Abstract

Electrohydrodynamic jetting behaviors of liquid menisci were analyzed experimentally by three-dimensional optical shadowgraphic tomography. The tomographic algorithm was developed after a series of multiplicative algebraic reconstruction techniques updated the object’s intensities by using a cubic cosine basis function to determine the weighting coefficients of the projection matrix. The algorithm was evaluated initially by using a synthesized three-dimensional droplet phantom. Three-dimensional reconstructions of several jetting modes were built based on three images of projection data captured by three high-speed cameras, which were positioned at an offset angle of 45° relative to one another.

© 2013 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. I. Hayati, A. I. Bailey, and Th. F. Tadros, “Investigations into the mechanisms of electrohydrodynamic spraying of liquids: I. Effect of electric field, and the environment on pendant drops, and factors affecting the formation of stable jets, and atomization,” J. Colloid Interface Sci. 117, 205–221 (1987).
    [CrossRef]
  5. A. Jaworek and A. Krupa, “Jet, and drops formation in electrohydrodynamic spraying of liquids,” Exp. Fluids 27, 43–52 (1999).
    [CrossRef]
  6. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1987).
  7. H. S. Ko, S. S. Ahn, and H. J. Kim, “Measurement of impinging butane flame using combined optical system with digital speckle tomography,” Opt. Lasers Eng. 49, 1320–1329 (2011).
    [CrossRef]
  8. S. Petra, A. Schröder, and C. Schnörr, “3D Tomography from few projections in experimental fluid dynamics,” in Imaging Measurement Methods for Flow Analysis, Vol. 106 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design (Springer, 2009), pp. 63–72.
  9. X. H. Nguyen, S. H. Lee, and H. S. Ko, “Comparative study on basis functions for projection matrix of three-dimensional tomographic reconstruction for analysis of droplet behavior from electrohydrodynamic jet,” Appl. Opt. 51, 5834–5844 (2012).
    [CrossRef]
  10. X. Wan, Y. Q. Gao, and S. L. Yu, “Limited-view tomography algorithms for plasma diagnostics,” Proc. SPIE 4927, 625–633 (2002).
    [CrossRef]
  11. J. Klinner and C. Willert, “Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions,” Exp. Fluids 53, 531–543 (2012).
    [CrossRef]
  12. R. Gordon and G. T. Herman, “Three-dimensional reconstructions from projections—review of algorithms,” Int. Rev. Cytol. 38, 111–151 (1974).
    [CrossRef]
  13. D. Verhoeven, “Multiplicative algebraic computed tomographic algorithms for the reconstruction of multidirectional interferometric data,” Opt. Eng. 32, 410–419 (1993).
    [CrossRef]
  14. 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]
  15. G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
    [CrossRef]
  16. C. Atkinson and J. Soria, “An efficient simultaneous reconstruction technique for tomographic particle image velocimetry,” Exp. Fluids 47, 553–568 (2009).
    [CrossRef]

2012 (2)

2011 (1)

H. S. Ko, S. S. Ahn, and H. J. Kim, “Measurement of impinging butane flame using combined optical system with digital speckle tomography,” Opt. Lasers Eng. 49, 1320–1329 (2011).
[CrossRef]

2009 (1)

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

2008 (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]

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

2007 (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]

2006 (1)

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

2004 (1)

2002 (1)

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

1999 (1)

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

1993 (1)

D. Verhoeven, “Multiplicative algebraic computed tomographic algorithms for the reconstruction of multidirectional interferometric data,” Opt. Eng. 32, 410–419 (1993).
[CrossRef]

1987 (1)

I. Hayati, A. I. Bailey, and Th. F. Tadros, “Investigations into the mechanisms of electrohydrodynamic spraying of liquids: I. Effect of electric field, and the environment on pendant drops, and factors affecting the formation of stable jets, and atomization,” J. Colloid Interface Sci. 117, 205–221 (1987).
[CrossRef]

1974 (1)

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]

Ahn, S. S.

H. S. Ko, S. S. Ahn, and H. J. Kim, “Measurement of impinging butane flame using combined optical system with digital speckle tomography,” Opt. Lasers Eng. 49, 1320–1329 (2011).
[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]

Bailey, A. I.

I. Hayati, A. I. Bailey, and Th. F. Tadros, “Investigations into the mechanisms of electrohydrodynamic spraying of liquids: I. Effect of electric field, and the environment on pendant drops, and factors affecting the formation of stable jets, and atomization,” J. Colloid Interface Sci. 117, 205–221 (1987).
[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]

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. 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]

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]

Hayati, I.

I. Hayati, A. I. Bailey, and Th. F. Tadros, “Investigations into the mechanisms of electrohydrodynamic spraying of liquids: I. Effect of electric field, and the environment on pendant drops, and factors affecting the formation of stable jets, and atomization,” J. Colloid Interface Sci. 117, 205–221 (1987).
[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]

Kim, H. J.

H. S. Ko, S. S. Ahn, and H. J. Kim, “Measurement of impinging butane flame using combined optical system with digital speckle tomography,” Opt. Lasers Eng. 49, 1320–1329 (2011).
[CrossRef]

Klinner, J.

J. Klinner and C. Willert, “Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions,” Exp. Fluids 53, 531–543 (2012).
[CrossRef]

Ko, H. S.

X. H. Nguyen, S. H. Lee, and H. S. Ko, “Comparative study on basis functions for projection matrix of three-dimensional tomographic reconstruction for analysis of droplet behavior from electrohydrodynamic jet,” Appl. Opt. 51, 5834–5844 (2012).
[CrossRef]

H. S. Ko, S. S. Ahn, and H. J. Kim, “Measurement of impinging butane flame using combined optical system with digital speckle tomography,” Opt. Lasers Eng. 49, 1320–1329 (2011).
[CrossRef]

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]

Lee, S. H.

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]

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]

Nguyen, X. H.

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, Vol. 106 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design (Springer, 2009), pp. 63–72.

Prasad, V.

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]

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, Vol. 106 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design (Springer, 2009), 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, Vol. 106 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design (Springer, 2009), 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]

Tadros, Th. F.

I. Hayati, A. I. Bailey, and Th. F. Tadros, “Investigations into the mechanisms of electrohydrodynamic spraying of liquids: I. Effect of electric field, and the environment on pendant drops, and factors affecting the formation of stable jets, and atomization,” J. Colloid Interface Sci. 117, 205–221 (1987).
[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.

D. Verhoeven, “Multiplicative algebraic computed tomographic algorithms for the reconstruction of multidirectional interferometric data,” Opt. Eng. 32, 410–419 (1993).
[CrossRef]

Wan, X.

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

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]

Willert, C.

J. Klinner and C. Willert, “Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions,” Exp. Fluids 53, 531–543 (2012).
[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]

Appl. Opt. (2)

Exp. Fluids (4)

J. Klinner and C. Willert, “Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions,” Exp. Fluids 53, 531–543 (2012).
[CrossRef]

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

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

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

Int. Rev. Cytol. (1)

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

J. Colloid Interface Sci. (1)

I. Hayati, A. I. Bailey, and Th. F. Tadros, “Investigations into the mechanisms of electrohydrodynamic spraying of liquids: I. Effect of electric field, and the environment on pendant drops, and factors affecting the formation of stable jets, and atomization,” J. Colloid Interface Sci. 117, 205–221 (1987).
[CrossRef]

J. Electrost. (1)

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

J. Phys. Chem. A (1)

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. (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]

Opt. Eng. (1)

D. Verhoeven, “Multiplicative algebraic computed tomographic algorithms for the reconstruction of multidirectional interferometric data,” Opt. Eng. 32, 410–419 (1993).
[CrossRef]

Opt. Lasers Eng. (1)

H. S. Ko, S. S. Ahn, and H. J. Kim, “Measurement of impinging butane flame using combined optical system with digital speckle tomography,” Opt. Lasers Eng. 49, 1320–1329 (2011).
[CrossRef]

Proc. SPIE (1)

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

Other (2)

S. Petra, A. Schröder, and C. Schnörr, “3D Tomography from few projections in experimental fluid dynamics,” in Imaging Measurement Methods for Flow Analysis, Vol. 106 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design (Springer, 2009), pp. 63–72.

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

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Figures (11)

Fig. 1.
Fig. 1.

Synthetic phantom and projection arrangement. (a) Four-droplet distribution of phantom. (b) Arrangement of three projections corresponding to object volume.

Fig. 2.
Fig. 2.

Average error of tomographic reconstruction: (a) MART-1, (b) MART-2, (c) MART-3.

Fig. 3.
Fig. 3.

Quality of tomographic reconstruction: (a) MART-1, (b) MART-2, (c) MART-3.

Fig. 4.
Fig. 4.

(a) Average error and (b) quality with λ=1.0.

Fig. 5.
Fig. 5.

Reconstructed results for (b) MART-1, (c) MART-2, and (d) MART-3 compared with (a) real phantom.

Fig. 6.
Fig. 6.

Schematic of experimental setup.

Fig. 7.
Fig. 7.

Recorded images of EHD jetting modes: (a) cone-jet (from left to right, Cameras 1, 2, and 3, respectively), (b) asymmetric cone-jet, (c) multiple jets.

Fig. 8.
Fig. 8.

Preprocessing images of EHD jetting modes: (a) cone-jet, (b) asymmetric cone-jet, (c) multiple jets.

Fig. 9.
Fig. 9.

Reconstructed results of cone-jet mode: (a) three-dimensional view, (b) side view of reconstructed object.

Fig. 10.
Fig. 10.

Reconstructed results of asymmetric cone-jet mode: (a) three-dimensional view, (b) side view of reconstructed object.

Fig. 11.
Fig. 11.

Reconstructed results of multijet mode (a) three-dimensional view, (b) side view of reconstructed object.

Equations (13)

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

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)=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|,
Oq+1=CjqOq,Cjq=[ψiψ^i]λWi,j=[ψij=1NWi,jOq]λWi,j,
Oq+1=CjqOq,Cjq=[ψiψ^i]λWi,j*=[ψij=1NWi,jOq]λWi,j*,
Oq+1=CjqOq,Cjq={1λWij*(1ψiψ^i)=1λWij*(1ψij=1NWi,jOq),ψ^i01,otherwise,
f(x,y,z)={1,(x0.2)2+(y+0.1)2+(z0.1)20.12,1,(xy2)2+(yz3)2+z120.01&z1,1,(x+0.1)2+(y0.15)2+z20.082,1,(x0.1)2+(y0.1)2+(z0.4)20.12,0,otherwise.
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^2(xj,yj,zj).
Cjq=[ψij=1NWi,jOq]λWi,j=1+λWi,jln(ψij=1NWi,jOq),
Cjq=[ψij=1NWi,jOq]λWi,j*=1+λWi,j*ln(ψij=1NWi,jOq).
ψij=1NWi,jOq1,ln(ψij=1NWi,jOq)and(1ψij=1NWi,jOq)

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