Experiments in Fluids

, Volume 53, Issue 2, pp 531–543

Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions

Research Article

DOI: 10.1007/s00348-012-1308-2

Cite this article as:
Klinner, J. & Willert, C. Exp Fluids (2012) 53: 531. doi:10.1007/s00348-012-1308-2

Abstract

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

cII

Cross-correlation coefficient

d0

Nozzle orifice diameter

dA

Airy disk diameter

f

Focal length

f#

f-number

If,max

Maximum continuous forward current

M

Magnification

s

Sensor resolution [Pixel/mm]

\(\Updelta t\)

Delay between two illumination pulses (for PIV)

wq

Arbitrary scale factors in projective geometry

\(\varepsilon\)

Back-projection error

λ

Wavelength of light

τp

Pulse duration

\(\varphi\)

Camera yaw angle (around world y axis)

ψ

Camera pitch angle (around new x axis)

Subscripts

d

Distorted camera coordinates

I

Image coordinates

p

Projected camera coordinates

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

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