Abstract

A new heterodyne technique for the quantitative analysis of schlieren images is described. The technique is based on phase measurements of signals generated by a photodetector observing the variations in light intensity caused by a traveling grating of slits located at the knife-edge plane of a conventional schlieren system. The phase of the signal is proportional to the displacement of the slit image on the knife-edge plane as a result of the light deflection passing through a phase object. The displacement is proportional to the ray deflection angle and hence to the local gradient of the index of refraction. The technique, which is quantitatively precise and sensitive, is demonstrated by measurement of deflections caused by a lens with a focal length of f=20 m. A displacement of 0.22 mm and a deflection of an angle of 5.2×10-4 rad were detected.

© 2003 Optical Society of America

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References

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  1. G. S. Settles, Schlieren and Shadowgraph Techniques (Springer, New York, 2001).
    [CrossRef]
  2. R. Dandliker, in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1980), Vol. XVII, pp. 3–82.
  3. J. Stricker, Opt. Lett. 10, 247 (1985).
    [CrossRef] [PubMed]
  4. G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, and J. Stein, Icarus 41, 205 (1980).
    [CrossRef]
  5. L. A. Vasiliev, Schlieren Methods, A. Baruch, trans. (Israel Program for Scientific Translations, New York, 1971).

2001 (1)

G. S. Settles, Schlieren and Shadowgraph Techniques (Springer, New York, 2001).
[CrossRef]

1985 (1)

1980 (2)

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, and J. Stein, Icarus 41, 205 (1980).
[CrossRef]

R. Dandliker, in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1980), Vol. XVII, pp. 3–82.

1971 (1)

L. A. Vasiliev, Schlieren Methods, A. Baruch, trans. (Israel Program for Scientific Translations, New York, 1971).

Breakiron, L.

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, and J. Stein, Icarus 41, 205 (1980).
[CrossRef]

Dandliker, R.

R. Dandliker, in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1980), Vol. XVII, pp. 3–82.

Gatewood, G.

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, and J. Stein, Icarus 41, 205 (1980).
[CrossRef]

Goebel, R.

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, and J. Stein, Icarus 41, 205 (1980).
[CrossRef]

Kipp, S.

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, and J. Stein, Icarus 41, 205 (1980).
[CrossRef]

Russel, J.

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, and J. Stein, Icarus 41, 205 (1980).
[CrossRef]

Settles, G. S.

G. S. Settles, Schlieren and Shadowgraph Techniques (Springer, New York, 2001).
[CrossRef]

Stein, J.

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, and J. Stein, Icarus 41, 205 (1980).
[CrossRef]

Stricker, J.

Vasiliev, L. A.

L. A. Vasiliev, Schlieren Methods, A. Baruch, trans. (Israel Program for Scientific Translations, New York, 1971).

Icarus (1)

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, and J. Stein, Icarus 41, 205 (1980).
[CrossRef]

Opt. Lett. (1)

Other (3)

L. A. Vasiliev, Schlieren Methods, A. Baruch, trans. (Israel Program for Scientific Translations, New York, 1971).

G. S. Settles, Schlieren and Shadowgraph Techniques (Springer, New York, 2001).
[CrossRef]

R. Dandliker, in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1980), Vol. XVII, pp. 3–82.

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Figures (3)

Fig. 1
Fig. 1

Schematics of the heterodyne schlieren system. L1, L2, L3, lenses; S, mat screen, RS, reference signal; TS, test signal.

Fig. 2
Fig. 2

(a) Schematic description of the knife-edge plane. The rectangles with solid borders represent the source image produced by the reference point, and the rectangles with dotted borders represent the source image produced by the test point. The test image is displaced by d=a/2. Superimposed are four positions of the moving grating: (1) h/a=0, (2) h/a=0.5, (3) h/a=1, and (4) h/a=1.5. (b) Intensity of the reference (triangles) and test (diamonds) photodetectors, corresponding to the h/a values shown in (a). The phase difference between the signals is π/2.

Fig. 3
Fig. 3

Detector signals. Triangles, reference signal; diamonds, test signal.

Equations (5)

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Irdr=f2ϕr,
Ir=A sin2πh/2a+ψr,
ψr=2πdr/2a.
Δψ/Δϕ=πf2/a.
Ir,t=A sin2πut/2a+ψr,

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