Experiments in Fluids

, Volume 53, Issue 2, pp 531–543 | Cite as

Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions

Research Article


Tomographic shadowgraphy is an image-based optical technique capable of reconstructing the three dimensional instantaneous spray distributions within a given volume. The method is based on a multiple view imaging setup with inline illumination provided by current-pulsed LEDs, which results in droplet shadows being projected onto multiple sensor planes. Each camera records image pairs with short inter-framing times that allow the trajectories of the individual droplets to be estimated using conventional three-dimensional particle tracking approaches. The observed volume is calibrated with a traversed micro-target. A comparison is made between several photogrammetric and polynomial least-square camera calibration techniques regarding their accuracy in deep volume calibration at magnifications close to unity. A calibration method based on volume calibration from multiple planar homographies at equally spaced z-planes was found to produce the most reliable calibration. The combination of back-projected images at each voxel plane efficiently reproduces the droplet positions in three-dimensional space by line-of-sight (LOS) intensity reconstruction. Further improvement of the reconstruction can be achieved by iterative tomographic reconstruction, namely simultaneous multiplicative algebraic reconstruction technique (SMART). The quality of spray reconstruction is investigated using experimental data from multiple view shadowgraphs of hollow cone and flat fan water sprays. The investigations are further substantiated with simulations using synthetic data.

List of symbols


Cross-correlation coefficient


Nozzle orifice diameter


Airy disk diameter


Focal length




Maximum continuous forward current




Sensor resolution [Pixel/mm]

\(\Updelta t\)

Delay between two illumination pulses (for PIV)


Arbitrary scale factors in projective geometry


Back-projection error


Wavelength of light


Pulse duration


Camera yaw angle (around world y axis)


Camera pitch angle (around new x axis)



Distorted camera coordinates


Image coordinates


Projected camera coordinates


  1. Adrian RJ, Westerweel J (2011) Particle image velocimetry. Cambridge University Press, New YorkGoogle Scholar
  2. Atkinson C, Soria J (2009) An efficient simultaneous reconstruction technique for tomographic particle image velocimetry. Exp Fluids 47:553–568CrossRefGoogle Scholar
  3. Bachalo WD, Houser MJ (1984) Development of the phase/doppler spray analyzer for liquid drop size and velocity characterizations. Opt Eng 23:583–590Google Scholar
  4. Bradski G (2000) The openCV library. Dr. Dobb’s J Softw ToolsGoogle Scholar
  5. Bradski G, Kaehler A (2008) Learning openCV, 1st edn. O’ Reilly Media, Inc., SebastopolGoogle Scholar
  6. Brown DC (1971) Close-range camera calibration. Photogramm Eng 37:855–866Google Scholar
  7. Cai W, Powell CF, Yue Y, Narayanan S, Wang J, Tate MW, Renzi MJ, Ercan A, Fontes E, Gruner SM (2003) Quantitative analysis of highly transient fuel sprays by time-resolved x-radiography. Appl Phys Lett 83(8):1671–1673CrossRefGoogle Scholar
  8. Cao L, Pan G, Jong J, Woodward S, Meng H (2008) Hybrid digital holographic imaging system for three-dimensional dense particle field measurement. Appl Opt 47(25):4501–4508CrossRefGoogle Scholar
  9. Durst F, Zaré M (1975) Laser-doppler measurements in two-phase flow. In: Proceedings of the LDA-Symposium, Copenhagen, pp 403–429Google Scholar
  10. Elsinga G, Scarano F, Wieneke B, van Oudheusden B (2006) Tomographic particle image velocimetry. Exp Fluids 41:933–947CrossRefGoogle Scholar
  11. Faugeras O (1994) Three-dimensional computer vision a geometric viewpoint. Artificial intelligence. MIT Press, Cambridge, MAGoogle Scholar
  12. Glover AR, Skippon SM, Boyle RD (1995) Interferometric laser imaging for droplet sizing: a method for droplet-size measurement in sparse spray systems. Appl Opt 34(36):8409–8421CrossRefGoogle Scholar
  13. Harris C, Stephens M (1988) A combined corner and edge detector. In: 4th Alvey Vision Conference, pp 147–151Google Scholar
  14. Hom J, Chigier N (2002) Rainbow refractometry: simultaneous measurement of temperature, refractive index, and size of droplets. Appl Opt 41(10):1899–1907CrossRefGoogle Scholar
  15. Jermy M, Greenhalgh D (2000) Planar dropsizing by elastic and fluorescence scattering in sprays too dense for phase doppler measurement. Appl Phys B: Lasers Optics 71:703–710CrossRefGoogle Scholar
  16. Jones AR, Sarjeant M, Davis CR, Denham RO (1978) Application of in-line holography to drop size measurement in dense fuel sprays. Appl Opt 17(3):328–330CrossRefGoogle Scholar
  17. Kang B, Poulikakos D (1996) Holography experiments in a dense high-speed impinging jet spray. J Propul Power 12(2):341–348CrossRefGoogle Scholar
  18. Kawaguchi T, Akasaka Y, Maeda M (2002) Size measurements of droplets and bubbles by advanced interferometric laser imaging technique. Meas Sci Technol 13(3):308CrossRefGoogle Scholar
  19. Le Gal P, Farrugia N, Greenhalgh D (1999) Laser sheet dropsizing of dense sprays. Optics Laser Technol 31(1):75–83CrossRefGoogle Scholar
  20. Lefebvre AH (1989) Atomization and sprays. CRC Press Taylor & Francis Group, New YorkGoogle Scholar
  21. Liu X, Cheong SK, Powell CF, Wang J, Hung DL, Winkelman JR, Tate MW, Ercan A, Schuette DR, Koerner L, Gruner SM (2005) Near-field characterization of direct injection gasoline sprays from multi-hole injector using ultrafast x-tomography. In: ILASS Americas, 18th Annual Conference on Liquid Atomization and Spray Systems, Irvine, CA (USA)Google Scholar
  22. Lü Q, Chen Y, Yuan R, Ge B, Gao Y, Zhang Y (2009) Trajectory and velocity measurement of a particle in spray by digital holography. Appl Opt 48(36):7000–7007CrossRefGoogle Scholar
  23. Maas H, Westfeld P, Putze T, Boetkjaer N, Kitzhofer J, Brücker C (2009) Photogrammetric techniques in multi-camera tomographic PIV. In: 8th International Symposium on Particle Image Velocimetry—(PIV09), Melbourne, AustraliaGoogle Scholar
  24. Maeda M, Kawaguchi T, Hishida K (2000) Novel interferometric measurement of size and velocity distributions of spherical particles in fluid flows. Meas Sci Technol 11(12):L13CrossRefGoogle Scholar
  25. Meng H, Pan G, Pu Y, Woodward SH (2004) Holographic particle image velocimetry: from film to digital recording. Meas Sci Technol 15(4):673CrossRefGoogle Scholar
  26. Michaelis D, Novara M, Scarano F, Wieneke B (2010) Comparison of volume reconstruction techniques at different particle densities. In: 15th International Symposium on Applications of Laser Techniques to Fluid MechanicsGoogle Scholar
  27. Miller B, Sallam KA, Lin KC, Carter C (2006) Digital holographic spray analyzer. In: ASME Conference Proceedings of 14th International Conference on Nuclear Engineering (FEDSM2006), vol. 2, pp 1023–1028Google Scholar
  28. Mishra D, Muralidhar K, Munshi P (1999) A robust MART algorithm for tomographic applications. Num Heat Transf Part B: Fundam 35(4):485–506CrossRefGoogle Scholar
  29. Raffel M, Willert C, Wereley S, Kompenhans J (2007) Particle image velocimetry, a practical guide. Springer, Berlin-HeidelbergGoogle Scholar
  30. Salvi J, Armangu X, Batlle J (2002) A comparative review of camera calibrating methods with accuracy evaluation. Pattern Recogn 35(7):1617–1635MATHCrossRefGoogle Scholar
  31. Santangelo PJ, Sojka PE (1994) Focused-image holography as a dense-spray diagnostic. Appl Opt 33(19):4132–4136CrossRefGoogle Scholar
  32. Schanz D, Gesemann S, Schroeder A, Wieneke B, Michaelis D (2010) Tomographic reconstruction with non-uniform optical transfer functions (otf). In: 15th International Symposium on Applications of Laser Techniques to Fluid MechanicsGoogle Scholar
  33. Soloff SM, Adrian RJ, Liu ZC (1997) Distortion compensation for generalized stereoscopic particle image velocimetry. Meas Sci Technol 8(12):1441CrossRefGoogle Scholar
  34. Soria J, Atkinson C (2008) Towards 3c-3d digital holographic fluid velocity vector field measurement—tomographic digital holographic PIV (Tomo-HPIV). Meas Sci Technol 19(7):074,002CrossRefGoogle Scholar
  35. Swithenbank J, Beer JM, Taylor DS, Abbot D, McCreath GC (1976) A laser diagnostic technique for the measurement of droplet and particle size distribution. In: 14th Aerospace Sciences Meeting, AIAA, Washington, DC, Jan 26–28, 1976Google Scholar
  36. Tsai R (1987) A versatile camera calibration technique for high-accuracy 3d machine vision metrology using off-the-shelf tv cameras and lenses. IEEE J Robot Autom RA-3:323–344CrossRefGoogle Scholar
  37. Upton T, Verhoeven D, Hudgins D (2011) High-resolution computed tomography of a turbulent reacting flow. Exp Fluids 50:125–134CrossRefGoogle Scholar
  38. Wieneke B (2008) Volume self-calibration for 3d particle image velocimetry. Exp Fluids 45:549–556CrossRefGoogle Scholar
  39. Willert C (2006) Assessment of camera models for use in planar velocimetry calibration. Exp Fluids 41:135–143CrossRefGoogle Scholar
  40. Willert C, Stasicki B, Klinner J, Moessner S (2010) Pulsed operation of high-power light emitting diodes for imaging flow velocimetry. Meas Sci Technol 21(7):1–12CrossRefGoogle Scholar
  41. Yang Y, Kang B (2009) Measurements of the characteristics of spray droplets using in-line digital particle holography. J Mech Sci Technol 23:1670–1679CrossRefGoogle Scholar
  42. Zhang Z (1999) A flexible new technique for camera calibration. Technical report, Microsoft ResearchGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institute of Propulsion Technology, Measurement TechnologyGerman Aerospace Center (DLR)CologneGermany

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