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Measurement sensitivity and resolution for background oriented schlieren during image recording

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Abstract

Background oriented schlieren (BOS) visualization technique is examined by means of optical geometry. Two most important results are the calculation of the sensitivity and spatial resolution of a BOS system, which allows for the determination of the experiment design space. A set of relations that characterize the performance of a BOS measurement is given, with emphasis on the design of background pattern and spatial placement of optical components.

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Notes

  1. Lorentz–Lorenz equation relates polarizability of an assembly of molecules to the refractive index. For gases, this relation can be approximated by the Gladstone–Dale equation (Born and Wolf 2005).

  2. This equation holds for a ray of light that images a point from the physical space into a point in image space. As it is known from image analysis, the determination of pixel shifts with subpixel resolution is possible, but only over an area.

  3. There are examples of the usage of BOS technique for visualizing open air blast waves with \(s_o \approx 400\) and \(s_t \approx 100\) m (Mizukaki et al. 2012).

  4. In order to eliminate diffraction effects, Eq. (9) with k = 0 may serve as a threshold for the coherence length of the light source.

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Acknowledgments

This work was supported by Global COE Program “World Center of Education and Research for Trans-disciplinary Flow Dynamics,” Tohoku University, Japan. ABG thanks the anonymous reviewers for their insightful comments.

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Authors and Affiliations

  1. Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba, Sendai, 980-8577, Japan

    Ardian B. Gojani & Shigeru Obayashi

  2. Department of Physics, Faculty of Mathematical and Natural Sciences, University of Prishtina, Mother Teresa str, nn, 10 000, Prishtina, Kosovo

    Burim Kamishi

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  1. Ardian B. Gojani
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  2. Burim Kamishi
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Correspondence to Ardian B. Gojani.

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Gojani, A.B., Kamishi, B. & Obayashi, S. Measurement sensitivity and resolution for background oriented schlieren during image recording. J Vis 16, 201–207 (2013). https://doi.org/10.1007/s12650-013-0170-5

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