Abstract

This paper reports on a new technique of measurements of microbubble position in three dimensions with high time-resolution. The technique is based on micro digital holographic particle tracking velocimetry. In this technique, an intensity profile is constructed from a holographic image of a microbubble where the profile results in showing two peaks. The distance between the two peaks appears to relate to the size of the microbubble’s diameter. The three-dimensional position of the bubble can be detected by the center of the two peaks and the center point of the bubble image focused by a digital hologram. We also theoretically obtained the intensity profile of a microbubble by considering a refraction of light on a bubble surface to a ring-shaped aperture model. The theoretically obtained distance between the two peaks is found to be in good agreement with the values obtained experimentally.

© 2011 Optical Society of America

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References

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  1. S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647–1651 (2006).
    [CrossRef]
  2. S. Satake, G. Sorimachi, T. Kanai, J. Taniguchi, and N. Unno, “Three-dimensional measurements of photo-curing process with photo-curable resin for UV-nanoimprint by micro-digital-Holographic-PTV,” J. Electron. Packag. 132, 031003(2010).
    [CrossRef]
  3. D. S. Burch, “Fresnel diffraction by a circular aperture,” Am. J. Phys. 53255–260 (1985).
    [CrossRef]
  4. E. A. Hovenac, “Fresnel diffraction by spherical obstacles,” Am. J. Phys. 5779–84 (1989).
    [CrossRef]
  5. G. E. Sommargren and H. J. Weaver, “Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern,” Appl. Opt. 29,4646–4657 (1990).
    [CrossRef]
  6. G. E. Sommargren and H. J. Weaver, “Diffraction of light by an opaque sphere. 2: Image formation and resolution considerations,” Appl. Opt. 31, 1385–1398 (1992).
    [CrossRef] [PubMed]
  7. M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

2010 (1)

S. Satake, G. Sorimachi, T. Kanai, J. Taniguchi, and N. Unno, “Three-dimensional measurements of photo-curing process with photo-curable resin for UV-nanoimprint by micro-digital-Holographic-PTV,” J. Electron. Packag. 132, 031003(2010).
[CrossRef]

2006 (1)

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647–1651 (2006).
[CrossRef]

1992 (1)

1990 (1)

G. E. Sommargren and H. J. Weaver, “Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern,” Appl. Opt. 29,4646–4657 (1990).
[CrossRef]

1989 (1)

E. A. Hovenac, “Fresnel diffraction by spherical obstacles,” Am. J. Phys. 5779–84 (1989).
[CrossRef]

1985 (1)

D. S. Burch, “Fresnel diffraction by a circular aperture,” Am. J. Phys. 53255–260 (1985).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

Burch, D. S.

D. S. Burch, “Fresnel diffraction by a circular aperture,” Am. J. Phys. 53255–260 (1985).
[CrossRef]

Hovenac, E. A.

E. A. Hovenac, “Fresnel diffraction by spherical obstacles,” Am. J. Phys. 5779–84 (1989).
[CrossRef]

Ito, T.

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647–1651 (2006).
[CrossRef]

Kanai, T.

S. Satake, G. Sorimachi, T. Kanai, J. Taniguchi, and N. Unno, “Three-dimensional measurements of photo-curing process with photo-curable resin for UV-nanoimprint by micro-digital-Holographic-PTV,” J. Electron. Packag. 132, 031003(2010).
[CrossRef]

Kanamori, H.

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647–1651 (2006).
[CrossRef]

Kunugi, T.

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647–1651 (2006).
[CrossRef]

Satake, S.

S. Satake, G. Sorimachi, T. Kanai, J. Taniguchi, and N. Unno, “Three-dimensional measurements of photo-curing process with photo-curable resin for UV-nanoimprint by micro-digital-Holographic-PTV,” J. Electron. Packag. 132, 031003(2010).
[CrossRef]

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647–1651 (2006).
[CrossRef]

Sato, K.

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647–1651 (2006).
[CrossRef]

Sommargren, G. E.

G. E. Sommargren and H. J. Weaver, “Diffraction of light by an opaque sphere. 2: Image formation and resolution considerations,” Appl. Opt. 31, 1385–1398 (1992).
[CrossRef] [PubMed]

G. E. Sommargren and H. J. Weaver, “Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern,” Appl. Opt. 29,4646–4657 (1990).
[CrossRef]

Sorimachi, G.

S. Satake, G. Sorimachi, T. Kanai, J. Taniguchi, and N. Unno, “Three-dimensional measurements of photo-curing process with photo-curable resin for UV-nanoimprint by micro-digital-Holographic-PTV,” J. Electron. Packag. 132, 031003(2010).
[CrossRef]

Taniguchi, J.

S. Satake, G. Sorimachi, T. Kanai, J. Taniguchi, and N. Unno, “Three-dimensional measurements of photo-curing process with photo-curable resin for UV-nanoimprint by micro-digital-Holographic-PTV,” J. Electron. Packag. 132, 031003(2010).
[CrossRef]

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647–1651 (2006).
[CrossRef]

Unno, N.

S. Satake, G. Sorimachi, T. Kanai, J. Taniguchi, and N. Unno, “Three-dimensional measurements of photo-curing process with photo-curable resin for UV-nanoimprint by micro-digital-Holographic-PTV,” J. Electron. Packag. 132, 031003(2010).
[CrossRef]

Weaver, H. J.

G. E. Sommargren and H. J. Weaver, “Diffraction of light by an opaque sphere. 2: Image formation and resolution considerations,” Appl. Opt. 31, 1385–1398 (1992).
[CrossRef] [PubMed]

G. E. Sommargren and H. J. Weaver, “Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern,” Appl. Opt. 29,4646–4657 (1990).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

Am. J. Phys. (2)

D. S. Burch, “Fresnel diffraction by a circular aperture,” Am. J. Phys. 53255–260 (1985).
[CrossRef]

E. A. Hovenac, “Fresnel diffraction by spherical obstacles,” Am. J. Phys. 5779–84 (1989).
[CrossRef]

Appl. Opt. (2)

G. E. Sommargren and H. J. Weaver, “Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern,” Appl. Opt. 29,4646–4657 (1990).
[CrossRef]

G. E. Sommargren and H. J. Weaver, “Diffraction of light by an opaque sphere. 2: Image formation and resolution considerations,” Appl. Opt. 31, 1385–1398 (1992).
[CrossRef] [PubMed]

J. Electron. Packag. (1)

S. Satake, G. Sorimachi, T. Kanai, J. Taniguchi, and N. Unno, “Three-dimensional measurements of photo-curing process with photo-curable resin for UV-nanoimprint by micro-digital-Holographic-PTV,” J. Electron. Packag. 132, 031003(2010).
[CrossRef]

Meas. Sci. Technol. (1)

S. Satake, T. Kunugi, K. Sato, T. Ito, H. Kanamori, and J. Taniguchi, “Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking velocimetry,” Meas. Sci. Technol. 17, 1647–1651 (2006).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

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Figures (8)

Fig. 1
Fig. 1

Fresnel diffraction of a circular aperture.

Fig. 2
Fig. 2

Simple refraction model at a microbubble interface.

Fig. 3
Fig. 3

Aperture model for microbubble.

Fig. 4
Fig. 4

Experimental apparatus.

Fig. 5
Fig. 5

Intensity along the ray direction from theoretical equation.

Fig. 6
Fig. 6

Camera image of a hologram image of microbubbles.

Fig. 7
Fig. 7

Distributions of reconstruction profile: (a) Microbubble A, (b) microbubble B.

Fig. 8
Fig. 8

Relationship between d x and microbubble diameter: Black circles are the experimental points, white circles are the theoretical points, and the solid line is a reference line.

Equations (25)

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E P = 2 i E p , 0 0 1 ( cos ( u ρ 2 2 ) i sin ( u ρ 2 2 ) ) J 0 ( v ρ ) ρ d ρ i E p , 0 [ C ( u , v ) i S ( u , v ) ] ,
C ( u , v ) 2 0 1 J 0 ( v ρ ) cos ( u ρ 2 2 ) ρ d ρ ,
S ( u , v ) 2 0 1 J 0 ( v ρ ) sin ( u ρ 2 2 ) ρ d ρ ,
u k a 2 s , v k a h 0 s ,
1 s = 1 x 0 + 1 x 1 ,
E p , 0 = π a 2 u 0 λ s exp ( i k h 0 2 2 s ) ,
u 0 = E 0 x 0 + x 1 exp ( i k ( x 0 + x 1 ) ) ,
I p = | E p | 2 = I p , 0 [ C 2 ( u , v ) + S 2 ( u , v ) ] ,
x [ x n J n ( x ) ] = x n J n + 1 ( x ) ,
lim x 0 [ x n J n ( x ) ] = 1 / ( 2 n n ! ) .
C ( u , v ) = 2 u sin v 2 2 u + sin ( u / 2 ) u / 2 V 0 ( u , v ) cos ( u / 2 ) u / 2 V 1 ( u , v ) ,
S ( u , v ) = 2 u cos v 2 2 u cos ( u / 2 ) u / 2 V 0 ( u , v ) sin ( u / 2 ) u / 2 V 1 ( u , v ) ,
V n ( u , v ) = s = 0 ( 1 ) s ( v u ) n + 2 s J n + 2 s ( v ) ( n = 0 , 1 ) .
I p = I p , 0 ( 2 u ) 2 { 1 + V 0 2 ( u , v ) + V 1 2 ( u , v ) 2 V 0 ( u , v ) cos 1 2 ( u + v 2 u ) 2 V 1 ( u , v ) sin 1 2 ( u + v 2 u ) } .
n L sin θ in = n G sin θ out ,
R C = n G n L R .
E p = i u R C 2 u 0 exp ( i k h 0 2 2 s ) ( C ( u R C , v R C ) i S ( u R C , v R C ) ) + u 0 { 1 i u R 2 exp ( i k h 0 2 2 s ) ( C ( u R , v R ) i S ( u R , v R ) ) } .
u R C = k R C 2 ( 1 x 0 + 1 x 1 ) = k ( n G n L ) 2 R 2 ( 1 x 0 + 1 x 1 ) ,
u R = k R 2 ( 1 x 0 + 1 x 1 ) .
C ( u i , 0 ) = 2 u i sin u i 2 ,
S ( u i , 0 ) = 2 u i ( 1 cos u i 2 ) ( i = R c or R ) .
E p = i u R C 2 u 0 ( C ( u R C , 0 ) i S ( u R C , 0 ) ) + u 0 { 1 i u R 2 ( C ( u R , 0 ) i S ( u R , 0 ) ) } .
I p = | u 0 | 2 + 4 | u 0 | 2 sin 2 u R C 4 + | u 0 | 2 u R C { ( 1 u R 2 S ( u R , 0 ) ) S ( u R , 0 ) u R 2 C ( u R , 0 ) C ( u R C , 0 ) } ,
I p = I 0 + 4 I 0 sin 2 u R C 4 + I 0 u R C { ( 1 u R 2 S ( u R , 0 ) ) S ( u R , 0 ) u R 2 C ( u R , 0 ) C ( u R C , 0 ) } .
I p = I 0 [ 1 + 8 sin 2 u R C 4 8 sin 2 u R C 4 sin 2 u R 4 2 sin u R C 2 sin u R 2 ] .

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