Single camera volumetric shadowgraphy system for simultaneous droplet sizing and depth location, including empirical determination of the effective optical aperture Articles uri icon

publication date

  • September 2016

start page

  • 135

end page

  • 145


  • 76

International Standard Serial Number (ISSN)

  • 0894-1777

Electronic International Standard Serial Number (EISSN)

  • 1879-2286


  • This work proposes an improvement of the shadowgraphy technique by allowing for 3-D droplet/particle location and sizing in a volumetric measurement with a single camera. The shadowgraphy technique implemented in this work uses a diffuse backward illuminated screen as background stage. Using this setup, the shadow image of droplets or particles is recorded on a camera. As particles get out of focus, apparent shape, size and visibility of the gray level profiles registered from the particle images change. Based on these effects, this work proposes an improved methodology to extract out-of-plane location information. Thus, the mentioned camera is enough for obtaining the 3D location of the shadow images of the particles/droplets in a control volume, and no additional hardware is needed. A simple geometrical optics model links the defocused particle image to the sizes of the circle of confusion and the particle itself. Based on this connection, a robust practical procedure is proposed to determine the circle of confusion size from the gray scale gradients of the particle image profile and from image contrast considerations. This knowledge of the circle of confusion size provides the particle depth location. The proposed approach is tested on real opaque images of a calibrated target. The proposal includes a practical procedure to double-check relevant optical parameters like the effective aperture of the lens setup. The empirical determination of the effective optical aperture is essential as it may significantly deviate from the nominal expected value, depending on the optical setup. Results obtained are satisfactory, allowing for an accurate volumetric measurement with displacements up to 30 particle diameters away in the out of focus direction (less than 20% error in particle sizing and 2 mm in particle depth location).


  • shadowgraphy; droplet sizing; effective optical aperture; depth of field; piv; ptv