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Digital phase-stepping holographic interferometry in measuring 2-D density fields

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Abstract

This paper presents a holographic interferometer technique for measuring transparent (2-D or quasi 2-D) density fields. To be able to study the realization of such a field at a certain moment of time, the field is “frozen” on a holographic plate. During the reconstruction of the density field from the hologram the length of the path traversed by the reconstruction beam is diminished in equal steps by applying a computer controlled voltage to a piezo-electric crystal that translates a mirror. Four phase-stepped interferograms resulting from this pathlength variation are digitized and serve as input to an algorithm for computing the phase surface. The method is illustrated by measuring the basically 2-D density field existing around a heated horizontal cylinder in free convection.

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Abbreviations

λ :

wavelength

x, y :

cartesian coordinate system

Φ :

phase

ΔΦ :

phase step

K :

Gladstone-Dale constant

L :

width of 2-D density field

ϱ :

density

ϱ 0 :

density at reference conditions

I 0, I 1, I 2, I 3 :

recorded interferograms

I mod :

modulation intensity

I bias :

bias intensity

N :

numerator determining tan {ϱ (x, y)}

D :

denominator determining tan {ϕ (x, y)}

θ :

dimensionless temperature

T :

temperature

T c :

temperature of cylinder

T ∞ :

temperature of environment

p :

pressure

R :

gas constant

References

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Authors and Affiliations

  1. Dept. of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, P.O. Box 5058, NL-2629, HS Delft, The Netherlands

    T. A. W. M. Lanen, C. Nebbeling & J. L. van Ingen

Authors
  1. T. A. W. M. Lanen
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  2. C. Nebbeling
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  3. J. L. van Ingen
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Lanen, T.A.W.M., Nebbeling, C. & van Ingen, J.L. Digital phase-stepping holographic interferometry in measuring 2-D density fields. Experiments in Fluids 9, 231–235 (1990). https://doi.org/10.1007/BF00190424

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  • DOI: https://doi.org/10.1007/BF00190424

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