Abstract

To achieve approximately parallel projection geometry, traditional optical projection tomography (OPT) requires the use of low numerical aperture (NA) objectives, which have a long depth-of-field at the expense of poor lateral resolution. Particularly promising methods to improve spatial resolution include ad-hoc post-processing filters that limit the effect of the system’s MTF and focal-plane-scanning OPT (FPS-OPT), an alternative acquisition procedure that allows the use of higher NA objectives by limiting the effect of their shallow depth of field yet still assumes parallel projection rays during reconstruction. Here, we provide a detailed derivation that establishes the existence of a direct inversion formula for FPS-OPT. Based on this formula, we propose a point spread function-aware algorithm that is similar in form and complexity to traditional filtered backprojection (FBP). With simulations, we demonstrate that our point-spread-function aware FBP for FPS-OPT leads to more accurate images than both traditional OPT with deconvolution and FPS-OPT with naive FBP reconstruction. We further illustrate the technique on experimental zebrafish data, which shows that our approach reduces out-of-focus blur compared to a direct FBP reconstruction with FPS-OPT.

© 2017 Optical Society of America

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References

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  1. J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
    [Crossref] [PubMed]
  2. R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
    [Crossref] [PubMed]
  3. M. Fauver, E. J. Seibel, J. R. Rahn, M. G. Meyer, F. W. Patten, T. Neumann, and A. C. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express 13(11), 4210–4223 (2005).
    [Crossref] [PubMed]
  4. Q. Miao, J. Hayenga, M. G. Meyer, T. Neumann, A. C. Nelson, and E. J. Seibel, “Resolution improvement in optical projection tomography by the focal scanning method,” Opt. Letters 35(20), 3363–3365 (2010).
    [Crossref]
  5. A. Bassi, B. Schmid, and J. Huisken, “Optical tomography complements light sheet microscopy for in toto imaging of zebrafish development,” Development 142(5), 1016–1020 (2015).
    [Crossref] [PubMed]
  6. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE1988).
  7. J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Resolution improvement in emission optical projection tomography,” Phys. Med. Biol. 52(10), 2775–2790 (2007).
    [Crossref] [PubMed]
  8. L. Chen, J. McGinty, H. B. Taylor, L. Bugeon, J. R. Lamb, M. J. Dallman, and P. M. W. French, “Incorporation of an experimentally determined MTF for spatial frequency filtering and deconvolution during optical projection tomography reconstruction,” Opt. Express 20(7), 7323–7337 (2012).
    [Crossref] [PubMed]
  9. J. Guo, Y. Yang, D. Dong, L. Shi, H. Hui, M. Xu, J. Tian, and X. Liu, “A projection selection method to improve image quality in optical projection tomography,” in International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2014), pp. 206–209.
  10. J. van der Horst and J. Kalkman, “Image resolution and deconvolution in optical tomography,” Opt. Express 24(21), 24460–24472 (2016).
    [Crossref] [PubMed]
  11. U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
    [Crossref]
  12. K. G. Chan and M. Liebling, “A point-spread-function-aware filtered backprojection algorithm for focal-plane-scanning optical projection tomography,” International Symposium on Biomedical Imaging (IEEE, 2016), pp. 253–256.
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    [Crossref] [PubMed]
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    [Crossref]
  15. M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 2003), Chap. 8.
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    [Crossref]
  17. S. G. Azevedo, D. J. Schneberk, J. Fitch, and H. E. Martz, “Calculation of the rotational centers in computerized tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
    [Crossref]
  18. U. J. Birk, M. Rieckher, N. Konstantinides, A. Darrell, A. Sarasa-Renedo, H. Meyer, N. Tavernarakis, and J. Ripoll, “Correction for specimen movement and rotation errors for in-vivo Optical Projection Tomography,” Biomed. Opt. Express 1(1), 87–96 (2010).
    [Crossref]
  19. D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
    [Crossref] [PubMed]

2017 (1)

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

2016 (2)

J. van der Horst and J. Kalkman, “Image resolution and deconvolution in optical tomography,” Opt. Express 24(21), 24460–24472 (2016).
[Crossref] [PubMed]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

2015 (1)

A. Bassi, B. Schmid, and J. Huisken, “Optical tomography complements light sheet microscopy for in toto imaging of zebrafish development,” Development 142(5), 1016–1020 (2015).
[Crossref] [PubMed]

2013 (1)

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249(1), 13–25 (2013).
[Crossref]

2012 (1)

2010 (2)

U. J. Birk, M. Rieckher, N. Konstantinides, A. Darrell, A. Sarasa-Renedo, H. Meyer, N. Tavernarakis, and J. Ripoll, “Correction for specimen movement and rotation errors for in-vivo Optical Projection Tomography,” Biomed. Opt. Express 1(1), 87–96 (2010).
[Crossref]

Q. Miao, J. Hayenga, M. G. Meyer, T. Neumann, A. C. Nelson, and E. J. Seibel, “Resolution improvement in optical projection tomography by the focal scanning method,” Opt. Letters 35(20), 3363–3365 (2010).
[Crossref]

2007 (2)

J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Resolution improvement in emission optical projection tomography,” Phys. Med. Biol. 52(10), 2775–2790 (2007).
[Crossref] [PubMed]

R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
[Crossref] [PubMed]

2005 (1)

2002 (2)

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
[Crossref] [PubMed]

S. Horbelt, M. Liebling, and M. Unser, “Discretization of the Radon transform and of its inverse by spline convolution,” IEEE Trans. Med. Imag. 21(4) 363–376 (2002).
[Crossref]

1997 (1)

Z. P. Liang and D. C. Munson, “Partial Radon transforms,” IEEE Trans. Image Process. 6(10), 1467–1469 (1997).
[Crossref] [PubMed]

1990 (1)

S. G. Azevedo, D. J. Schneberk, J. Fitch, and H. E. Martz, “Calculation of the rotational centers in computerized tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[Crossref]

Aguet, F.

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249(1), 13–25 (2013).
[Crossref]

Ahlgren, U.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
[Crossref] [PubMed]

Azevedo, S. G.

S. G. Azevedo, D. J. Schneberk, J. Fitch, and H. E. Martz, “Calculation of the rotational centers in computerized tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[Crossref]

Baldock, R.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
[Crossref] [PubMed]

Bassi, A.

A. Bassi, B. Schmid, and J. Huisken, “Optical tomography complements light sheet microscopy for in toto imaging of zebrafish development,” Development 142(5), 1016–1020 (2015).
[Crossref] [PubMed]

Berger, S.

R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
[Crossref] [PubMed]

Birk, U. J.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 2003), Chap. 8.

Bryson-Richardson, R. J.

R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
[Crossref] [PubMed]

Bugeon, L.

Chan, K. G.

K. G. Chan and M. Liebling, “A point-spread-function-aware filtered backprojection algorithm for focal-plane-scanning optical projection tomography,” International Symposium on Biomedical Imaging (IEEE, 2016), pp. 253–256.

Chen, L.

Cole, N. J.

R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
[Crossref] [PubMed]

Currie, P. D.

R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
[Crossref] [PubMed]

Dallman, M. J.

Darrell, A.

Davidson, D.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
[Crossref] [PubMed]

Donati, L.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Dong, D.

J. Guo, Y. Yang, D. Dong, L. Shi, H. Hui, M. Xu, J. Tian, and X. Liu, “A projection selection method to improve image quality in optical projection tomography,” in International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2014), pp. 206–209.

Fauver, M.

Fitch, J.

S. G. Azevedo, D. J. Schneberk, J. Fitch, and H. E. Martz, “Calculation of the rotational centers in computerized tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[Crossref]

Fortun, D.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

French, P. M. W.

Gibson, A. J.

R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
[Crossref] [PubMed]

Goy, A.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Guiet, R.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Guo, J.

J. Guo, Y. Yang, D. Dong, L. Shi, H. Hui, M. Xu, J. Tian, and X. Liu, “A projection selection method to improve image quality in optical projection tomography,” in International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2014), pp. 206–209.

Hall, T. E.

R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
[Crossref] [PubMed]

Hayenga, J.

Q. Miao, J. Hayenga, M. G. Meyer, T. Neumann, A. C. Nelson, and E. J. Seibel, “Resolution improvement in optical projection tomography by the focal scanning method,” Opt. Letters 35(20), 3363–3365 (2010).
[Crossref]

Hecksher-Sørensen, J.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
[Crossref] [PubMed]

Henkelman, R. M.

J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Resolution improvement in emission optical projection tomography,” Phys. Med. Biol. 52(10), 2775–2790 (2007).
[Crossref] [PubMed]

Hill, B.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
[Crossref] [PubMed]

Horbelt, S.

S. Horbelt, M. Liebling, and M. Unser, “Discretization of the Radon transform and of its inverse by spline convolution,” IEEE Trans. Med. Imag. 21(4) 363–376 (2002).
[Crossref]

Hui, H.

J. Guo, Y. Yang, D. Dong, L. Shi, H. Hui, M. Xu, J. Tian, and X. Liu, “A projection selection method to improve image quality in optical projection tomography,” in International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2014), pp. 206–209.

Huisken, J.

A. Bassi, B. Schmid, and J. Huisken, “Optical tomography complements light sheet microscopy for in toto imaging of zebrafish development,” Development 142(5), 1016–1020 (2015).
[Crossref] [PubMed]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE1988).

Kalkman, J.

Kamilov, U. S.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Kirshner, H.

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249(1), 13–25 (2013).
[Crossref]

Konstantinides, N.

Lamb, J. R.

Liang, Z. P.

Z. P. Liang and D. C. Munson, “Partial Radon transforms,” IEEE Trans. Image Process. 6(10), 1467–1469 (1997).
[Crossref] [PubMed]

Liebling, M.

S. Horbelt, M. Liebling, and M. Unser, “Discretization of the Radon transform and of its inverse by spline convolution,” IEEE Trans. Med. Imag. 21(4) 363–376 (2002).
[Crossref]

K. G. Chan and M. Liebling, “A point-spread-function-aware filtered backprojection algorithm for focal-plane-scanning optical projection tomography,” International Symposium on Biomedical Imaging (IEEE, 2016), pp. 253–256.

Liu, X.

J. Guo, Y. Yang, D. Dong, L. Shi, H. Hui, M. Xu, J. Tian, and X. Liu, “A projection selection method to improve image quality in optical projection tomography,” in International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2014), pp. 206–209.

Martz, H. E.

S. G. Azevedo, D. J. Schneberk, J. Fitch, and H. E. Martz, “Calculation of the rotational centers in computerized tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[Crossref]

McGinty, J.

Meyer, H.

Meyer, M. G.

Q. Miao, J. Hayenga, M. G. Meyer, T. Neumann, A. C. Nelson, and E. J. Seibel, “Resolution improvement in optical projection tomography by the focal scanning method,” Opt. Letters 35(20), 3363–3365 (2010).
[Crossref]

M. Fauver, E. J. Seibel, J. R. Rahn, M. G. Meyer, F. W. Patten, T. Neumann, and A. C. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express 13(11), 4210–4223 (2005).
[Crossref] [PubMed]

Miao, Q.

Q. Miao, J. Hayenga, M. G. Meyer, T. Neumann, A. C. Nelson, and E. J. Seibel, “Resolution improvement in optical projection tomography by the focal scanning method,” Opt. Letters 35(20), 3363–3365 (2010).
[Crossref]

Munson, D. C.

Z. P. Liang and D. C. Munson, “Partial Radon transforms,” IEEE Trans. Image Process. 6(10), 1467–1469 (1997).
[Crossref] [PubMed]

Nelson, A. C.

Q. Miao, J. Hayenga, M. G. Meyer, T. Neumann, A. C. Nelson, and E. J. Seibel, “Resolution improvement in optical projection tomography by the focal scanning method,” Opt. Letters 35(20), 3363–3365 (2010).
[Crossref]

M. Fauver, E. J. Seibel, J. R. Rahn, M. G. Meyer, F. W. Patten, T. Neumann, and A. C. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express 13(11), 4210–4223 (2005).
[Crossref] [PubMed]

Neumann, T.

Q. Miao, J. Hayenga, M. G. Meyer, T. Neumann, A. C. Nelson, and E. J. Seibel, “Resolution improvement in optical projection tomography by the focal scanning method,” Opt. Letters 35(20), 3363–3365 (2010).
[Crossref]

M. Fauver, E. J. Seibel, J. R. Rahn, M. G. Meyer, F. W. Patten, T. Neumann, and A. C. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express 13(11), 4210–4223 (2005).
[Crossref] [PubMed]

Papadopoulos, I. N.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Patten, F. W.

Perry, P.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
[Crossref] [PubMed]

Psaltis, D.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Rahn, J. R.

Rieckher, M.

Ripoll, J.

Ross, A.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
[Crossref] [PubMed]

Sage, D.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249(1), 13–25 (2013).
[Crossref]

Sarasa-Renedo, A.

Schilling, T. F.

R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
[Crossref] [PubMed]

Schmid, B.

A. Bassi, B. Schmid, and J. Huisken, “Optical tomography complements light sheet microscopy for in toto imaging of zebrafish development,” Development 142(5), 1016–1020 (2015).
[Crossref] [PubMed]

Schmit, G.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Schneberk, D. J.

S. G. Azevedo, D. J. Schneberk, J. Fitch, and H. E. Martz, “Calculation of the rotational centers in computerized tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[Crossref]

Seibel, E. J.

Q. Miao, J. Hayenga, M. G. Meyer, T. Neumann, A. C. Nelson, and E. J. Seibel, “Resolution improvement in optical projection tomography by the focal scanning method,” Opt. Letters 35(20), 3363–3365 (2010).
[Crossref]

M. Fauver, E. J. Seibel, J. R. Rahn, M. G. Meyer, F. W. Patten, T. Neumann, and A. C. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express 13(11), 4210–4223 (2005).
[Crossref] [PubMed]

Seitz, A.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Sharpe, J.

J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Resolution improvement in emission optical projection tomography,” Phys. Med. Biol. 52(10), 2775–2790 (2007).
[Crossref] [PubMed]

R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
[Crossref] [PubMed]

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
[Crossref] [PubMed]

Shi, L.

J. Guo, Y. Yang, D. Dong, L. Shi, H. Hui, M. Xu, J. Tian, and X. Liu, “A projection selection method to improve image quality in optical projection tomography,” in International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2014), pp. 206–209.

Shoreh, M. H.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE1988).

Sled, J. G.

J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Resolution improvement in emission optical projection tomography,” Phys. Med. Biol. 52(10), 2775–2790 (2007).
[Crossref] [PubMed]

Soulez, F.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Tavernarakis, N.

Taylor, H. B.

Tian, J.

J. Guo, Y. Yang, D. Dong, L. Shi, H. Hui, M. Xu, J. Tian, and X. Liu, “A projection selection method to improve image quality in optical projection tomography,” in International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2014), pp. 206–209.

Unser, M.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249(1), 13–25 (2013).
[Crossref]

S. Horbelt, M. Liebling, and M. Unser, “Discretization of the Radon transform and of its inverse by spline convolution,” IEEE Trans. Med. Imag. 21(4) 363–376 (2002).
[Crossref]

van der Horst, J.

Vonesch, C.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Walls, J. R.

J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Resolution improvement in emission optical projection tomography,” Phys. Med. Biol. 52(10), 2775–2790 (2007).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 2003), Chap. 8.

Xu, M.

J. Guo, Y. Yang, D. Dong, L. Shi, H. Hui, M. Xu, J. Tian, and X. Liu, “A projection selection method to improve image quality in optical projection tomography,” in International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2014), pp. 206–209.

Yang, Y.

J. Guo, Y. Yang, D. Dong, L. Shi, H. Hui, M. Xu, J. Tian, and X. Liu, “A projection selection method to improve image quality in optical projection tomography,” in International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2014), pp. 206–209.

Biomed. Opt. Express (1)

BMC Biol. (1)

R. J. Bryson-Richardson, S. Berger, T. F. Schilling, T. E. Hall, N. J. Cole, A. J. Gibson, J. Sharpe, and P. D. Currie, “FishNet: an online database of zebrafish anatomy,” BMC Biol. 5(1) 34 (2007).
[Crossref] [PubMed]

Development (1)

A. Bassi, B. Schmid, and J. Huisken, “Optical tomography complements light sheet microscopy for in toto imaging of zebrafish development,” Development 142(5), 1016–1020 (2015).
[Crossref] [PubMed]

IEEE Trans. Comput. Imag. (1)

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

IEEE Trans. Image Process. (1)

Z. P. Liang and D. C. Munson, “Partial Radon transforms,” IEEE Trans. Image Process. 6(10), 1467–1469 (1997).
[Crossref] [PubMed]

IEEE Trans. Med. Imag. (1)

S. Horbelt, M. Liebling, and M. Unser, “Discretization of the Radon transform and of its inverse by spline convolution,” IEEE Trans. Med. Imag. 21(4) 363–376 (2002).
[Crossref]

IEEE Trans. Nucl. Sci. (1)

S. G. Azevedo, D. J. Schneberk, J. Fitch, and H. E. Martz, “Calculation of the rotational centers in computerized tomography sinograms,” IEEE Trans. Nucl. Sci. 37(4), 1525–1540 (1990).
[Crossref]

J. Microsc. (1)

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249(1), 13–25 (2013).
[Crossref]

Methods (1)

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Letters (1)

Q. Miao, J. Hayenga, M. G. Meyer, T. Neumann, A. C. Nelson, and E. J. Seibel, “Resolution improvement in optical projection tomography by the focal scanning method,” Opt. Letters 35(20), 3363–3365 (2010).
[Crossref]

Phys. Med. Biol. (1)

J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Resolution improvement in emission optical projection tomography,” Phys. Med. Biol. 52(10), 2775–2790 (2007).
[Crossref] [PubMed]

Science (1)

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002).
[Crossref] [PubMed]

Other (4)

J. Guo, Y. Yang, D. Dong, L. Shi, H. Hui, M. Xu, J. Tian, and X. Liu, “A projection selection method to improve image quality in optical projection tomography,” in International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2014), pp. 206–209.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE1988).

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 2003), Chap. 8.

K. G. Chan and M. Liebling, “A point-spread-function-aware filtered backprojection algorithm for focal-plane-scanning optical projection tomography,” International Symposium on Biomedical Imaging (IEEE, 2016), pp. 253–256.

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Figures (6)

Fig. 1
Fig. 1 (a) In ideal tomography, acquisitions are assumed to be straight line projections through the entire object. Here, a projection in the direction parallel to a vector θ̂ = shown for an OPT system with an axis of rotation parallel to the z-axis. (b) In traditional OPT, acquisitions are better described as the result of the 3D convolution between the object and the PSF, sampled on a single focal plane. (c) In FPS-OPT, each acquisition is obtained by summing up images obtained while scanning through all focal planes.
Fig. 2
Fig. 2 The Fourier transform of an object’s projection is equivalent to a slice from the underlying object’s Fourier transform. The inclusion of the system’s point spread function introduces an extra convolution in space, or equivalently, an extra multiplication in the Fourier domain.
Fig. 3
Fig. 3 In practice, our PSF-aware filtered backprojection algorithm is implemented as two-step process consisting of an initial PSF inverse filtering followed by traditional filtered backprojection.
Fig. 4
Fig. 4 Using point spread functions generated with numerical apertures of (a,f) 0.3 and (k,p) 0.5, we compared the following reconstruction algorithms: (b,g,l,q) traditional FBP under fixed-plane OPT, (c,h,m,r) MTF deconvolution [8] under fixed-plane OPT, (d,i,n,s) traditional FBP under FPS-OPT, and (e,j,o,t) our proposed PSF-aware FBP under FPS-OPT. (b–e) Reconstructions under the 0.3 NA PSF in (a,f) with a small phantom and no noise. (g–j) Reconstructions under the 0.3 NA PSF in (a,f) with a phantom larger than the depth-of-field and no noise. (l–o) Reconstructions under the 0.5 NA PSF in (k,p) with a phantom much larger than the depth-of-field and no noise. (q–t) Reconstructions under the 0.5 NA PSF in (k,p) with a phantom much larger than the depth-of-field and with projections corrupted by shot noise. Specifically, for each observed projection, the measured value y at any given detector followed a Poisson distribution y ∼ Poisson(x), where x was the deterministic (noise-free) projection value at that detector, scaled so all deterministic projection values were in the interval [0, 104].
Fig. 5
Fig. 5 Diagram of the OPT rotational acquisition procedure for zebrafish. For each projection angle θ, the focal plane is scanned through the entire zebrafish to create a full projection, even with a shallow depth-of-field objective.
Fig. 6
Fig. 6 We used focal plane scanning OPT (FPS-OPT) to image the head of a Tg(fli1a:eGFP) zebrafish in 3D fluorescence with a 10 ×/0.3 NA air objective. Under such conditions, single-plane OPT would be unable to produce an acceptable reconstruction due to the large sample thickness and shallow depth-of-field. With FPS-OPT, we compare 3D reconstructions from (a) standard filtered backprojection (FBP) and (b) our proposed PSF-aware FBP. Our proposed PSF-aware FBP algorithm reconstructs an image with less out-of-focus blur. Scalebar is 100 μm.

Tables (1)

Tables Icon

Table 1 PSNR comparisons between traditional FBP, the MTF deconvolution reconstruction in [8], and our PSF-aware FBP with different numerical apertures. We computed both the overall PSNR of the entire image, as well as the PSNR for the Shepp-Logan phantom itself (excluding the background pixels). We performed all simulations using the full size phantom as in Fig. 4 (f–o), except where indicated by , where we used the smaller phantom as in Fig. 4 (a–e). In addition, we performed all simulations assuming noise-free conditions, except where indicated by , where we assumed the projections were taken with Poisson-distributed shot noise as in Fig. 4 (q–t). To generate data corrupted by shot noise, we assumed that the measured value y at any given detector followed a Poisson distribution y ∼ Poisson(x), where x was the deterministic (noise-free) projection value at that detector, scaled so all deterministic projection values were in the interval [0, 104].

Equations (12)

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p ( u , v , θ ) = 3 f ( x , y , z ) δ ( x cos θ + y sin θ u , z v ) d x d y d z ,
I ˜ ( u , v , θ ) = ( f * T θ { h } ) ( u cos θ , u sin θ , v ) ,
p ˜ ( u , v , θ ) = 3 ( f * T θ { h } ) ( x , y , z ) δ ( x cos θ + y sin θ u , z v ) d x d y d z .
M 𝒫 θ N M = 𝒮 θ N M N ,
2 { p ˜ ( u , v , θ ) } = 𝒮 θ 3 2 { 3 { f * T θ { h } ( x , y , ) } } .
2 { p ˜ ( u , v , θ ) } = 𝒮 θ 3 2 { 3 { f ( x , y , z ) } } 𝒮 θ 3 2 { 3 { T θ { h } ( x , y ) } } .
𝒮 θ 3 2 { 3 { f ( x , y , z ) } } = 2 { p ˜ ( u , v , θ ) } 2 * { 𝒫 θ 3 2 { T θ { h } ( x , y , z ) } } | 2 { 𝒫 θ 3 2 { T θ { h } ( x , y , z ) } } | 2 .
f ( x , y , z ) k = 1 K Q θ k ( x cos θ k + y sin θ k , z ) ,
2 ( Q θ ( u , v ) ) = 𝒮 θ 3 2 { 3 { f ( x , y , z ) } } W ( ω u , ω v ) .
2 { Q θ ( u , v ) } = 2 { p ˜ ( u , v , θ ) } W ˜ ( ω u , ω v ) ,
W ˜ ( ω u , ω v ) = W ( ω u , ω v ) H inv ( ω u , ω v ) ,
H inv ( ω u , ω v ) = 2 * { 𝒫 θ 3 2 { T θ { h } ( x , y , z ) } } | 2 { 𝒫 θ 3 2 { T θ { h } ( x , y , z ) } } | 2 + λ | 2 { r ( u , v ) } | 2 ,

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