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Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions

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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.

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Notes

  1. The term shadowgraphy is frequently used to describe shadow images of refractive index gradients in gases but describes images of droplet shadows projected onto the image plane just as well.

Abbreviations

c II :

Cross-correlation coefficient

d 0 :

Nozzle orifice diameter

d A :

Airy disk diameter

f :

Focal length

f # :

f-number

I f,max :

Maximum continuous forward current

M :

Magnification

s :

Sensor resolution [Pixel/mm]

\(\Updelta t\) :

Delay between two illumination pulses (for PIV)

w, q :

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)

d :

Distorted camera coordinates

I :

Image coordinates

p :

Projected camera coordinates

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Acknowledgments

The authors would like to thank D. Schanz and S. Gesemann of the Dept. Experimental Methods of the DLR Institute of Aerodynamics and Flow Technology for providing the SMART implementation and the corresponding Matlab calibration routine. T. Kusserow of the Institute of Nanostructure Technologies and Analytics at University of Kassel is acknowledged for his support regarding micro-lithographic photo masks. Part of the work presented herein is supported by the EU-project AFDAR (Advanced Flow Diagnostics for Aeronautical Research, project no. 265695) of the 7th Framework Programme whose support is gratefully acknowledged.

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  1. Institute of Propulsion Technology, Measurement Technology, German Aerospace Center (DLR), Linder Hoehe, Cologne, 51147, Germany

    Joachim Klinner & Christian Willert

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  1. Joachim Klinner
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  2. Christian Willert
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Correspondence to Joachim Klinner.

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Klinner, J., Willert, C. Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions. Exp Fluids 53, 531–543 (2012). https://doi.org/10.1007/s00348-012-1308-2

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