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Institute of Turbomachinery and Fluid Dynamics
Logo Leibniz Universität Hannover
Institute of Turbomachinery and Fluid Dynamics
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Background-Oriented Schlieren (BOS)

Field of Application

Measurement of three-dimensional density distribution of gases

Measured Quantities

  • Displacement vector
  • Refraction index gradient
  • Density


Local information from optical density measurements can only be determined by inverse methods from a series of measurements with different viewing directions. With traditional methods, this results in a highly complex set-up and execution. The background oriented schlieren method in contrast, has the advantage of a simple experimental set-up using comparatively low priced components.

The main components of a BOS set-up are a background with a randomly dotted pattern, a camera to record the background and a computer for storage of the images and further processing. The measurement process is as follows: first, a reference image of the dotted pattern is recorded without the measurement volume. Then the actual measurement image is taken with the measurement object. A point on the background appears with a certain distance on the photo sensor due to the refraction of the light through the present density field (see Figure 1).

The displacement of the points is determined with cross correlation algorithms. With the geometry of the set-up and displacement of the point, the deflection angle in the center of the measured object can be determined and therefore the gradient of the refractive index can be derived.

By applying a tomographic algorithm (filtered back projection) and simultaneously recording from different viewing directions the three-dimensional refraction index and using the Gladstone -Dale relationship, the density of the gas can be determined (see Figure 3). If, in addition, the pressure is measured the temperature can be determined with the ideal gas equation.


Dipl.-Ing. Ulrich Hartmann