Abstract

We demonstrate two techniques to improve the quality of reconstructed optical projection tomography (OPT) images using the modulation transfer function (MTF) as a function of defocus experimentally determined from tilted knife-edge measurements. The first employs a 2-D binary filter based on the MTF frequency cut-off as an additional filter during back-projection reconstruction that restricts the high frequency information to the region around the focal plane and progressively decreases the spatial frequency bandwidth with defocus. This helps to suppress “streak” artifacts in OPT data acquired at reduced angular sampling, thereby facilitating faster OPT acquisitions. This method is shown to reduce the average background by approximately 72% for an NA of 0.09 and by approximately 38% for an NA of 0.07 compared to standard filtered back-projection. As a biological illustration, a Fli:GFP transgenic zebrafish embryo (3 days post-fertilisation) was imaged to demonstrate the improved imaging speed (a quarter of the acquisition time). The second method uses the MTF to produce an appropriate deconvolution filter that can be used to correct for the spatial frequency modulation applied by the imaging system.

© 2012 OSA

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2011

2010

2008

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, “In vivo imaging of Drosophila melanogaster pupae with mesoscopic fluorescence tomography,” Nat. Methods 5(1), 45–47 (2008).
[CrossRef] [PubMed]

2007

H. U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4(4), 331–336 (2007).
[CrossRef] [PubMed]

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]

2005

M. A. Haidekker, “Optical transillumination tomography with tolerance against refraction mismatch,” Comput. Methods Programs Biomed. 80(3), 225–235 (2005).
[CrossRef] [PubMed]

J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Correction of artefacts in optical projection tomography,” Phys. Med. Biol. 50(19), 4645–4665 (2005).
[CrossRef] [PubMed]

J. A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods 2(12), 920–931 (2005).
[CrossRef] [PubMed]

2004

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

2002

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]

1997

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922–924 (1997).
[CrossRef]

1996

S. A. Boppart, M. E. Brezinski, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Investigation of developing embryonic morphology using optical coherence tomography,” Dev. Biol. 177(1), 54–63 (1996).
[CrossRef] [PubMed]

1995

W. Xia, R. M. Lewitt, and P. R. Edholm, “Fourier correction for spatially variant collimator blurring in SPECT,” IEEE Trans. Med. Imaging 14(1), 100–115 (1995).
[CrossRef] [PubMed]

1994

J. M. Boone and J. A. Seibert, “An analytical edge spread function model for computer fitting and subsequent calculation of the LSF and MTF,” Med. Phys. 21(10), 1541–1545 (1994).
[CrossRef] [PubMed]

1991

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30(2), 170–177 (1991).
[CrossRef]

1990

W. Denk, J. H. Strickler, and W. W. Webb, “2-Photon Laser Scanning Fluorescence Microscopy,” Science 248(4951), 73–76 (1990).
[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]

Balciunas, D.

A. M. Petzold, V. M. Bedell, N. J. Boczek, J. J. Essner, D. Balciunas, K. J. Clark, and S. C. Ekker, “SCORE imaging: specimen in a corrected optical rotational enclosure,” Zebrafish 7(2), 149–154 (2010).
[CrossRef] [PubMed]

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]

Barad, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922–924 (1997).
[CrossRef]

Becker, K.

H. U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4(4), 331–336 (2007).
[CrossRef] [PubMed]

Bedell, V. M.

A. M. Petzold, V. M. Bedell, N. J. Boczek, J. J. Essner, D. Balciunas, K. J. Clark, and S. C. Ekker, “SCORE imaging: specimen in a corrected optical rotational enclosure,” Zebrafish 7(2), 149–154 (2010).
[CrossRef] [PubMed]

Birk, U. J.

Boczek, N. J.

A. M. Petzold, V. M. Bedell, N. J. Boczek, J. J. Essner, D. Balciunas, K. J. Clark, and S. C. Ekker, “SCORE imaging: specimen in a corrected optical rotational enclosure,” Zebrafish 7(2), 149–154 (2010).
[CrossRef] [PubMed]

Boone, J. M.

J. M. Boone and J. A. Seibert, “An analytical edge spread function model for computer fitting and subsequent calculation of the LSF and MTF,” Med. Phys. 21(10), 1541–1545 (1994).
[CrossRef] [PubMed]

Boppart, S. A.

S. A. Boppart, M. E. Brezinski, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Investigation of developing embryonic morphology using optical coherence tomography,” Dev. Biol. 177(1), 54–63 (1996).
[CrossRef] [PubMed]

Bouma, B. E.

S. A. Boppart, M. E. Brezinski, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Investigation of developing embryonic morphology using optical coherence tomography,” Dev. Biol. 177(1), 54–63 (1996).
[CrossRef] [PubMed]

Brezinski, M. E.

S. A. Boppart, M. E. Brezinski, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Investigation of developing embryonic morphology using optical coherence tomography,” Dev. Biol. 177(1), 54–63 (1996).
[CrossRef] [PubMed]

Bugeon, L.

Chen, L.

Clark, K. J.

A. M. Petzold, V. M. Bedell, N. J. Boczek, J. J. Essner, D. Balciunas, K. J. Clark, and S. C. Ekker, “SCORE imaging: specimen in a corrected optical rotational enclosure,” Zebrafish 7(2), 149–154 (2010).
[CrossRef] [PubMed]

Conchello, J. A.

J. A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods 2(12), 920–931 (2005).
[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]

Deininger, K.

H. U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4(4), 331–336 (2007).
[CrossRef] [PubMed]

Del Bene, F.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “2-Photon Laser Scanning Fluorescence Microscopy,” Science 248(4951), 73–76 (1990).
[CrossRef]

Deussing, J. M.

H. U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4(4), 331–336 (2007).
[CrossRef] [PubMed]

Dodt, H. U.

H. U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4(4), 331–336 (2007).
[CrossRef] [PubMed]

Eder, M.

H. U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4(4), 331–336 (2007).
[CrossRef] [PubMed]

Edholm, P. R.

W. Xia, R. M. Lewitt, and P. R. Edholm, “Fourier correction for spatially variant collimator blurring in SPECT,” IEEE Trans. Med. Imaging 14(1), 100–115 (1995).
[CrossRef] [PubMed]

Eisenberg, H.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922–924 (1997).
[CrossRef]

Ekker, S. C.

A. M. Petzold, V. M. Bedell, N. J. Boczek, J. J. Essner, D. Balciunas, K. J. Clark, and S. C. Ekker, “SCORE imaging: specimen in a corrected optical rotational enclosure,” Zebrafish 7(2), 149–154 (2010).
[CrossRef] [PubMed]

Essner, J. J.

A. M. Petzold, V. M. Bedell, N. J. Boczek, J. J. Essner, D. Balciunas, K. J. Clark, and S. C. Ekker, “SCORE imaging: specimen in a corrected optical rotational enclosure,” Zebrafish 7(2), 149–154 (2010).
[CrossRef] [PubMed]

French, P. M. W.

Fujimoto, J. G.

S. A. Boppart, M. E. Brezinski, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Investigation of developing embryonic morphology using optical coherence tomography,” Dev. Biol. 177(1), 54–63 (1996).
[CrossRef] [PubMed]

Haidekker, M. A.

M. A. Haidekker, “Optical transillumination tomography with tolerance against refraction mismatch,” Comput. Methods Programs Biomed. 80(3), 225–235 (2005).
[CrossRef] [PubMed]

Hayenga, J.

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]

J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Correction of artefacts in optical projection tomography,” Phys. Med. Biol. 50(19), 4645–4665 (2005).
[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]

Horowitz, M.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922–924 (1997).
[CrossRef]

Huisken, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Jährling, N.

H. U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4(4), 331–336 (2007).
[CrossRef] [PubMed]

Konstantinides, N.

Lamb, J. R.

Leischner, U.

H. U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4(4), 331–336 (2007).
[CrossRef] [PubMed]

Lewitt, R. M.

W. Xia, R. M. Lewitt, and P. R. Edholm, “Fourier correction for spatially variant collimator blurring in SPECT,” IEEE Trans. Med. Imaging 14(1), 100–115 (1995).
[CrossRef] [PubMed]

Lichtman, J. W.

J. A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods 2(12), 920–931 (2005).
[CrossRef] [PubMed]

Mauch, C. P.

H. U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4(4), 331–336 (2007).
[CrossRef] [PubMed]

McGinty, J.

Meyer, H.

Meyer, M. G.

Miao, Q.

Narayanswamy, R.

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30(2), 170–177 (1991).
[CrossRef]

Nelson, A. C.

Neumann, T.

Ntziachristos, V.

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, “In vivo imaging of Drosophila melanogaster pupae with mesoscopic fluorescence tomography,” Nat. Methods 5(1), 45–47 (2008).
[CrossRef] [PubMed]

Park, S. K.

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30(2), 170–177 (1991).
[CrossRef]

Perrimon, N.

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, “In vivo imaging of Drosophila melanogaster pupae with mesoscopic fluorescence tomography,” Nat. Methods 5(1), 45–47 (2008).
[CrossRef] [PubMed]

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]

Petzold, A. M.

A. M. Petzold, V. M. Bedell, N. J. Boczek, J. J. Essner, D. Balciunas, K. J. Clark, and S. C. Ekker, “SCORE imaging: specimen in a corrected optical rotational enclosure,” Zebrafish 7(2), 149–154 (2010).
[CrossRef] [PubMed]

Pitsouli, C.

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, “In vivo imaging of Drosophila melanogaster pupae with mesoscopic fluorescence tomography,” Nat. Methods 5(1), 45–47 (2008).
[CrossRef] [PubMed]

Razansky, D.

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, “In vivo imaging of Drosophila melanogaster pupae with mesoscopic fluorescence tomography,” Nat. Methods 5(1), 45–47 (2008).
[CrossRef] [PubMed]

Reichenbach, S. E.

S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30(2), 170–177 (1991).
[CrossRef]

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]

Sarasa-Renedo, A.

Schierloh, A.

H. U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods 4(4), 331–336 (2007).
[CrossRef] [PubMed]

Seibel, E. J.

Seibert, J. A.

J. M. Boone and J. A. Seibert, “An analytical edge spread function model for computer fitting and subsequent calculation of the LSF and MTF,” Med. Phys. 21(10), 1541–1545 (1994).
[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]

J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Correction of artefacts in optical projection tomography,” Phys. Med. Biol. 50(19), 4645–4665 (2005).
[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]

Silberberg, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922–924 (1997).
[CrossRef]

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]

J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Correction of artefacts in optical projection tomography,” Phys. Med. Biol. 50(19), 4645–4665 (2005).
[CrossRef] [PubMed]

Stelzer, E. H. K.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “2-Photon Laser Scanning Fluorescence Microscopy,” Science 248(4951), 73–76 (1990).
[CrossRef]

Swoger, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Tavernarakis, N.

Taylor, H. B.

Tearney, G. J.

S. A. Boppart, M. E. Brezinski, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Investigation of developing embryonic morphology using optical coherence tomography,” Dev. Biol. 177(1), 54–63 (1996).
[CrossRef] [PubMed]

Vinegoni, C.

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Supplementary Material (5)

» Media 1: AVI (2622 KB)     
» Media 2: AVI (2850 KB)     
» Media 3: AVI (2862 KB)     
» Media 4: AVI (2850 KB)     
» Media 5: AVI (4392 KB)     

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Figures (14)

Fig. 1
Fig. 1

(a) Schematic of OPT system. O – objective, AP – aperture, L1 – condenser lens, F1 – excitation filter, DM – dichroic mirror, L2 – tube lens, F2 – emission filter, M – mirror. (b) Photograph of the custom built chamber.

Fig. 2
Fig. 2

Schematic of OPT imaging system with (a) focal plane coincident with the rotation axis and (b) focal plane shifted to half front of the sample. DOF – depth of field; Dotted lines are a schematic representation of the axial PSF.

Fig. 3
Fig. 3

(a) The measured edge spread data are plotted as discrete data points. The fit to these points is illustrated by the red solid line. The linear correlation coefficient between these two is 0.9999. (b) Three pairs of MTFs at the different positions from the analytical method, shown as the red solid line, and the numerical Fourier transform procedure, shown as data points. MTF1 is the MTF in focus; MTF2 and MTF3 are for 70 and 200 µm defocus, respectively.

Fig. 4
Fig. 4

MTFs as a function of defocus (z) for different effective NAs (0.09, 0.07, 0.05 and 0.03) of the OPT system. The blue lines indicate the DOFs for different NAs (1040 × 1040, Δkx = 0.596 mm−1, Δz = 1.6125 µm) (Media 1).

Fig. 5
Fig. 5

(a) 2-D ramp filter and (b) 2-D back-projection at one angle with ramp filter applied; (c) binary MTF-mask filter and (d) back-projection with the MTF-mask filter and ramp filter applied; (e) deconvolution filter and (f) back-projection with deconvolution filter and ramp filter applied (effective NA of 0.07 for the OPT system; 1040 × 1040 pixels).

Fig. 6
Fig. 6

Schematic of radial and tangential resolution used to evaluate the image quality.

Fig. 7
Fig. 7

The simulated (a) standard FBP; (b) MTF-mask filtered reconstruction from 90 projections (every 4°) for an effective NA of 0.07. (c) and (d) show the background for (a) and (b) respectively. The images of the background are on the same intensity scale to show the differences. Scale bar, 200 µm.

Fig. 8
Fig. 8

The experimental (a) standard FBP; (b) MTF-mask filtered reconstruction from 90 projections (every 4°) for an effective NA of 0.07. (c) and (d) show the background for (a) and (b) respectively. The images of the background are on the same intensity scale to show the differences. Scale bar, 200 µm (Media 3).

Fig. 9
Fig. 9

(a) Simulated (S) and experimental (E) correlation results of standard FBP and MTF-mask filtered reconstructions for an effective NA of 0.07. (b) Experimental correlation results for different effective NAs (0.06, 0.07, 0.09), with standard FBP correlations as the dotted lines and the MTF-mask filtered reconstruction correlations as the solid lines (three dotted lines are similar and cannot be distinguished in this figure and thus only use black color to represent them).

Fig. 10
Fig. 10

(a) Standard FBP reconstruction and (b) MTF-mask filtered reconstruction of a zebrafish embryo with an effective NA of 0.07 from 360 projections (every 1°) and (c) Standard reconstruction and (d) MTF-mask filtered reconstruction of zebrafish embryo with an effective NA 0.07 from 90 projections (every 4°). Scale bar, 200 µm (Media 5).

Fig. 11
Fig. 11

The experimental results with shifted focal plane (200 µm) from 90 projections (every 4°) for an effective NA of 0.07. (a) Standard FBP reconstruction and (b) MTF-mask filtered reconstruction (Scale bar, 200 µm) with (c) and (d) showing the magnified beads respectively (Scale bar, 100 µm).

Fig. 12
Fig. 12

Plots through the radial (a) and the tangential (b) directions of the off-axis bead and the radial (c) and the tangential (d) axes of the on-axis bead of simulated results with an effective NA of 0.07.

Fig. 13
Fig. 13

The experimental results for (a) standard FBP reconstruction; (b) deconvolution reconstruction (Scale bar, 200 µm) from 360 projections for an effective NA of 0.07 with (c) and (d) showing the magnified reconstructions respectively (Scale bar, 100 µm).

Fig. 14
Fig. 14

The experimental results for (a) standard FBP reconstruction; (b) deconvolution reconstruction of zebrafish embryo with an effective NA 0.07 from 360 projections (every 1°). The images are on the same intensity scale to show the differences. Scale bar, 200 µm.

Tables (3)

Tables Icon

Table 1 The resolution and DOF for different effective NAs of the OPT system

Tables Icon

Table 2 The average background from standard FBP and MTF-mask filtered reconstruction for different effective NAs (based on 90 experimental projections)

Tables Icon

Table 3 The radial and tangential FWHM of reconstructed beads for different effective NAs (FBP – standard FBP reconstruction, MTF – MTF-mask filtered reconstruction; average bead diameter 14.8 ± 0.13 µm)

Equations (6)

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e s f ( x ) = a [ 1 exp ( b | x x 0 | ) ] + c e r f ( d 1 2 | x x 0 | )
D O F = n b a t h ( n λ N A 2 + n e M a N A )
M = π N = π D N A 0.61 n λ = π D r A i r y
H d e c o n v = H W _ lim 1 H M m
H W 1 = H M S x | H M | 2 S x + S u
H W _ lim 1 = { | H W 1 | : | H W 1 | C t C t + C r ( 1 exp [ | H W 1 | C t C r ] ) : | H W 1 | > C t

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