Abstract

Shearing interferometers are classified as instruments in which interference is produced between rays that are sheared in the test object by a small lateral distance. When applied to gas dynamic investigations these interferometers respond to changes of the gradient of the gas density in the test field. A generalized first-order analysis is described that applies to all arrangements of such shearing interferometers and emphasizes the application for the study of compressible gas flows.

© 1974 Optical Society of America

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References

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  1. R. Ladenburg, D. Bershader, “Interferometry,” in Physical Measurements in Gas Dynamics and Combustion, R. Ladenburg, Ed. (Princeton U. P., Princeton, N. J., 1954), pp. 47–78.
  2. F. J. Weinberg, Optics of Flames (Butterworths, London, 1963).
  3. O. Bryngdahl, Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1965), Vol. 4, pp. 39–83.
    [CrossRef]
  4. M. Hugenschmidt, K. Vollrath, Institute St. Louis (France), Report ISL T 14/67 (1967).
  5. W. Merzkirch, W. Erdmann, Appl. Phys. 2, 119 (1973).
    [CrossRef]
  6. O. Bryngdahl, J. Opt. Soc. Am. 59, 142 (1969).
    [CrossRef]
  7. J. G. Kelley, R. A. Hargraves, Appl. Opt. 9, 948 (1970).
    [CrossRef] [PubMed]
  8. C. J. Wick, S. Winnikow, Appl. Opt. 12, 841 (1973).
    [CrossRef] [PubMed]
  9. A. K. Oppenheim, P. A. Urtiew, F. J. Weinberg, Proc. Roy. Soc. (London) A291, 279 (1966).
  10. S. Yokozeki, T. Suzuki, Appl. Opt. 10, 1575 (1971).
    [CrossRef] [PubMed]
  11. M. Francon, Rev. Opt. (31), 65 (1952).
  12. G. Nomarski, J. Phys. 17, 15 (1956).
  13. R. Chevalerias, Y. Latron, C. Véret, J. Opt. Soc. Am. 47, 703 (1957).
    [CrossRef]
  14. G. Gontier, Publ. Scientifiques et Techniques de l’Air 338 (Paris, 1957).
  15. C. Véret, in Proceed. 4th Int. Congress on High-Speed Photography (Helwich, Darmstadt, Germany, 1959), pp. 66–69.
  16. W. F. Merzkirch, AIAA J. 3, 1974 (1965).
    [CrossRef]
  17. W. Z. Black, W. W. Carr, Rev. Sci. Instrum. 42, 337 (1971).
    [CrossRef]
  18. R. D. Small, V. A. Sernas, R. H. Page, Appl. Opt. 11, 858 (1972).
    [CrossRef] [PubMed]

1973

W. Merzkirch, W. Erdmann, Appl. Phys. 2, 119 (1973).
[CrossRef]

C. J. Wick, S. Winnikow, Appl. Opt. 12, 841 (1973).
[CrossRef] [PubMed]

1972

1971

W. Z. Black, W. W. Carr, Rev. Sci. Instrum. 42, 337 (1971).
[CrossRef]

S. Yokozeki, T. Suzuki, Appl. Opt. 10, 1575 (1971).
[CrossRef] [PubMed]

1970

1969

1966

A. K. Oppenheim, P. A. Urtiew, F. J. Weinberg, Proc. Roy. Soc. (London) A291, 279 (1966).

1965

W. F. Merzkirch, AIAA J. 3, 1974 (1965).
[CrossRef]

1957

1956

G. Nomarski, J. Phys. 17, 15 (1956).

1952

M. Francon, Rev. Opt. (31), 65 (1952).

Bershader, D.

R. Ladenburg, D. Bershader, “Interferometry,” in Physical Measurements in Gas Dynamics and Combustion, R. Ladenburg, Ed. (Princeton U. P., Princeton, N. J., 1954), pp. 47–78.

Black, W. Z.

W. Z. Black, W. W. Carr, Rev. Sci. Instrum. 42, 337 (1971).
[CrossRef]

Bryngdahl, O.

O. Bryngdahl, J. Opt. Soc. Am. 59, 142 (1969).
[CrossRef]

O. Bryngdahl, Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1965), Vol. 4, pp. 39–83.
[CrossRef]

Carr, W. W.

W. Z. Black, W. W. Carr, Rev. Sci. Instrum. 42, 337 (1971).
[CrossRef]

Chevalerias, R.

Erdmann, W.

W. Merzkirch, W. Erdmann, Appl. Phys. 2, 119 (1973).
[CrossRef]

Francon, M.

M. Francon, Rev. Opt. (31), 65 (1952).

Gontier, G.

G. Gontier, Publ. Scientifiques et Techniques de l’Air 338 (Paris, 1957).

Hargraves, R. A.

Hugenschmidt, M.

M. Hugenschmidt, K. Vollrath, Institute St. Louis (France), Report ISL T 14/67 (1967).

Kelley, J. G.

Ladenburg, R.

R. Ladenburg, D. Bershader, “Interferometry,” in Physical Measurements in Gas Dynamics and Combustion, R. Ladenburg, Ed. (Princeton U. P., Princeton, N. J., 1954), pp. 47–78.

Latron, Y.

Merzkirch, W.

W. Merzkirch, W. Erdmann, Appl. Phys. 2, 119 (1973).
[CrossRef]

Merzkirch, W. F.

W. F. Merzkirch, AIAA J. 3, 1974 (1965).
[CrossRef]

Nomarski, G.

G. Nomarski, J. Phys. 17, 15 (1956).

Oppenheim, A. K.

A. K. Oppenheim, P. A. Urtiew, F. J. Weinberg, Proc. Roy. Soc. (London) A291, 279 (1966).

Page, R. H.

Sernas, V. A.

Small, R. D.

Suzuki, T.

Urtiew, P. A.

A. K. Oppenheim, P. A. Urtiew, F. J. Weinberg, Proc. Roy. Soc. (London) A291, 279 (1966).

Véret, C.

R. Chevalerias, Y. Latron, C. Véret, J. Opt. Soc. Am. 47, 703 (1957).
[CrossRef]

C. Véret, in Proceed. 4th Int. Congress on High-Speed Photography (Helwich, Darmstadt, Germany, 1959), pp. 66–69.

Vollrath, K.

M. Hugenschmidt, K. Vollrath, Institute St. Louis (France), Report ISL T 14/67 (1967).

Weinberg, F. J.

A. K. Oppenheim, P. A. Urtiew, F. J. Weinberg, Proc. Roy. Soc. (London) A291, 279 (1966).

F. J. Weinberg, Optics of Flames (Butterworths, London, 1963).

Wick, C. J.

Winnikow, S.

Yokozeki, S.

AIAA J.

W. F. Merzkirch, AIAA J. 3, 1974 (1965).
[CrossRef]

Appl. Opt.

Appl. Phys.

W. Merzkirch, W. Erdmann, Appl. Phys. 2, 119 (1973).
[CrossRef]

J. Opt. Soc. Am.

J. Phys.

G. Nomarski, J. Phys. 17, 15 (1956).

Proc. Roy. Soc. (London)

A. K. Oppenheim, P. A. Urtiew, F. J. Weinberg, Proc. Roy. Soc. (London) A291, 279 (1966).

Rev. Opt. (31)

M. Francon, Rev. Opt. (31), 65 (1952).

Rev. Sci. Instrum.

W. Z. Black, W. W. Carr, Rev. Sci. Instrum. 42, 337 (1971).
[CrossRef]

Other

G. Gontier, Publ. Scientifiques et Techniques de l’Air 338 (Paris, 1957).

C. Véret, in Proceed. 4th Int. Congress on High-Speed Photography (Helwich, Darmstadt, Germany, 1959), pp. 66–69.

R. Ladenburg, D. Bershader, “Interferometry,” in Physical Measurements in Gas Dynamics and Combustion, R. Ladenburg, Ed. (Princeton U. P., Princeton, N. J., 1954), pp. 47–78.

F. J. Weinberg, Optics of Flames (Butterworths, London, 1963).

O. Bryngdahl, Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1965), Vol. 4, pp. 39–83.
[CrossRef]

M. Hugenschmidt, K. Vollrath, Institute St. Louis (France), Report ISL T 14/67 (1967).

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Figures (8)

Fig. 1
Fig. 1

Principle arrangement of an interferometer of the Mach-Zehnder type (above) and of a shearing interferometer (below) with parallel light through the test object. The camera lens focuses a plane of the object onto the recording plane.

Fig. 2
Fig. 2

Coordinate system for the analysis of the shearing interferometer.

Fig. 3
Fig. 3

Infinite fringe width interferogram of the conventive air flow along a vertical heated plate.

Fig. 4
Fig. 4

Finite fringe width interferogram of the same flow pattern as in Fig. 3.

Fig. 5
Fig. 5

Visualization of a plane shock wave in a gas with the fringes being aligned parallel or oblique to the shock front. The fringe shift is a measure of the density difference through the shock.

Fig. 6
Fig. 6

Shearing interferometer using a second surface mirror.

Fig. 7
Fig. 7

Shearing interferometer using a transparent diffraction grating.

Fig. 8
Fig. 8

Interferometer unit of the Wollaston prism shearing interferometer.

Equations (14)

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l = ζ ζ ¯ n ( x , y , z ) d z ,
Δ l = ζ 1 ζ ¯ 1 n ( x , y + d 2 , z ) d z - ζ 2 ζ ¯ 2 n ( x , y - d 2 , z ) d z ζ ζ ¯ [ n ( x , y + d 2 , z ) - n ( x , y - d 2 , z ) ] d z .
Δ l = d ζ ζ ¯ n ( x , y , z ) y d z .
Δ l = K · d ζ ζ ¯ ρ ( x , y , z ) y d z .
b = ζ ζ ¯ d z ,
K · d · b [ ρ ( x , y ) ] / y = i · λ , i = 0 , ± 1 , .
Δ I I = f a ζ ζ ¯ ln n y d z K f a ζ ζ ¯ ρ y d z .
l w = ζ w ζ w + c y 2 n w d z = c n w y 2 .
Δ l + Δ l w = K · d ζ ζ ¯ ρ y d z + c · n w [ ( y + d 2 ) 2 - ( y - d 2 ) 2 ] .
K · d ζ ζ ¯ ρ y d z + 2 c · n w · y · d = i · λ             i = 0 , ± 1 , .
S = λ / ( 2 c n w d ) .
Δ S Δ = K · d λ ζ ζ ¯ ρ ( x , y , z ) y · d z = D ( x , y ) .
( Δ S / S ) 2 - dim = [ ( K · d · b ) / λ ] · ( ρ / y ) .
Δ l shock = K ζ ζ ¯ Δ ρ d z ,

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