D = 1.22 λ ( NA obj + NA cond )

Metrics