Abstract

The correlation coefficient (CC) method, which was proposed by our research group, is applied to digital particle holography to locate the focal plane of particles. It uses the fact that the CC is maximum at the focal plane. The factors influencing this method are discussed with a numerical simulation of holograms. For real holograms, the Wiener filter was proposed to process both recorded holograms and reconstructed images. The application results using the dot array target showed that the Wiener filter is a very effective tool for processing holography-related images. The effects of the dot size and the object distance on the errors in the determination of the focal plane by the CC method were investigated by using the calibration target.

© 2008 Optical Society of America

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  1. U. Schnars and W. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85-101 (2002).
    [CrossRef]
  2. L. Yu and L. Cai, “Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram,” J. Opt. Soc. Am. A 18, 1033-1045 (2001).
    [CrossRef]
  3. F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express. 14, 5895-5980 (2006).
    [CrossRef] [PubMed]
  4. C. B. Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409-421 (2000).
    [CrossRef]
  5. Y. Zhang, D. X. Zheng, J. L. Shen, and C. L. Zhang, “3D locations of the object directly from in-line holograms using the Gabor transform,” Proc. SPIE 5636, 116-120 (2005).
    [CrossRef]
  6. Y. J. Choo and B. S. Kang, “The characteristics of the particle position along an optical axis in particle holography,” Meas. Sci. Technol. 17, 761-770 (2006).
    [CrossRef]
  7. U. Schnars and W. Jueptner, “Digital holography,” in Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005), pp. 41-45.
    [PubMed]
  8. Y. Yang and B. S. Kang, “Numerical simulation of in-line digital holograms,” in Proceedings of Asia Display 2007, H. S. Kwok, ed. (East China Normal U. Press, 2007), pp. 2055-2059.
  9. J. W. Goodman, “Fresnel and Fraunhofer diffraction,” in Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 68-72.
  10. V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123-128 (2005).
    [CrossRef]
  11. L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148-161 (2005).
  12. V. R. Singh and A. K. Asundi, “Amplitude contrast image enhancement in digital holography for particles analysis,” Proc. SPIE 5878, 17.1-17.8 (2005).
  13. S. Kim and S. J. Lee, “Effect of particle concentration on digital holographic PTV measurement,” J. Korea Soc. Mech. Eng. B 30, 929-934 (2006).
  14. A. K. Jain, “Image filtering and restoration,” in Fundamentals of Digital Image Processing, T. Kailath, ed. (Prentice-Hall, 1989), pp. 276-306.

2006 (3)

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express. 14, 5895-5980 (2006).
[CrossRef] [PubMed]

Y. J. Choo and B. S. Kang, “The characteristics of the particle position along an optical axis in particle holography,” Meas. Sci. Technol. 17, 761-770 (2006).
[CrossRef]

S. Kim and S. J. Lee, “Effect of particle concentration on digital holographic PTV measurement,” J. Korea Soc. Mech. Eng. B 30, 929-934 (2006).

2005 (4)

Y. Zhang, D. X. Zheng, J. L. Shen, and C. L. Zhang, “3D locations of the object directly from in-line holograms using the Gabor transform,” Proc. SPIE 5636, 116-120 (2005).
[CrossRef]

V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123-128 (2005).
[CrossRef]

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148-161 (2005).

V. R. Singh and A. K. Asundi, “Amplitude contrast image enhancement in digital holography for particles analysis,” Proc. SPIE 5878, 17.1-17.8 (2005).

2002 (1)

U. Schnars and W. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85-101 (2002).
[CrossRef]

2001 (1)

2000 (1)

C. B. Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Asundi, A. K.

V. R. Singh and A. K. Asundi, “Amplitude contrast image enhancement in digital holography for particles analysis,” Proc. SPIE 5878, 17.1-17.8 (2005).

Cai, L.

Callens, N.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express. 14, 5895-5980 (2006).
[CrossRef] [PubMed]

Choo, Y. J.

Y. J. Choo and B. S. Kang, “The characteristics of the particle position along an optical axis in particle holography,” Meas. Sci. Technol. 17, 761-770 (2006).
[CrossRef]

Coëtmellec, S.

C. B. Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Denis, L.

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148-161 (2005).

Dubois, F.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express. 14, 5895-5980 (2006).
[CrossRef] [PubMed]

Ducottet, C.

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148-161 (2005).

Fournel, T.

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148-161 (2005).

Fournier, C.

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148-161 (2005).

Goodman, J. W.

J. W. Goodman, “Fresnel and Fraunhofer diffraction,” in Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 68-72.

Ilchenko, V.

V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123-128 (2005).
[CrossRef]

Jain, A. K.

A. K. Jain, “Image filtering and restoration,” in Fundamentals of Digital Image Processing, T. Kailath, ed. (Prentice-Hall, 1989), pp. 276-306.

Jueptner, W.

U. Schnars and W. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85-101 (2002).
[CrossRef]

U. Schnars and W. Jueptner, “Digital holography,” in Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005), pp. 41-45.
[PubMed]

Kang, B. S.

Y. J. Choo and B. S. Kang, “The characteristics of the particle position along an optical axis in particle holography,” Meas. Sci. Technol. 17, 761-770 (2006).
[CrossRef]

Y. Yang and B. S. Kang, “Numerical simulation of in-line digital holograms,” in Proceedings of Asia Display 2007, H. S. Kwok, ed. (East China Normal U. Press, 2007), pp. 2055-2059.

Kim, S.

S. Kim and S. J. Lee, “Effect of particle concentration on digital holographic PTV measurement,” J. Korea Soc. Mech. Eng. B 30, 929-934 (2006).

Lebrun, D.

C. B. Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Lee, S. J.

S. Kim and S. J. Lee, “Effect of particle concentration on digital holographic PTV measurement,” J. Korea Soc. Mech. Eng. B 30, 929-934 (2006).

Lefebvre, C. B.

C. B. Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Lex, T.

V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123-128 (2005).
[CrossRef]

Özkul, C.

C. B. Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Sattelmayer, T.

V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123-128 (2005).
[CrossRef]

Schnars, U.

U. Schnars and W. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85-101 (2002).
[CrossRef]

U. Schnars and W. Jueptner, “Digital holography,” in Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005), pp. 41-45.
[PubMed]

Schockaert, C.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express. 14, 5895-5980 (2006).
[CrossRef] [PubMed]

Shen, J. L.

Y. Zhang, D. X. Zheng, J. L. Shen, and C. L. Zhang, “3D locations of the object directly from in-line holograms using the Gabor transform,” Proc. SPIE 5636, 116-120 (2005).
[CrossRef]

Singh, V. R.

V. R. Singh and A. K. Asundi, “Amplitude contrast image enhancement in digital holography for particles analysis,” Proc. SPIE 5878, 17.1-17.8 (2005).

Yang, Y.

Y. Yang and B. S. Kang, “Numerical simulation of in-line digital holograms,” in Proceedings of Asia Display 2007, H. S. Kwok, ed. (East China Normal U. Press, 2007), pp. 2055-2059.

Yourassowsky, C.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express. 14, 5895-5980 (2006).
[CrossRef] [PubMed]

Yu, L.

Zhang, C. L.

Y. Zhang, D. X. Zheng, J. L. Shen, and C. L. Zhang, “3D locations of the object directly from in-line holograms using the Gabor transform,” Proc. SPIE 5636, 116-120 (2005).
[CrossRef]

Zhang, Y.

Y. Zhang, D. X. Zheng, J. L. Shen, and C. L. Zhang, “3D locations of the object directly from in-line holograms using the Gabor transform,” Proc. SPIE 5636, 116-120 (2005).
[CrossRef]

Zheng, D. X.

Y. Zhang, D. X. Zheng, J. L. Shen, and C. L. Zhang, “3D locations of the object directly from in-line holograms using the Gabor transform,” Proc. SPIE 5636, 116-120 (2005).
[CrossRef]

J. Korea Soc. Mech. Eng. B (1)

S. Kim and S. J. Lee, “Effect of particle concentration on digital holographic PTV measurement,” J. Korea Soc. Mech. Eng. B 30, 929-934 (2006).

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (2)

Y. J. Choo and B. S. Kang, “The characteristics of the particle position along an optical axis in particle holography,” Meas. Sci. Technol. 17, 761-770 (2006).
[CrossRef]

U. Schnars and W. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85-101 (2002).
[CrossRef]

Opt. Express. (1)

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express. 14, 5895-5980 (2006).
[CrossRef] [PubMed]

Opt. Lasers Eng. (1)

C. B. Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Proc. SPIE (4)

Y. Zhang, D. X. Zheng, J. L. Shen, and C. L. Zhang, “3D locations of the object directly from in-line holograms using the Gabor transform,” Proc. SPIE 5636, 116-120 (2005).
[CrossRef]

V. Ilchenko, T. Lex, and T. Sattelmayer, “Depth position detection of the particles in digital holographic particle image velocimetry (DHPIV),” Proc. SPIE 5851, 123-128 (2005).
[CrossRef]

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-line digital holography,” Proc. SPIE 5914, 148-161 (2005).

V. R. Singh and A. K. Asundi, “Amplitude contrast image enhancement in digital holography for particles analysis,” Proc. SPIE 5878, 17.1-17.8 (2005).

Other (4)

A. K. Jain, “Image filtering and restoration,” in Fundamentals of Digital Image Processing, T. Kailath, ed. (Prentice-Hall, 1989), pp. 276-306.

U. Schnars and W. Jueptner, “Digital holography,” in Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005), pp. 41-45.
[PubMed]

Y. Yang and B. S. Kang, “Numerical simulation of in-line digital holograms,” in Proceedings of Asia Display 2007, H. S. Kwok, ed. (East China Normal U. Press, 2007), pp. 2055-2059.

J. W. Goodman, “Fresnel and Fraunhofer diffraction,” in Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 68-72.

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Figures (17)

Fig. 1
Fig. 1

(Color online) Optical setup of in-line digital holography.

Fig. 2
Fig. 2

Coordinate system.

Fig. 3
Fig. 3

CC method.

Fig. 4
Fig. 4

Typical curve shape of intensity distribution of reconstruction images with particle size, D d = 300 μ m and object distance, d = 190   mm .

Fig. 5
Fig. 5

CC method applied to different size particles in optical holography (from [6]).

Fig. 6
Fig. 6

CCs by different correlation intervals (object distance, d = 150   mm ).

Fig. 7
Fig. 7

Effect of correlation interval on the CC (object distance, d = 150   mm ).

Fig. 8
Fig. 8

(Color online) Effect of particle size and object distance on the CC: (a) D d = 16 μ m , (b) D d = 100 μ m , (c) D d = 230 μ m , (d) D d = 3 0 0 μ m .

Fig. 9
Fig. 9

(Color online) Comparison of errors for the CC and gradient methods.

Fig. 10
Fig. 10

Characteristics of self-adaptive Wiener filter.

Fig. 11
Fig. 11

Experimental setup of in-line digital holography.

Fig. 12
Fig. 12

Dot array target and its hologram: (a) dot array target and (b) hologram of local target showing ROIs of 81 dots.

Fig. 13
Fig. 13

(Color online) Application of Wiener filter: (a) without filtering and (b) with filtering.

Fig. 14
Fig. 14

Calibration target with different sized particles: (a) calibration target and (b) magnified images of different sized dots.

Fig. 15
Fig. 15

Reconstruction images of particles at different reconstruction distances: (a) D d = 3 0 0 μ m ; (b) D d = 230 μ m ; (c) D d = 100 μ m ; (d) D d = 51 μ m [the scale is two times of (c)]; (e) D d = 10 μ m [the scale is five times of (c)].

Fig. 16
Fig. 16

Variation of the CC for different dot sizes.

Fig. 17
Fig. 17

(Color online) Errors of the focal plane for different dot sizes.

Tables (3)

Tables Icon

Table 1 Errors of Focal Plane Determination by CC Method a

Tables Icon

Table 2 Errors of Focal Plane Determination by Gradient Method a

Tables Icon

Table 3 Effect of Wiener Filter on Errors of Focal Plane Determination

Equations (9)

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

R ( ξ , η ) = i λ h ( x , y ) E R ( x , y ) × exp ( i 2 π λ ρ ) ρ d x d y ,
ρ = ( ξ x ) 2 + ( η y ) 2 + d 2 .
R ( ξ , η ) = F 1 { F [ h ( x , y ) ] F [ i λ exp [ i 2 π λ ( d 2 + ( x N 2 ) 2 Δ x 2 + ( y N 2 ) 2 Δ y 2 ) ] ( d 2 + ( x N 2 ) 2 Δ x 2 + ( y N 2 ) 2 Δ y 2 ) ] } ,
I = R ( ξ , η ) 2 .
h ( x , y ) = i λ O ( ξ , η ) E R ( ξ , η ) × exp ( i 2 π λ ρ ) ρ d ξ d η ,
ρ = ( x ξ ) 2 + ( y η ) 2 + d 2 ,
d 1 8 [ ( ξ x ) 2 + ( η y ) 2 ] 2 λ 3 = 1 8 [ N 2 ( Δ ξ Δ x ) 2 + N 2 ( Δ η Δ y ) 2 ] 2 λ 3 ,
CC = [ m n ( F m n F ¯ ) ( G m n G ¯ ) [ m n ( F m n F ¯ ) 2 [ m n ( G m n G ¯ ) 2 ] ] ] ,
G ( ω 1 , ω 2 ) = H * ( ω 1 , ω 2 ) S u u ( ω 1 , ω 2 ) H ( ω 1 , ω 2 ) 2 S u u ( ω 1 , ω 2 ) + S η η ( ω 1 , ω 2 ) ,

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