Abstract

Three-dimensional optical tomography techniques were developed to reconstruct three-dimensional objects using a set of two-dimensional projection images. Five basis functions, such as cubic B-spline, o-Moms, keys, and cosine functions and Gaussian basis functions, were used to calculate the weighting coefficients for a projection matrix. Two different forms of a multiplicative algebraic reconstruction technique were also used to solve inverse problems. The reconstruction algorithm was examined by using several phantoms, which included droplet behaviors and random distributions of particles in a volume. The three-dimensional volume comprised of particles was reconstructed from four projection angles, which were positioned at an offset angle of 45° between each other. Then, three-dimensional velocity fields were obtained from the reconstructed particle volume by three-dimensional cross correlation. The velocity field of the synthetic vortex flow was reconstructed to analyze the three-dimensional tomography algorithm.

© 2012 Optical Society of America

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  1. J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
    [CrossRef]
  2. W. D. Luedtke, U. Landman, Y. H. Chiu, D. J. Levandier, R. A. Dressler, S. Sok, and M. S. Gordon, “Nanojets, electrospray, and ion field evaporation: molecular dynamics simulations and laboratory experiments,” J. Phys. Chem. A 112, 9628–9649 (2008).
    [CrossRef]
  3. A. Jaworek and A. T. Sobczyk, “Electrospraying route to nanotechnology: An overview,” J. Electrost. 66, 197–219 (2008).
    [CrossRef]
  4. A. Jaworek and A. Krupa, “Jet and drops formation in electrohydrodynamic spraying of liquids,” Exp. Fluids 27, 43–52 (1999).
    [CrossRef]
  5. X. Wan, S. Yu, Y. Gao, and Q. Zhu, “Self-adaptive reconstruction algorithm for emission spectral volume tomography,” Opt. Eng. 43, 1244–1250 (2004).
    [CrossRef]
  6. D. Mishra, J. P. Longtin, R. P. Singh, and V. Prasad, “Performance evaluation of iterative tomography algorithms for incomplete projection data,” Appl. Opt. 43, 1522–1532 (2004).
    [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]
  16. X. Wan, Y. Q. Gao, and S. L. Yu, “Limited-view tomography algorithms for plasma diagnostics,” Proc. SPIE 4927, 625–633 (2002).
    [CrossRef]
  17. C. Chen, Y. J. Kim, and H. S. Ko, “Three-dimensional tomographic reconstruction of unstable ejection phenomena of droplets for electrohydrodynamic jet,” Exp. Therm. Fluid. Sci. 35, 433–441 (2011).
    [CrossRef]
  18. K. Lynch, “Development of a 3-D fluid velocimetry technique based on light field imaging,” Master’s thesis (Auburn University, 2011).
  19. H. S. Ko, D. P. Lyons, and K. D. Kihm, “A comparative study of algebraic reconstruction (ART) and genetic algorithms (GA) for beam deflection tomography,” in ASME Fluids Engineering Division Summer Meeting (ASME, 1997), paper FEDSM 97-3104 .
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    [CrossRef]
  21. F. Scarano and M. L. Riethmuller, “Advances in iterative multigrid PIV image processing,” Exp. Fluids Suppl.S51–S60 (2000).
    [CrossRef]

2011

C. Chen, Y. J. Kim, and H. S. Ko, “Three-dimensional tomographic reconstruction of unstable ejection phenomena of droplets for electrohydrodynamic jet,” Exp. Therm. Fluid. Sci. 35, 433–441 (2011).
[CrossRef]

2009

C. Atkinson and J. Soria, “An efficient simultaneous reconstruction technique for tomographic particle image velocimetry,” Exp. Fluids 47, 553–568 (2009).
[CrossRef]

2008

W. D. Luedtke, U. Landman, Y. H. Chiu, D. J. Levandier, R. A. Dressler, S. Sok, and M. S. Gordon, “Nanojets, electrospray, and ion field evaporation: molecular dynamics simulations and laboratory experiments,” J. Phys. Chem. A 112, 9628–9649 (2008).
[CrossRef]

A. Jaworek and A. T. Sobczyk, “Electrospraying route to nanotechnology: An overview,” J. Electrost. 66, 197–219 (2008).
[CrossRef]

2007

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

2006

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

2004

X. Wan, S. Yu, Y. Gao, and Q. Zhu, “Self-adaptive reconstruction algorithm for emission spectral volume tomography,” Opt. Eng. 43, 1244–1250 (2004).
[CrossRef]

D. Mishra, J. P. Longtin, R. P. Singh, and V. Prasad, “Performance evaluation of iterative tomography algorithms for incomplete projection data,” Appl. Opt. 43, 1522–1532 (2004).
[CrossRef]

2002

X. Wan, Y. Q. Gao, and S. L. Yu, “Limited-view tomography algorithms for plasma diagnostics,” Proc. SPIE 4927, 625–633 (2002).
[CrossRef]

2000

P. Thévenaz, T. Blu, and M. Unser, “Interpolation revisited,” IEEE Trans. Med. Imaging 19, 739–758 (2000).
[CrossRef]

F. Scarano and M. L. Riethmuller, “Advances in iterative multigrid PIV image processing,” Exp. Fluids Suppl.S51–S60 (2000).
[CrossRef]

1999

A. Jaworek and A. Krupa, “Jet and drops formation in electrohydrodynamic spraying of liquids,” Exp. Fluids 27, 43–52 (1999).
[CrossRef]

1993

1985

1981

R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 29, 1153–1160 (1981).
[CrossRef]

1974

R. Gordon, “A tutorial on ART,” IEEE Trans. Nucl. Sci. NS-21, 78–92 (1974).

R. Gordon and G. T. Herman, “Three-dimensional reconstructions from projections—review of algorithms,” Int. Rev. Cytol. 38, 111–151 (1974).
[CrossRef]

Adair, K.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Alleyne, A. G.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Atkinson, C.

C. Atkinson and J. Soria, “An efficient simultaneous reconstruction technique for tomographic particle image velocimetry,” Exp. Fluids 47, 553–568 (2009).
[CrossRef]

Barton, K.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Blu, T.

P. Thévenaz, T. Blu, and M. Unser, “Interpolation revisited,” IEEE Trans. Med. Imaging 19, 739–758 (2000).
[CrossRef]

Chen, C.

C. Chen, Y. J. Kim, and H. S. Ko, “Three-dimensional tomographic reconstruction of unstable ejection phenomena of droplets for electrohydrodynamic jet,” Exp. Therm. Fluid. Sci. 35, 433–441 (2011).
[CrossRef]

Chiu, Y. H.

W. D. Luedtke, U. Landman, Y. H. Chiu, D. J. Levandier, R. A. Dressler, S. Sok, and M. S. Gordon, “Nanojets, electrospray, and ion field evaporation: molecular dynamics simulations and laboratory experiments,” J. Phys. Chem. A 112, 9628–9649 (2008).
[CrossRef]

Dressler, R. A.

W. D. Luedtke, U. Landman, Y. H. Chiu, D. J. Levandier, R. A. Dressler, S. Sok, and M. S. Gordon, “Nanojets, electrospray, and ion field evaporation: molecular dynamics simulations and laboratory experiments,” J. Phys. Chem. A 112, 9628–9649 (2008).
[CrossRef]

Elsinga, G. E.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

Ferreira, P. M.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Gao, Y.

X. Wan, S. Yu, Y. Gao, and Q. Zhu, “Self-adaptive reconstruction algorithm for emission spectral volume tomography,” Opt. Eng. 43, 1244–1250 (2004).
[CrossRef]

Gao, Y. Q.

X. Wan, Y. Q. Gao, and S. L. Yu, “Limited-view tomography algorithms for plasma diagnostics,” Proc. SPIE 4927, 625–633 (2002).
[CrossRef]

Georgiadis, J. G.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Gordon, M. S.

W. D. Luedtke, U. Landman, Y. H. Chiu, D. J. Levandier, R. A. Dressler, S. Sok, and M. S. Gordon, “Nanojets, electrospray, and ion field evaporation: molecular dynamics simulations and laboratory experiments,” J. Phys. Chem. A 112, 9628–9649 (2008).
[CrossRef]

Gordon, R.

R. Gordon and G. T. Herman, “Three-dimensional reconstructions from projections—review of algorithms,” Int. Rev. Cytol. 38, 111–151 (1974).
[CrossRef]

R. Gordon, “A tutorial on ART,” IEEE Trans. Nucl. Sci. NS-21, 78–92 (1974).

Hanson, K. M.

Hardy, M.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Herman, G. T.

R. Gordon and G. T. Herman, “Three-dimensional reconstructions from projections—review of algorithms,” Int. Rev. Cytol. 38, 111–151 (1974).
[CrossRef]

Jaworek, A.

A. Jaworek and A. T. Sobczyk, “Electrospraying route to nanotechnology: An overview,” J. Electrost. 66, 197–219 (2008).
[CrossRef]

A. Jaworek and A. Krupa, “Jet and drops formation in electrohydrodynamic spraying of liquids,” Exp. Fluids 27, 43–52 (1999).
[CrossRef]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1987).

Kang, S. J.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Keys, R. G.

R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 29, 1153–1160 (1981).
[CrossRef]

Kihm, K. D.

H. S. Ko, D. P. Lyons, and K. D. Kihm, “A comparative study of algebraic reconstruction (ART) and genetic algorithms (GA) for beam deflection tomography,” in ASME Fluids Engineering Division Summer Meeting (ASME, 1997), paper FEDSM 97-3104 .

Kim, Y. J.

C. Chen, Y. J. Kim, and H. S. Ko, “Three-dimensional tomographic reconstruction of unstable ejection phenomena of droplets for electrohydrodynamic jet,” Exp. Therm. Fluid. Sci. 35, 433–441 (2011).
[CrossRef]

Ko, H. S.

C. Chen, Y. J. Kim, and H. S. Ko, “Three-dimensional tomographic reconstruction of unstable ejection phenomena of droplets for electrohydrodynamic jet,” Exp. Therm. Fluid. Sci. 35, 433–441 (2011).
[CrossRef]

H. S. Ko, D. P. Lyons, and K. D. Kihm, “A comparative study of algebraic reconstruction (ART) and genetic algorithms (GA) for beam deflection tomography,” in ASME Fluids Engineering Division Summer Meeting (ASME, 1997), paper FEDSM 97-3104 .

Krupa, A.

A. Jaworek and A. Krupa, “Jet and drops formation in electrohydrodynamic spraying of liquids,” Exp. Fluids 27, 43–52 (1999).
[CrossRef]

Landman, U.

W. D. Luedtke, U. Landman, Y. H. Chiu, D. J. Levandier, R. A. Dressler, S. Sok, and M. S. Gordon, “Nanojets, electrospray, and ion field evaporation: molecular dynamics simulations and laboratory experiments,” J. Phys. Chem. A 112, 9628–9649 (2008).
[CrossRef]

Lee, C. Y.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Levandier, D. J.

W. D. Luedtke, U. Landman, Y. H. Chiu, D. J. Levandier, R. A. Dressler, S. Sok, and M. S. Gordon, “Nanojets, electrospray, and ion field evaporation: molecular dynamics simulations and laboratory experiments,” J. Phys. Chem. A 112, 9628–9649 (2008).
[CrossRef]

Longtin, J. P.

Luedtke, W. D.

W. D. Luedtke, U. Landman, Y. H. Chiu, D. J. Levandier, R. A. Dressler, S. Sok, and M. S. Gordon, “Nanojets, electrospray, and ion field evaporation: molecular dynamics simulations and laboratory experiments,” J. Phys. Chem. A 112, 9628–9649 (2008).
[CrossRef]

Lynch, K.

K. Lynch, “Development of a 3-D fluid velocimetry technique based on light field imaging,” Master’s thesis (Auburn University, 2011).

Lyons, D. P.

H. S. Ko, D. P. Lyons, and K. D. Kihm, “A comparative study of algebraic reconstruction (ART) and genetic algorithms (GA) for beam deflection tomography,” in ASME Fluids Engineering Division Summer Meeting (ASME, 1997), paper FEDSM 97-3104 .

Mishra, D.

Mukhopadhyay, D. K.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Park, J. U.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Petra, S.

S. Petra, A. Schröder, and C. Schnörr, “3D tomography from few projections in experimental fluid dynamics,” in Imaging Measurement Methods for Flow Analysis (Springer, 2009), Vol. 106, pp. 63–72.

Prasad, V.

Riethmuller, M. L.

F. Scarano and M. L. Riethmuller, “Advances in iterative multigrid PIV image processing,” Exp. Fluids Suppl.S51–S60 (2000).
[CrossRef]

Rogers, J. A.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Scarano, F.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

F. Scarano and M. L. Riethmuller, “Advances in iterative multigrid PIV image processing,” Exp. Fluids Suppl.S51–S60 (2000).
[CrossRef]

Schnörr, C.

S. Petra, A. Schröder, and C. Schnörr, “3D tomography from few projections in experimental fluid dynamics,” in Imaging Measurement Methods for Flow Analysis (Springer, 2009), Vol. 106, pp. 63–72.

Schröder, A.

S. Petra, A. Schröder, and C. Schnörr, “3D tomography from few projections in experimental fluid dynamics,” in Imaging Measurement Methods for Flow Analysis (Springer, 2009), Vol. 106, pp. 63–72.

Singh, R. P.

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1987).

Sobczyk, A. T.

A. Jaworek and A. T. Sobczyk, “Electrospraying route to nanotechnology: An overview,” J. Electrost. 66, 197–219 (2008).
[CrossRef]

Sok, S.

W. D. Luedtke, U. Landman, Y. H. Chiu, D. J. Levandier, R. A. Dressler, S. Sok, and M. S. Gordon, “Nanojets, electrospray, and ion field evaporation: molecular dynamics simulations and laboratory experiments,” J. Phys. Chem. A 112, 9628–9649 (2008).
[CrossRef]

Soria, J.

C. Atkinson and J. Soria, “An efficient simultaneous reconstruction technique for tomographic particle image velocimetry,” Exp. Fluids 47, 553–568 (2009).
[CrossRef]

Strano, M. S.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Thévenaz, P.

P. Thévenaz, T. Blu, and M. Unser, “Interpolation revisited,” IEEE Trans. Med. Imaging 19, 739–758 (2000).
[CrossRef]

Unser, M.

P. Thévenaz, T. Blu, and M. Unser, “Interpolation revisited,” IEEE Trans. Med. Imaging 19, 739–758 (2000).
[CrossRef]

van Oudheusden, B. W.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

Verhoeven, D.

Wan, X.

X. Wan, S. Yu, Y. Gao, and Q. Zhu, “Self-adaptive reconstruction algorithm for emission spectral volume tomography,” Opt. Eng. 43, 1244–1250 (2004).
[CrossRef]

X. Wan, Y. Q. Gao, and S. L. Yu, “Limited-view tomography algorithms for plasma diagnostics,” Proc. SPIE 4927, 625–633 (2002).
[CrossRef]

Wecksung, G. W.

Wieneke, B.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

Yu, S.

X. Wan, S. Yu, Y. Gao, and Q. Zhu, “Self-adaptive reconstruction algorithm for emission spectral volume tomography,” Opt. Eng. 43, 1244–1250 (2004).
[CrossRef]

Yu, S. L.

X. Wan, Y. Q. Gao, and S. L. Yu, “Limited-view tomography algorithms for plasma diagnostics,” Proc. SPIE 4927, 625–633 (2002).
[CrossRef]

Zhu, Q.

X. Wan, S. Yu, Y. Gao, and Q. Zhu, “Self-adaptive reconstruction algorithm for emission spectral volume tomography,” Opt. Eng. 43, 1244–1250 (2004).
[CrossRef]

Appl. Opt.

Exp. Fluids

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

A. Jaworek and A. Krupa, “Jet and drops formation in electrohydrodynamic spraying of liquids,” Exp. Fluids 27, 43–52 (1999).
[CrossRef]

C. Atkinson and J. Soria, “An efficient simultaneous reconstruction technique for tomographic particle image velocimetry,” Exp. Fluids 47, 553–568 (2009).
[CrossRef]

Exp. Fluids Suppl.

F. Scarano and M. L. Riethmuller, “Advances in iterative multigrid PIV image processing,” Exp. Fluids Suppl.S51–S60 (2000).
[CrossRef]

Exp. Therm. Fluid. Sci.

C. Chen, Y. J. Kim, and H. S. Ko, “Three-dimensional tomographic reconstruction of unstable ejection phenomena of droplets for electrohydrodynamic jet,” Exp. Therm. Fluid. Sci. 35, 433–441 (2011).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process.

R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 29, 1153–1160 (1981).
[CrossRef]

IEEE Trans. Med. Imaging

P. Thévenaz, T. Blu, and M. Unser, “Interpolation revisited,” IEEE Trans. Med. Imaging 19, 739–758 (2000).
[CrossRef]

IEEE Trans. Nucl. Sci.

R. Gordon, “A tutorial on ART,” IEEE Trans. Nucl. Sci. NS-21, 78–92 (1974).

Int. Rev. Cytol.

R. Gordon and G. T. Herman, “Three-dimensional reconstructions from projections—review of algorithms,” Int. Rev. Cytol. 38, 111–151 (1974).
[CrossRef]

J. Electrost.

A. Jaworek and A. T. Sobczyk, “Electrospraying route to nanotechnology: An overview,” J. Electrost. 66, 197–219 (2008).
[CrossRef]

J. Phys. Chem. A

W. D. Luedtke, U. Landman, Y. H. Chiu, D. J. Levandier, R. A. Dressler, S. Sok, and M. S. Gordon, “Nanojets, electrospray, and ion field evaporation: molecular dynamics simulations and laboratory experiments,” J. Phys. Chem. A 112, 9628–9649 (2008).
[CrossRef]

Nat. Mater.

J. U. Park, M. Hardy, S. J. Kang, K. Barton, K. Adair, D. K. Mukhopadhyay, C. Y. Lee, M. S. Strano, A. G. Alleyne, J. G. Georgiadis, P. M. Ferreira, and J. A. Rogers, “High-resolution electrohydrodynamic jet printing,” Nat. Mater. 6, 782–789 (2007).
[CrossRef]

Opt. Eng.

X. Wan, S. Yu, Y. Gao, and Q. Zhu, “Self-adaptive reconstruction algorithm for emission spectral volume tomography,” Opt. Eng. 43, 1244–1250 (2004).
[CrossRef]

Proc. SPIE

X. Wan, Y. Q. Gao, and S. L. Yu, “Limited-view tomography algorithms for plasma diagnostics,” Proc. SPIE 4927, 625–633 (2002).
[CrossRef]

Other

S. Petra, A. Schröder, and C. Schnörr, “3D tomography from few projections in experimental fluid dynamics,” in Imaging Measurement Methods for Flow Analysis (Springer, 2009), Vol. 106, pp. 63–72.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1987).

K. Lynch, “Development of a 3-D fluid velocimetry technique based on light field imaging,” Master’s thesis (Auburn University, 2011).

H. S. Ko, D. P. Lyons, and K. D. Kihm, “A comparative study of algebraic reconstruction (ART) and genetic algorithms (GA) for beam deflection tomography,” in ASME Fluids Engineering Division Summer Meeting (ASME, 1997), paper FEDSM 97-3104 .

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Figures (11)

Fig. 1.
Fig. 1.

Distribution of basis functions.

Fig. 2.
Fig. 2.

Synthetic phantoms of droplets.

Fig. 3.
Fig. 3.

Synthetic phantom of particle distribution in volume.

Fig. 4.
Fig. 4.

Positions of projection views corresponding to object field.

Fig. 5.
Fig. 5.

Reconstructed results of three droplets using MART-1 and MART-2.

Fig. 6.
Fig. 6.

Reconstructed results of four droplets using MART-1 and MART-2.

Fig. 7.
Fig. 7.

Quality and average error for reconstructions using MART-1 and MART-2.

Fig. 8.
Fig. 8.

Reconstructed result of particle distribution.

Fig. 9.
Fig. 9.

Quality and average error for particle reconstruction.

Fig. 10.
Fig. 10.

Velocity vectors using three-dimensional cross correlations.

Fig. 11.
Fig. 11.

Displacements in x direction.

Equations (16)

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ψ(s,θ)=+f(x,y)dt,
f^(x,y,z)=j=1NOjb(xxj,yyj,zzj),
ψitif^(x,y,z)dtj=1NOjtibi(xxj,yyj,zzj)dt=j=1NOjWij,
ψi=WijOj,
b(dj)=(2Δ|dj|)34(Δ|dj|)34Δ3,|dj|<Δ=(2Δ|dj|)34Δ3,Δ|dj|2Δ=0,2Δ<|dj|,
b(dj)=12|dj|3|dj|2+114|dj|+1321,|dj|<Δ=16|dj|3+|dj|2842|dj|+2921,Δ|dj|2Δ=0,2Δ<|dj|.
b(dj)=(a+2)|dj|3(a+3)|dj|2+1,|dj|<Δ=a|dj|35a|dj|2+8a|dj|+4a,Δ|dj|2Δ=0,2Δ<|dj|,
b(dj)=12π2(5π2+16)[(13|dj|2)(1+14cos3π|dj|)+|dj|4πsin3π|dj|+23π2(1+cos3π|dj|)],|dj|<13Δ=24π2(5π216)[0.5(|dj|1)2(1+14cos3π|dj|)+3(1|dj|)8πsin3π|dj|],13Δ|dj|Δ=0,Δ<|dj|.
b(dj)=e|dj|22σ2,|dj|Δ=0,|dj|>Δ,
Oq+1=Oq[ψiψ^i]μWi,j=Oq[ψij=1NWi,jOq]μWi,j,
Oq+1=CjqOqCjq={10.5Wij*(1ψiψ^i)=10.5Wij*(1ψij=1NWi,jOq),ψ^i01,otherwise,
f1(x,y,z)={1,(x0.15)2+(y0.15)2+z20.221,(x+0.3)2+(y+0.3)2+(z+0.1)20.1521,(x0.1)2+(y+0.3)2+(z0.1)20.120,otherwise,
f2(x,y,z)={1,(x0.3)2+(y0.3)2+(z0.1)20.121,(xy+0.15)2+(yz+0.54)2+z12&z01,(x+0.2)2+(y0.3)2+(z+0.1)20.0821,(x0.1)2+(y)2+(z0.1)20.120,otherwise.
f3(x,y,z)=j=1NImax4π2d3(exp(0.5(xxj)20.5(yyj)20.5(zzj)2d2)),
Φavg=j=1N|f(xj,yj,zj)f^(xj,yj,zj)|N.
Q=f(xj,yj,zj)·f^(xj,yj,zj)f2(xj,yj,zj)·f^(xj,yj,zj).

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