Abstract

In this modification of the schlieren apparatus the knife-edge is replaced by a radial-rainbow filter with a transparent center and opaque surround. Consequently, refractive-index inhomogeneities in the test section appear varicolored, whereas uniformities appear white. The rainbow schlieren is simple, is easy to use, and accentuates detail regarding inhomogeneities more than the ordinary schlieren. The rainbow schlieren permits quantitative evaluation of certain refractive-index distributions, including turbulence, by simple calculations from observations of hue rather than irradiance.

© 1984 Optical Society of America

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References

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  1. H. Schardin, “Schlieren Methods and Their Applications,” NASA TT-F-12731 (Apr.1970) [translation from Ergeb. Exakten Naturewiss. 20, 303 (1942)].
  2. W. Merzkirch, Flow Visualization (Academic, New York, 1974), pp. 86–102.
  3. G. S. Settles, ‘Color Schlieren Optics—A Review of Techniques and Applications,” in Flow Visualization, Vol. 2W. Merzkirch, Ed. (Hemisphere, New York, 1982), pp. 749–759.
  4. R. K. Luneburg, Mathematical Theory of Optics (U. California, Berkeley, 1964).
  5. W. L. Howes, D. R. Buchele, “Optical Interferometry of Inhomogeneous Gases,” J. Opt. Soc. Am. 56, 1517 (1966) [also “Generalization of Gas-Flow-Interferometry Theory and Interferogram Evaluation Equations for One-Dimensional Density Fields,” NASA Tech. Note 3340 (Feb. 1955)].
    [CrossRef]
  6. L. A. Chernov, Wave Propagation in a Random Medium (Dover, New York, 1967), pp. 12–34.
  7. W. L. Howes, “Rainbow Schlieren,” NASA TP-2166 (May1983).
  8. R. Prescott, E. L. Gayhart, “A Method of Correction of Astigmatism in Schlieren Systems,” J. Aeronaut. Sci. 18, 69 (1951).
  9. R. E. Faw, T. A. Dullforce, “Holographic Interferometry Measurement of Convective Heat Transport Beneath a Heated Horizontal Plate in Air,” Int. J. Heat Mass Transfer, 24, 859 (1981).
    [CrossRef]
  10. H. Schardin, “Theory and Applications of the Mach-Zehnder Interference-Refractometer,” Defense Research Laboratory, Texas, UT/DRL T-3 (1946) [translation from Z. Instrumentenk. 53, 396 (1933)].
  11. J. W. Bradley, “Density Determination from Axisymmetric Interferograms,” AIAA J. 6, 1190 (1968).
    [CrossRef]
  12. F. J. Weinberg, Optics of Flames (Butterworths, Washington, 1963), p. 29.
  13. B. Lewis, G. von Elbe, Combustion, Flames and Explosions of Gases (Academic, New York, 1961), pp. 280, 706.
  14. A. von Hippel, in Handbook of Physics, E. U. Condon, H. Odishaw, Eds. (McGraw-Hill, New York, 1958), pp. 4–113.
  15. A. C. Hardy, F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932).
  16. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), p. 122.

1983 (1)

W. L. Howes, “Rainbow Schlieren,” NASA TP-2166 (May1983).

1981 (1)

R. E. Faw, T. A. Dullforce, “Holographic Interferometry Measurement of Convective Heat Transport Beneath a Heated Horizontal Plate in Air,” Int. J. Heat Mass Transfer, 24, 859 (1981).
[CrossRef]

1968 (1)

J. W. Bradley, “Density Determination from Axisymmetric Interferograms,” AIAA J. 6, 1190 (1968).
[CrossRef]

1966 (1)

1951 (1)

R. Prescott, E. L. Gayhart, “A Method of Correction of Astigmatism in Schlieren Systems,” J. Aeronaut. Sci. 18, 69 (1951).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), p. 122.

Bradley, J. W.

J. W. Bradley, “Density Determination from Axisymmetric Interferograms,” AIAA J. 6, 1190 (1968).
[CrossRef]

Buchele, D. R.

Chernov, L. A.

L. A. Chernov, Wave Propagation in a Random Medium (Dover, New York, 1967), pp. 12–34.

Dullforce, T. A.

R. E. Faw, T. A. Dullforce, “Holographic Interferometry Measurement of Convective Heat Transport Beneath a Heated Horizontal Plate in Air,” Int. J. Heat Mass Transfer, 24, 859 (1981).
[CrossRef]

Faw, R. E.

R. E. Faw, T. A. Dullforce, “Holographic Interferometry Measurement of Convective Heat Transport Beneath a Heated Horizontal Plate in Air,” Int. J. Heat Mass Transfer, 24, 859 (1981).
[CrossRef]

Gayhart, E. L.

R. Prescott, E. L. Gayhart, “A Method of Correction of Astigmatism in Schlieren Systems,” J. Aeronaut. Sci. 18, 69 (1951).

Hardy, A. C.

A. C. Hardy, F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932).

Howes, W. L.

Lewis, B.

B. Lewis, G. von Elbe, Combustion, Flames and Explosions of Gases (Academic, New York, 1961), pp. 280, 706.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (U. California, Berkeley, 1964).

Merzkirch, W.

W. Merzkirch, Flow Visualization (Academic, New York, 1974), pp. 86–102.

Perrin, F. H.

A. C. Hardy, F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932).

Prescott, R.

R. Prescott, E. L. Gayhart, “A Method of Correction of Astigmatism in Schlieren Systems,” J. Aeronaut. Sci. 18, 69 (1951).

Schardin, H.

H. Schardin, “Schlieren Methods and Their Applications,” NASA TT-F-12731 (Apr.1970) [translation from Ergeb. Exakten Naturewiss. 20, 303 (1942)].

H. Schardin, “Theory and Applications of the Mach-Zehnder Interference-Refractometer,” Defense Research Laboratory, Texas, UT/DRL T-3 (1946) [translation from Z. Instrumentenk. 53, 396 (1933)].

Settles, G. S.

G. S. Settles, ‘Color Schlieren Optics—A Review of Techniques and Applications,” in Flow Visualization, Vol. 2W. Merzkirch, Ed. (Hemisphere, New York, 1982), pp. 749–759.

von Elbe, G.

B. Lewis, G. von Elbe, Combustion, Flames and Explosions of Gases (Academic, New York, 1961), pp. 280, 706.

von Hippel, A.

A. von Hippel, in Handbook of Physics, E. U. Condon, H. Odishaw, Eds. (McGraw-Hill, New York, 1958), pp. 4–113.

Weinberg, F. J.

F. J. Weinberg, Optics of Flames (Butterworths, Washington, 1963), p. 29.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), p. 122.

AIAA J. (1)

J. W. Bradley, “Density Determination from Axisymmetric Interferograms,” AIAA J. 6, 1190 (1968).
[CrossRef]

Int. J. Heat Mass Transfer (1)

R. E. Faw, T. A. Dullforce, “Holographic Interferometry Measurement of Convective Heat Transport Beneath a Heated Horizontal Plate in Air,” Int. J. Heat Mass Transfer, 24, 859 (1981).
[CrossRef]

J. Aeronaut. Sci. (1)

R. Prescott, E. L. Gayhart, “A Method of Correction of Astigmatism in Schlieren Systems,” J. Aeronaut. Sci. 18, 69 (1951).

J. Opt. Soc. Am. (1)

NASA TP-2166 (1)

W. L. Howes, “Rainbow Schlieren,” NASA TP-2166 (May1983).

Other (11)

L. A. Chernov, Wave Propagation in a Random Medium (Dover, New York, 1967), pp. 12–34.

H. Schardin, “Theory and Applications of the Mach-Zehnder Interference-Refractometer,” Defense Research Laboratory, Texas, UT/DRL T-3 (1946) [translation from Z. Instrumentenk. 53, 396 (1933)].

F. J. Weinberg, Optics of Flames (Butterworths, Washington, 1963), p. 29.

B. Lewis, G. von Elbe, Combustion, Flames and Explosions of Gases (Academic, New York, 1961), pp. 280, 706.

A. von Hippel, in Handbook of Physics, E. U. Condon, H. Odishaw, Eds. (McGraw-Hill, New York, 1958), pp. 4–113.

A. C. Hardy, F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), p. 122.

H. Schardin, “Schlieren Methods and Their Applications,” NASA TT-F-12731 (Apr.1970) [translation from Ergeb. Exakten Naturewiss. 20, 303 (1942)].

W. Merzkirch, Flow Visualization (Academic, New York, 1974), pp. 86–102.

G. S. Settles, ‘Color Schlieren Optics—A Review of Techniques and Applications,” in Flow Visualization, Vol. 2W. Merzkirch, Ed. (Hemisphere, New York, 1982), pp. 749–759.

R. K. Luneburg, Mathematical Theory of Optics (U. California, Berkeley, 1964).

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Figures (11)

Figure 1
Figure 1

Rainbow schlieren.

Figure 2
Figure 2

Typical rainbow filter. Actual diameter <10 mm.

Figure 3
Figure 3

Refraction field around heated flat plates. Arrows denote measurement locations.

Figure 4
Figure 4

Refractive index distribution near horizontal and vertical plates.

Figure 5
Figure 5

Refraction field from acetylene flame.

Figure 6
Figure 6

Ray trace in medium with spherical, or axial, symmetry.

Figure 7
Figure 7

Relative refractive index change above acetylene flame. Nozzle tilt approximately 3.7° from vertical.

Figure 8
Figure 8

(a) Turbulent mixture of glycerine and water. (b) Magnified region of glycerine-water mixture in figure 8(a).

Figure 9
Figure 9

Optical glass window.

Figure 10
Figure 10

Double-pass rainbow schlieren. S, light source; C, cylindrical lens; P, pellicle; M, spherical mirror; T, test object; F, rainbow filter; L, camera lens; I, image.

Figure 11
Figure 11

Bent and scratched plastic sheet.

Tables (1)

Tables Icon

Table I Turbulence Data Glycerine–Water Mixture

Equations (50)

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d = f tan θ f ,
η f = ½ d μ d η | η = 0 L 2 ,
μ ( η f ) - μ ( 0 ) = d μ d η | η = 0 η f .
d μ d η | η = 0
μ ( η f ) - μ ( 0 ) = 2 ( η f / L ) 2 .
η f = L d / 2 f ,
n ( y f ) - n ( y 0 ) n ( y 0 ) = μ ( η f ) - μ ( 0 ) μ ( 0 ) = ½ ( d f ) 2 ,
n i + ( ½ ) - n i - ( ½ ) n = d n d y | y i y i + 1 - y i - 1 2 = d L f y i + 1 - y i - 1 2
y i + ( ½ ) = y i + y i + 1 2 ,
n - n ( y ) n = i - ½ 0 n i + ( ½ ) - n i - ( ½ ) n
y p - r m < | r 0 θ max 4 | ,
Δ y p - y 0 < r 0 θ max 2 2
n m - n 0 n 0 = θ f 4 tan α 0 = d 4 f tan α 0 ,
sin α 0 = y 0 r 0 = y p r 0 .
δ rms = 2 π 1 / 4 3 μ rms n ¯ ( σ 3 a ) 1 / 2
θ ms = 4 π μ ms n ¯ 2 σ a
μ rms n ¯ = ( a 4 π L ) 1 / 2 d rms f .
A = θ f ( n - 1 ) = d ( n - 1 ) f ,
A = θ f 2 = d 2 f .
Δ L v L v = Δ w w = 0.03 ,
Δ λ λ = β Δ w λ 0 + β w = 0.005 ,
Δ w w = 0.005 λ 0 β w + 1
β = ( λ 1 - λ 0 ) w 1
Δ w w = 0.005 ( 1.75 w 1 w + 1 ) .
Δ w w 0.014 ,
p c = Δ w w 0 = 0.05 ,
n r sin φ = K = const ,
y 0 = r 0 sin φ 0 = K n 0 = r 0 sin α 0 ,
r m = K / n m ,
n m - n 0 n 0 = y 0 - r m r m ,
Δ y p - y 0 ,
y p - r m = y p - y f + y f - r m .
α f = φ f + θ f = π - α 0 + θ f
y f = y 0 cos θ f - x 0 sin θ f ,
x 0 = r 0 cos α 0 .
y p - y f = ( x 0 cos θ f + y 0 sin θ f ) tan θ f .
r m = y m / cos ( θ f / 2 ) .
y 0 < y m < y 0 + y f - y 0 2 if y f > y 0 , that is , if n 0 > n m , y 0 > y m > y 0 + y f - y 0 2 if y f < y 0 , that is , if n 0 < n m ,
y 0 + y f - y 0 2 = ½ y 0 ( 1 + cos θ f ) - ½ x 0 sin θ f
y m = y 0 + y f - y 0 4 = ¼ y 0 ( 3 + cos θ f ) - ¼ x 0 sin θ f ,
r m = ¼ ( cos θ f 2 ) - 1 [ y 0 ( 3 + cos θ f ) - x 0 sin θ f ] .
y p - r m = ¼ x 0 sin θ f ( cos θ f 2 ) - 1 - y 0 [ ¼ ( 3 + cos θ f ) ( cos θ f 2 ) - 1 - cos θ f - sin θ f tan θ f ] .
y p - r m = ( x 0 θ f ) / 4 ,
| y p - r m | < r 0 θ max 4
Δ = y p - y f + y f - y 0 ,
Δ = y 0 ( 1 - cos θ f cos θ f ) .
Δ = ( y 0 θ f 2 ) / 2 ,
Δ < ( r 0 θ max 2 ) / 2.
n m - n 0 n 0 = θ f / 4 tan α 0 - ( θ f / 4 )
n m - n 0 n 0 = θ f 4 tan α 0 ,

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