Abstract

It is demonstrated theoretically that if the stop in a schlieren system is no larger than the central maximum of the empty field Airy disk at the stop location, the system will behave as an interferometer for objects much smaller than the empty field. Interferograms produced by such a system are shown.

© 1977 Optical Society of America

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References

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  1. L. L. Thompson, L. S. Taylor, AIAA J. 7, 2030 (1969).
    [CrossRef]
  2. J. B. Brackenridge, W. P. Gilbert, Appl. Opt. 4, 819 (1965).
    [CrossRef]
  3. F. Emich, Monatsh. Chem. 50, 269 (1928).
    [CrossRef]
  4. F. Emich, Monatsh. Chem. 53/54, 312 (1969).
    [CrossRef]
  5. J. G. Dodd, Microscope 15, 167 (1966).
  6. J. G. Dodd, Microscope 17, 1 (1969).
  7. W. C. McCrone, Microscope 20, 309 (1972).
  8. L. C. Martin, Theory of the Microscope (American Elsevier, New York, 1966), Chap. 7, pp. 350–357.

1972 (1)

W. C. McCrone, Microscope 20, 309 (1972).

1969 (3)

J. G. Dodd, Microscope 17, 1 (1969).

L. L. Thompson, L. S. Taylor, AIAA J. 7, 2030 (1969).
[CrossRef]

F. Emich, Monatsh. Chem. 53/54, 312 (1969).
[CrossRef]

1966 (1)

J. G. Dodd, Microscope 15, 167 (1966).

1965 (1)

1928 (1)

F. Emich, Monatsh. Chem. 50, 269 (1928).
[CrossRef]

Brackenridge, J. B.

Dodd, J. G.

J. G. Dodd, Microscope 17, 1 (1969).

J. G. Dodd, Microscope 15, 167 (1966).

Emich, F.

F. Emich, Monatsh. Chem. 53/54, 312 (1969).
[CrossRef]

F. Emich, Monatsh. Chem. 50, 269 (1928).
[CrossRef]

Gilbert, W. P.

Martin, L. C.

L. C. Martin, Theory of the Microscope (American Elsevier, New York, 1966), Chap. 7, pp. 350–357.

McCrone, W. C.

W. C. McCrone, Microscope 20, 309 (1972).

Taylor, L. S.

L. L. Thompson, L. S. Taylor, AIAA J. 7, 2030 (1969).
[CrossRef]

Thompson, L. L.

L. L. Thompson, L. S. Taylor, AIAA J. 7, 2030 (1969).
[CrossRef]

AIAA J. (1)

L. L. Thompson, L. S. Taylor, AIAA J. 7, 2030 (1969).
[CrossRef]

Appl. Opt. (1)

Microscope (3)

J. G. Dodd, Microscope 15, 167 (1966).

J. G. Dodd, Microscope 17, 1 (1969).

W. C. McCrone, Microscope 20, 309 (1972).

Monatsh. Chem. (2)

F. Emich, Monatsh. Chem. 50, 269 (1928).
[CrossRef]

F. Emich, Monatsh. Chem. 53/54, 312 (1969).
[CrossRef]

Other (1)

L. C. Martin, Theory of the Microscope (American Elsevier, New York, 1966), Chap. 7, pp. 350–357.

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Figures (5)

Fig. 1
Fig. 1

Optical train of schlieren microscope.

Fig. 2
Fig. 2

Schlieren interferogram of crystal in oil.

Fig. 3
Fig. 3

Unit magnification imaging system.

Fig. 4
Fig. 4

Opaque objects, normal illumination.

Fig. 5
Fig. 5

Opaque objects, schlieren illumination.

Equations (11)

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A F = A o - L L exp ( i ω x ) d x ,
A = A o [ - l l t ( x ) exp ( i ω x ) d x + - L - l exp ( i ω x ) d x + l L exp ( i ω x ) d x ] = A o [ - l l t ( x ) exp ( i ω x ) d x + - L L exp ( i ω x ) d x - - l l exp ( i ω x ) d x ] = F l ( A o t ) + F L ( A o ) - F l ( A o ) .
u ~ f λ / a
u L = f λ / 2 L
A l = A o F l ( t - 1 ) ,
A i = F ( A l ) = A o [ t ( x ) - 1 ] ,
I = I o [ t t * + 1 - ( t + t * ) ] .
t ( x ) = exp [ i θ ( x ) ]
I = I o [ 2 - 2 cos θ ( x ) ] = 4 I o sin 2 [ θ ( x ) / 2 ] ,
A i = - A o
I = I o

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