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Applied Optics

Applied Optics


  • Vol. 34, Iss. 2 — Jan. 10, 1995
  • pp: 249–255

Two-dimensional wavelet transform and application to holographic particle velocimetry

W. L. Anderson and Hongyan Diao  »View Author Affiliations

Applied Optics, Vol. 34, Issue 2, pp. 249-255 (1995)

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The goal of holographic particle velocimetry is to infer fluid velocity patterns from images reconstructed from doubly exposed holograms of fluid volumes seeded with small particles. The advantages offered by in-line holography in this context usually make it the method of choice, but seeding densities sufficient to achieve high spatial resolution in the sampling of the velocity fields cause serious degradation, through speckle, of the signal-to-noise ratio in the reconstructed images. The in-line method also leads to a great depth of field in paraxial viewing of reconstructed images, making it essentially impossible to estimate particle depth with useful accuracy. We present here an analysis showing that these limitations can be circumvented by variably scaled correlation, or wavelet transformation. The shift variables of the wavelet transform are provided automatically by the optical correlation methodology. The variable scaling of the wavelet transform derives, in this case, directly from the need to accommodate varying particle depths. To provide such scaling, we use a special optical system incorporating prescribed variability in spacings and focal length of lenses to scan through the range of particle depths. Calculation shows, among other benefits, improvement by approximately two orders of magnitude in depth resolution. A much higher signal-to-noise ratio together with faster data extraction and processing should be attainable.

© 1995 Optical Society of America

Original Manuscript: December 2, 1993
Revised Manuscript: August 15, 1994
Published: January 10, 1995

W. L. Anderson and Hongyan Diao, "Two-dimensional wavelet transform and application to holographic particle velocimetry," Appl. Opt. 34, 249-255 (1995)

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  1. D. Gabor, “Theory of communication,” J. Inst. Electr. Eng. 93, 429–457 (1946).
  2. B. J. Thompson, “Diffraction by opaque and transparent objects,” in Photo-Optical Data Reduction, R. J. Gast, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2, 43–46 (1964).
  3. J. D. Trolinger, R. A. Belz, W. M. Farmer, “Holographic techniques for the study of dynamic particle fields,” Appl. Opt. 8, 957–961 (1969). [CrossRef] [PubMed]
  4. P. H. Malyak, B. J. Thompson, “Particle displacement and velocity measurement using holography,” Opt. Eng. 23, 567–576 (1984).
  5. Y. J. Lee, J. H. Kim, “A review of holography application in multiphase flow visualization study,” J. Fluids Eng. 108, 279–288 (1986). [CrossRef]
  6. L. M. Weinstein, G. R. Beeler, A. M. Lindemann, “High-speed holocinematographic velocimeter for studying turbulent flow control physics,” presented at the Processing American Institute of Aeronautics and Astronautics Shear Flow Control Conference, Boulder, Colo., 12–14 March 1985.
  7. H. Meng, F. Hussain, “Holographic particle velocimetry: a 3-D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dyn. Res. 8, 33–52 (1991). [CrossRef]
  8. H. Meng, W. L. Anderson, F. Hussain, D. D. Liu, “Intrinsic speckle noise in in-line holography,” J. Opt. Soc. Am. A 10, 2046–2058 (1993). [CrossRef]
  9. G. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory 6, 311–329 (1960). [CrossRef]
  10. J. R. Klauder, A. C. Price, S. Darlington, W. J. Albersheim, “The theory and design of chirp radars,” Bell Syst. Tech. J. 39, 745–806 (1960).
  11. L. Onural, M. T. Özgen, “Extraction of three-dimensional object-location information directly from in-line holograms using Wigner analysis,” J. Opt. Soc. Am. A 9, 252–260 (1992). [CrossRef]
  12. S. G. Mallet, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Machine Intell. 11, 674–693 (1989). [CrossRef]
  13. O. Rioul, M. Vetterli, “Wavelets and signal processing,” IEEE Signal Process. Mag. 8(10), 14–38 (1991). [CrossRef]
  14. F. Hlawatsch, G. F. Boudreaux-Bartels, “Linear and quadratic time-frequency signal representations,” IEEE Signal Process. Mag. 9(4), 21–67 (1992). [CrossRef]
  15. E. Freysz, B. Pouligny, F. Argoul, A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 7745–7748 (1990). [CrossRef]
  16. J. Caulfield, H. Szu, “Parallel discrete and continuous wavelet transforms,” Opt. Eng. 31, 1835–1839 (1992). [CrossRef]
  17. H. Szu, Y. Sheng, J. Chen, “Wavelet transform as a bank of matched filters,” Appl. Opt. 31, 3267–3277 (1992). [CrossRef] [PubMed]
  18. D. Mendlovic, N. Konforti, “Optical realization of the wavelet transform for two-dimensional objects,” Appl. Opt. 32, 6542–6546 (1993). [CrossRef] [PubMed]
  19. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964). [CrossRef]
  20. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3.
  21. V. Zimin, H. Meng, F. Hussain, “Innovative holographic particle velocimeter: a multibeam technique,” Opt. Lett. 18, 1101–1103 (1993). [CrossRef] [PubMed]
  22. H. Meng, F. Hussain, “IROV (in-line recording and off-axis viewing): a novel holographic technique for particle field measurement and holographic particle velocimetry,” Appl. Opt. (to be published).

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