Abstract
The present work is concerned with an experimental setup for studying phase objects using multi-directional speckle photography. A mathematical description of light propagation in an optically inhomogeneous medium and a means of speckle tomography of refractive coefficient distributions are given. Recommendations on two-dimensional refractive coefficient and temperature distributions in a flame of a candle illuminated in four directions are made. The obtained results evidence that speckle photography may be a basis for tomographic studies of temperature fields in different cross-sections of an object. A speckle shift error is about 5% while the one in reconstructing local temperatures does not exceed 10%.
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Abbreviations
- E :
-
radiation pulse energy
- I(η) :
-
light intensity at a point with the coordinate η
- I 0 :
-
light intensity at the Young's fringe centre
- I′ :
-
uniform illumination in the Young's fringe plane
- J :
-
integral in the Radon transform
- K :
-
Gladstone-Dale constant for a probing laser wavelength
- L 1 :
-
distance from the developed specklegram to the screen
- L i :
-
distance from the speckle generator to the coordinate system centre in the optical path direction
- δ f :
-
distance between the Young fringes
- T :
-
temperature
- n :
-
refractive index
- n 0 :
-
refractive index of an undisturbed medium
- p, s, x, y :
-
coordinates
- α i :
-
angle for its optical path direction
- β :
-
angle of inclination of the Young fringes relative to the horizontal axis
- δ :
-
speckle shift on a specklegram
- Δ :
-
speckle field shift at a given point due to inhomogeneity refraction
- Δx, Δy :
-
speckle shift at a point along the appropriate coordinate axes
- δ i (p) :
-
speckle field shift distribution for the ith direction
- {ovΔ} :
-
relative error
- Δ m :
-
error at a maximum point
- ɛ :
-
random error
- λ :
-
radiation wavelength
- ϱ :
-
medium density
- τ :
-
laser radiation pulse time
- ϕ :
-
refraction angle distribution for beams of the ith direction
- ψ :
-
function in the Radon transform
References
Achasov, O. V.; Kudryavtsev, N. N.; Novikov, S. S.; Soloukhin, R. I.; Fomin, N. A. 1985: Diagnostics of nonequilibrium states in molecular lasers. Nauka Tekh. 1–231
Almen, C. W. 1973: Astrophysical quantities. London: Atlone Press
Blinkov, G. N.; Soloukhin, R. I.; Fomin, N. A. 1986: Speckle photography of density gradients in a free flame. Probl. Heat Mass Trans. 86, 92–97
Born, M.; Wolf, E. 1964: Principles of optics. New York: Pergamon Press
Erbeck, R.; Merzkirch, W. 1988: Speckle photographic measurement of turbulence in an air stream with fluctuating temperature. Exp. Fluids 6, 89–93
Farrell, P. V.; Hofeldt, D. L. 1984: Temperature measurement in laser using speckle photography. Appl. Opt. 23, 1055–1059
Fomin, N. A. 1987: Speckle photography as applied for gas-dynamic flow diagnostics. Minsk: HMTI Press, Preprint 44, 43
Herman, G. T. 1980: Image reconstruction from projections. Fundamentals of computerized tomography. New York: Academic Press
Jones, P.; Wykes, C. 1983: Holographic and speckle interferometry. Cambridge: Cambridge University Press
Merzkirch, W. 1987: Speckle photography as an experimental tool for fluid flow measurements. Proc. Int. Congr. Laser Applications Electroopt. L. I. A. Vol. 63, pp. 85–88 (ICALEO '87), San Diego
Picalov, V. V.; Preobrazhensky, N. G. 1987: Reconstructive tomography in gasdynamics and physics of plasma. Novosibirsk: Nauka
Reuss, D. L. 1983: Temperature measurements in a radially symmetric flame using holographic interferometry. Combust. Flame 49, 207–219
Soloukhin, R. I.; Fomin, N. A. 1987: Speckle photography of density fields in gas-phase reacting flows. Proc. Int. Seminar Gas-Phase Flame Structure. Novosibirsk: Press Inst. Theor. Appl. Mech., Siberian Branch USSR Acad. Sci.
Wernekinck, U. 1985: Anwendung der Speckle-Photographie zur Sichtbarmachung und Messung von Strömungen mit veränderlicher Dichte. VDI-Fortschritt-Berichte, Reihe 8, Nr. 95. Düsseldorf: VDI-Verlag
Wernekinck, U.; Merzkirch, W.; Fomin, N. A. 1985: Measurement of light deflection in a turbulent density field. Exp. Fluids 3, 206–208
Zaviyalov, Yu. S.; Krasov, B. I.; Miroshnichenko, V. L. 1980: Methods of spline functions. Moscow: Nauka
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Blinkov, G.N., Fomin, N.A., Rolin, M.N. et al. Speckle tomography of a gas flame. Experiments in Fluids 8, 72–76 (1989). https://doi.org/10.1007/BF00203067
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DOI: https://doi.org/10.1007/BF00203067