Folie 1

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High precision image-based tracking of a rigid
body moving within a fluid

• Stuart Laurence, Jan Martinez Schramm
• German Aerospace Center (DLR), Göttingen, Germany
• APS/DFD, 23 November 2010

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Motivation

• Visualization-based techniques an attractive
  option for measuring displacements (and derived
  quantities) of rigid bodies in fluids, as they
  are completely non-intrusive
• Particularly attractive for force-measurement in
  short-duration hypersonic facilities, as few
  other options available
• However, measurement precision critical in past
  (film-based analog techniques) displacement
  measurements limited to 50 µm
• Focus here on edge-detection-based techniques
  combined with least-squares fitting (suitable for
  silhouette images from schlieren, etc.)
• Assumptions no changes to body profile motion
  two dimensional one axis of rotation

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Analytic-fitting technique
Edge detection
Model edge tracing and sub-pixel detection
Least-squares fitting
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Free-flight measurements with analytic-fitting
technique

• Image-based measurements show reasonable
  agreement with accelerometer measurements
• Response time for 14 kfps estimated to be 0.5 ms

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Problems with analytic-fitting technique

• Model cross-sectional profile must be expressible
  analytically (can be avoided by using, e.g.,
  splines)
• For all but simplest geometries, fitting
  procedure is iterative (slow!)
• Reasonably complete profile required for
  convergence

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Edge-tracking technique

• Based on matching closest edge-points in
  reference and displaced images
• Edge angle assumed to be the same for each
  edge-point pair

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Edge-tracking technique

• Based on matching closest edge-points in
  reference and displaced images
• Edge angle assumed to be the same for each
  edge-point pair

linear least-squares problem for ?x and ?y
b) with errors
a) no errors
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Application of edge-tracking technique
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Error estimation through artificial image analysis

• Errors introduced by pixellation/edge-detection
  (can be reduced through more precise algorithms)
  and CCD noise (unavoidable at given light
  conditions)
• Such errors can be estimated through analysis of
  artificially constructed images

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Error determination from calibrated sphere
measurements

• Precision-machined 40-mm diameter sphere
  controlled by linear displacement stepper
• Magnification 300 µm/pixel
• Position determination from tracking techniques
  compared with inputted displacements
• Standard error 1.3 µm

(A) Shimadzu HPV-1 (B) Telephoto lens (C)
Precision-machined sphere (D) Linear
displacement stage (E) Light source (F)
Light-diffusing material
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Errors in constant acceleration measurements

• Error in measured constant acceleration, a, can
  be determined from assumed displacement error
  (d)
• (n number of measurement points)
• For micron-level precision in displacement,
  accurate (1) acceleration measurements possible
  even for millisecond test times

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Errors in constant acceleration measurements

• Error in measured constant acceleration, a, can
  be determined from assumed displacement error
  (d)
• (n number of measurement points)
• For micron-level precision in displacement,
  accurate (1) acceleration measurements possible
  even for millisecond test times

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Conclusions

• Technique originally developed for bodies with
  analytically expressible cross-sections
• Generalized to arbitrary body geometries
• Displacement measurements to micron level for
  wind-tunnel scale models allows acceleration
  measurements to lt1 under typical conditions
• Generalization to three-dimensional motions?

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Application of edge-tracking technique
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Shock-wave surfing
Error in edge-point locations

• Optical distortions can become problematic for
  large fields-of-view
• Can be corrected for using reference images

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Shock-wave surfing
Displacements

• Optical distortions can become problematic for
  large fields-of-view
• Can be corrected for using reference images

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Shock-wave surfing
Force coefficients

• Optical distortions can become problematic for
  large fields-of-view
• Can be corrected for using reference images