ORIGINALS S. L. Pu Æ D. Allano Æ B. Patte-Rouland Æ M. Malek D. Lebrun Æ K. F. Cen Particle field characterization by digital in-line holography: 3D location and sizing Received: 4 May 2004 / Revised: 23 November 2004 / Accepted: 17 January 2005 / Published online: 7 June 2005 Ó Springer-Verlag 2005 Abstract Recent developments have shown the potential of digital in-line holography for diagnostics in fluids. This new method provides a low-cost and easy access method for measuring both size and velocity of small particles in a volume. Here it is shown that by applying traditional image processing tools on the particle images digitally reconstructed, statistically reliable results on particles size and location are provided. The method is experimentally illustrated by glass microspheres that are moving in a turbulent flow generated by an annular jet. A comparison with the histogram diameters provided by a common diffraction particle sizer are presented. List of symbols 1O (n, g) Amplitude distribution in the object field I z (x,y) Intensity distribution at a distance z Z e Distance from the object to the sensor plane Z r Reconstruction distance Z s Curvature radius of the illuminating wave front k Wavelength of the laser source H z (x,y) Fresnel Kernel w z (x,y) Reconstruction wavelet function R (x ,y) Reconstructed image PSF(x, y) Point spread function d CCD Pixel size d Theoretical diameter of the particle image D Diameter of the experimental particle im- age F Beam obscuration e Tolerance parameter for sampling condi- tion dz Measurement accuracy on axial coordinate 1 Introduction Recently, Digital In-line Holography (DIH) has been successfully applied on several domains. The 3D loca- tion of small fibers and particles by numerical recon- struction of holograms was reported by Belaid et al. (1997), Buraga-Lefebvre et al. (2000) and Lebrun et al. (1999, 2003). Biological applications like cell biology, imaging and tracking submicrometer particles in sea- water have been published by Xu et al. (2001, 2002, 2003), Owen et al. (2000) and Milgram et al. (2002). The use of DIH has also been demonstrated by Sun et al. (2002) for observation of erosion processes. In the field of fluid mechanics Coetmellec et al. (2001), Pan and Meng (2001), Sheng et al. (2003) and Malek et al. (2004a) have shown that velocity vector maps could be determined in several slices of interest within a sample volume by this technique. The main advantage of DIH is the simplicity of the recording apparatus: a collimated beam illuminates the objects to be holographied and the far-field diffraction pattern is directly recorded by the photosensitive plane of a camera. In fact, this system can be seen as a lensless imaging setup where the focusing stage is realized numerically. Consequently, this method takes the advantages offered by digital imaging methods: visualization of objects, identification of particle images and extraction of their characteristics by calculations on the image’s gray levels. Furthermore, by analyzing the diffraction pattern recorded on the camera (hologram), several slices of the volume can be digitally recon- structed and the 3D coordinates of each particle image S. L. Pu Æ D. Allano Æ B. Patte-Rouland M. Malek Æ D. Lebrun (&) UMR 6614 Coria, Technopole du Madrillet, 76801 Saint-Etienne du Rouvray, France E-mail: Denis.Lebrun@coria.fr Tel.: +33-232-953734 Fax: +33-232-910485 S. L. Pu Æ K. F. Cen Clean Energy And Environment Engineering Key Lab of MOE, Zhejiang University, Hangzhou, 310027, China Experiments in Fluids (2005) 39: 1–9 DOI 10.1007/s00348-005-0937-0