## Special purpose computer system for flow visualization using holography technology

Optics Express, Vol. 16, Issue 11, pp. 7686-7692 (2008)

http://dx.doi.org/10.1364/OE.16.007686

Acrobat PDF (1087 KB)

### Abstract

We have designed a special purpose computer system for visualizing fluid flow using digital holographic particle tracking velocimetry (DHPTV). This computer contains an Field Programmble Gate Array (FPGA) chip in which a pipeline for calculating the intensity of an object from a hologram by fast Fourier transform is installed. This system can produce 100 reconstructed images from a 1024×1024-grid hologram in 3.3 sec. It is expected that this system will contribute to fluid flow analysis.

© 2008 Optical Society of America

## 1. Introduction

1. D. H. Barnhart, R. J. Adrian, and G. C. Papen,“Phase-conjugate holographic system for high-resolution particle-image velocimetry,” Appl. Opt. **33**, 7159–7170 (1994). [CrossRef] [PubMed]

2. H. Memg and F. Hussain, “In-line recording and off-axis viewing technique for holographic particle velocimetry,” Appl. Opt. **34**, 1827–1840 (1995). [CrossRef]

3. J. Sheng, E. Malkiel, and J. Katz,“Single beam two-views holographic particle image velocimetry,” Appl. Opt. **42**, 235–250 (2003). [CrossRef] [PubMed]

4. U. Schnars, T. Kreis, and W. Juptner, “Direct recording of holograms by CCD target and numerical reconstruction,” Appl. Opt. **33**, 179–181 (1994). [CrossRef] [PubMed]

5. S. Murata and N. Yasuda, “Potential of digitalholography in particle measurement,” Opt. Laser Technol. **32**, 567–574 (2000). [CrossRef]

4. U. Schnars, T. Kreis, and W. Juptner, “Direct recording of holograms by CCD target and numerical reconstruction,” Appl. Opt. **33**, 179–181 (1994). [CrossRef] [PubMed]

5. S. Murata and N. Yasuda, “Potential of digitalholography in particle measurement,” Opt. Laser Technol. **32**, 567–574 (2000). [CrossRef]

7. N. Masuda, T. Ito, K. Kayama, H. Kono, S. Satake, T. Kunugi, and K. Sato, “Special purpose computer for digital holographic particle tracking velocimetry,” 14, Opt. Express , **14**, 587–592 (2006). [CrossRef]

## 2. Algorithm for DHPTV

*ϕ*(

*x*,

_{i}*y*,

_{i}*z*) is the amplitude of the object light at point (

_{i}*x*,

_{i}*y*,

_{i}*z*),

_{i}*λ*is the wavelength of the reference light,

*I*is the intensity of the hologram at point (

_{α}*x*,

_{α}*y*,0),

_{α}*k*is the wavenumber of the reference light, and

*N*is the number of divisions of the hologram grid in the x or y directions. Note that in Eq. (1), the hologram is in the

*z*=0 plane. Furthermore, using the Fresnel approximation under the assumption that |

*z*|≫|

_{i}*x*-

_{α}*x*|, |

_{i}*y*-

_{α}*y*|, we obtain

_{i}*x*and

*y*directions and is transformed by a two-dimensional Fourier transform,

*n*,

*m*) is the two-dimensional Fourier transform of

*ϕ*(

*x*,

_{i}*y*,

_{i}*z*),

_{i}*Î*(

*n*,

*m*) is the transform of

*I*, and

_{α}*G*(

*n*,

*m*) is the transform of

*g*(

*x*,

*y*).

*g*(

*x*,

*y*) and obtain

*P*is the grid size of the hologram.

*z*constant. To calculate Eq. (3), the method described below was developed:

- calculate
*Î*(*n*,*m*) from*I*_{α} - calculate Φ(
*n*,*m*)=*Î*(*n*,*m*)×*G*(*n*,*m*) - calculate
*ϕ*(*x*,_{i}*y*,_{i}*z*) by using a two-dimensional inverse Fourier transform._{i}

*Î*(

*n*,

*m*) is the same when the same hologram is used.

## 3. Hardware design of FFT–HORN2

*Î*(

*n*,

*m*)×

*G*(

*n*,

*m*). The POST–Processing unit operates normalization and threshold processing. The RAM control unit controls reading and writing to the external DDR–SDRAM unit.

*Î*(

*n*,

*m*). The FFT CALC unit can perform a one-dimensional FFT. Hence one-dimensional FFT is performed twice in this pipeline to calculate the two-dimensional FFT. During the calculation, the one-dimensional FFT results are saved temporarily in the DDR-RAM unit. Next, the G-pipeline unit evaluates

*G*(

*n*,

*m*) using the input data P1(

*P*1=(λ

*z*)/(

_{i}*N*

^{2}Δ

*P*)) and

*Î*(

*n*,

*m*)×

*G*(

*n*,

*m*) is calculated in the Multiplier unit. The results are sent to the FFT CALC unit and IFFT is performed in the FFT CALC unit. Lastly, the normalization of results and threshold processing are carried out in the POST–Processing unit.

9. T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie,“A special-purpose computer for electroholography HORN-5 to realize a real-time reconstruction,” Opt. Express , **13**, 1923–1932(2005). [CrossRef] [PubMed]

## 4. Performance

8. FFTW Home Page, http://www.fftw.org/

*µm*. The grid size of the hologram (Δ

*P*) was 0.4

*µm*. For this simulation, holograms were generated by the system described in detail in Ref. [10

10. S. Satake, T. Kunugi, K. Sato, T. Ito, and J. Taniguchi, “Three-dimensional flow tracking in a micro channel with high time resolution using micro digital-holographic particle-tracking velocimetry,” Opt. Rev. **12**, 442–444 (2005). [CrossRef]

*µm*from the CCD surface. In Fig. 3, the black small objects are the reconstructed particles. This result shows FFT–HORN2 reconstructs the image exactly. Figure 4 is the movie of reconstructed particles flow.

*x*−

*z*plane (Fig. 5). Here, sections parallel to the

*x*-

*y*plane were reconstructed at a fixed pitch in the

*z*-direction (Δ

*z*=0.4

*µm*) from

*z*=23.2

*µm*to

*z*=50.8

*µm*(reconstructing 70 images). The right side figure of Fig. 5 represents the

*x*-

*z*plane in the center of the black square region in the left side figure of Fig. 5. In this figure, the size of the particle changes in the

*z*direction. This occurs because

## 5. Conclusion and future work

## Acknowledgments

## References and links

1. | D. H. Barnhart, R. J. Adrian, and G. C. Papen,“Phase-conjugate holographic system for high-resolution particle-image velocimetry,” Appl. Opt. |

2. | H. Memg and F. Hussain, “In-line recording and off-axis viewing technique for holographic particle velocimetry,” Appl. Opt. |

3. | J. Sheng, E. Malkiel, and J. Katz,“Single beam two-views holographic particle image velocimetry,” Appl. Opt. |

4. | U. Schnars, T. Kreis, and W. Juptner, “Direct recording of holograms by CCD target and numerical reconstruction,” Appl. Opt. |

5. | S. Murata and N. Yasuda, “Potential of digitalholography in particle measurement,” Opt. Laser Technol. |

6. | S. Satake, T. Kunugi, K. Sato, and T. Ito, “Digital Holographic Particle Tracking Velocimetry for 3-D Transient Flow around an Obstacle in a Narrow Channel,” Opt. Rev. |

7. | N. Masuda, T. Ito, K. Kayama, H. Kono, S. Satake, T. Kunugi, and K. Sato, “Special purpose computer for digital holographic particle tracking velocimetry,” 14, Opt. Express , |

8. | FFTW Home Page, http://www.fftw.org/ |

9. | T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie,“A special-purpose computer for electroholography HORN-5 to realize a real-time reconstruction,” Opt. Express , |

10. | S. Satake, T. Kunugi, K. Sato, T. Ito, and J. Taniguchi, “Three-dimensional flow tracking in a micro channel with high time resolution using micro digital-holographic particle-tracking velocimetry,” Opt. Rev. |

**OCIS Codes**

(090.0090) Holography : Holography

(090.1760) Holography : Computer holography

(120.7250) Instrumentation, measurement, and metrology : Velocimetry

**ToC Category:**

Holography

**History**

Original Manuscript: March 27, 2008

Revised Manuscript: May 7, 2008

Manuscript Accepted: May 11, 2008

Published: May 13, 2008

**Citation**

Yukio Abe, Nobuyuki Masuda, Hideaki Wakabayashi, Yuta Kazo, Tomoyoshi Ito, Shin-ichi Satake, Tomoaki Kunugi, and Kazuho Sato, "Special purpose computer system for flow visualization using holography
technology," Opt. Express **16**, 7686-7692 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-7686

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### References

- D. H. Barnhart, R. J. Adrian and G. C. Papen,"Phase-conjugate holographic system for high-resolution particleimage velocimetry," Appl. Opt. 33, 7159-7170 (1994). [CrossRef] [PubMed]
- H. Memg and F. Hussain, "In-line recording and off-axis viewing technique for holographic particle velocimetry," Appl. Opt. 34, 1827-1840 (1995). [CrossRef]
- J. Sheng, E. Malkiel, and J. Katz,"Single beam two-views holographic particle image velocimetry," Appl. Opt. 42, 235-250 (2003). [CrossRef] [PubMed]
- U. Schnars, T. Kreis, and W. Juptner, "Direct recording of holograms by CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994). [CrossRef] [PubMed]
- S. Murata and N. Yasuda, "Potential of digitalholography in particle measurement," Opt. Laser Technol. 32, 567-574 (2000). [CrossRef]
- S. Satake, T. Kunugi, K. Sato, and T. Ito, "Digital Holographic Particle Tracking Velocimetry for 3-D Transient Flow around an Obstacle in a Narrow Channel," Opt. Rev. 11, 162-164 (2004).
- N. Masuda, T. Ito, K. Kayama, H. Kono, S. Satake, T. Kunugi, and K. Sato, "Special purpose computer for digital holographic particle tracking velocimetry," Opt. Express 14, 587-592 (2006). [CrossRef]
- FFTW Home Page, http://www.fftw.org/
- T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie,"A special-purpose computer for electroholography HORN-5 to realize a real-time reconstruction," Opt. Express 13, 1923-1932 (2005). [CrossRef] [PubMed]
- S. Satake, T. Kunugi, K. Sato, T. Ito and J. Taniguchi, "Three-dimensional flow tracking in a micro channel with high time resolution using micro digital-holographic particle-tracking velocimetry," Opt. Rev. 12, 442-444 (2005). [CrossRef]

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