Abstract

The reflection plate interferometer, which is similar to a Schlieren system but with a small glass shearing plate replacing the knife edge, has been investigated and the necessary relations to understand its operating characteristics are presented. It was found that the optimum operating range is for incident angles between 40° and 65°, and that the fringe spacing is approximately inversely proportional to the shearing-plate thickness. The undisturbed fringe direction can be adjusted at any angle with respect to a test object. The interferograms are of very good quality and can be interpreted to give the density gradient of the test fluid.

© 1973 Optical Society of America

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References

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  1. H. Schardin, Ver. Deutsch. Ingr. Forsch. 5, 367 (1934).
  2. E. B. Temple, J. Opt. Soc. Am. 47, 91 (1957).
    [CrossRef]
  3. A. K. Oppenheim, P. A. Urtiew, F. J. Weinberg, Proc. Roy. Soc. (London) A291, 279 (1966).
  4. L. H. Tanner, J. Sci. Instrum. 42, 834 (1965).
    [CrossRef]
  5. L. H. Tanner, J. Sci. Instrum. 43, 878 (1966).
    [CrossRef]
  6. S. Tolansky, An Introduction to Interferometry (Longmans, Green and Co., London, 1955).

1966 (2)

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

L. H. Tanner, J. Sci. Instrum. 43, 878 (1966).
[CrossRef]

1965 (1)

L. H. Tanner, J. Sci. Instrum. 42, 834 (1965).
[CrossRef]

1957 (1)

1934 (1)

H. Schardin, Ver. Deutsch. Ingr. Forsch. 5, 367 (1934).

Oppenheim, A. K.

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

Schardin, H.

H. Schardin, Ver. Deutsch. Ingr. Forsch. 5, 367 (1934).

Tanner, L. H.

L. H. Tanner, J. Sci. Instrum. 43, 878 (1966).
[CrossRef]

L. H. Tanner, J. Sci. Instrum. 42, 834 (1965).
[CrossRef]

Temple, E. B.

Tolansky, S.

S. Tolansky, An Introduction to Interferometry (Longmans, Green and Co., London, 1955).

Urtiew, P. A.

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

Weinberg, F. J.

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

J. Opt. Soc. Am. (1)

J. Sci. Instrum. (2)

L. H. Tanner, J. Sci. Instrum. 42, 834 (1965).
[CrossRef]

L. H. Tanner, J. Sci. Instrum. 43, 878 (1966).
[CrossRef]

Proc. Roy. Soc. (London) (1)

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

Ver. Deutsch. Ingr. Forsch. (1)

H. Schardin, Ver. Deutsch. Ingr. Forsch. 5, 367 (1934).

Other (1)

S. Tolansky, An Introduction to Interferometry (Longmans, Green and Co., London, 1955).

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Figures (7)

Fig. 1
Fig. 1

Schematic of reflection plate interferometer.

Fig. 2
Fig. 2

Path difference through shearing plate for test and reference rays.

Fig. 3
Fig. 3

Interpretation of fringe formation.

Fig. 4
Fig. 4

Influence of shearing-plate thickness on fringe spacing for incident angle of 52°. (a) W = 0.19 mm, magnification 1×; (b) W = 0.93 mm, magnification 2.5×; (c) W = 1.70 mm, magnification 3.5×.

Fig. 5
Fig. 5

Dependence of viewing screen position and lateral shear on incident angle.

Fig. 6
Fig. 6

Fringe pattern for a range of incident angles using 0.19-mm-thick shearing plate. (a) i1 = 17°, (b) i1 = 40°, (c) i1 = 72°.

Fig. 7
Fig. 7

Interferogram of heated flat plate in air inclined at ~ 45° to the vertical; i1 = 50°, W = 0.93 mm, (a) M = 1; (b) detail magnified 3×.

Equations (11)

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D = F B air = W sin 2 i 1 / ( n g 2 - sin 2 i 1 ) 1 / 2
Z = A R F air - A B air + ( λ / 2 ) = 2 W ( n g 2 - sin 2 i 1 ) 1 / 2 + ( λ / 2 ) ,
γ k = arcsin [ S A / ( Z 2 + D 2 ) 1 / 2 ] - .
S A = ± k λ
S A = ± ( k + ½ ) λ
S V ( γ k - γ k + 1 ) ,
S V λ ( Z 2 + D 2 ) - 1 / 2 .
= arctan ( Z / D ) arctan [ 2 ( n g 2 - sin 2 i 1 ) / sin 2 i 1 ] .
I L = f L { [ f m o m / ( o m - f m ) ] - L - f m } / { [ f m o m / ( o m - f m ) ] - L - f m + f L } ,
M = I L ( q m - f m ) / [ ( q m - L ) ( L + I L ) ] ,
n unknown - n known = ( λ / L ) ( m unknown - m known ) ,

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