Abstract

A portable, rugged, inexpensive shearing interferometer is described and evaluated. Originally intended for application to plasma and flow analysis, it is also a suitable instructional aid. The shearing is obtained by the offset of the reflection from the first surface of a mirror relative to the reflection from the second surface when the mirror is set at an angle to the illuminating beam. The sensitivity is equivalent to that of a schlieren system. However, no schlieren quality components are involved and there are no critical adjustments or dimensions.

© 1970 Optical Society of America

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References

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  1. R. S. Longhurst, Geometrical and Physical Optics (John Wiley & Sons, Inc., New York, 1967), p. 155.
  2. W. J. Bates, Proc. Phys. Soc. (London) 59, 940 (1947).
    [CrossRef]
  3. M. V. R. K. Murty, Appl. Opt. 3, 531 (1964).
    [CrossRef]
  4. R. L. Rowe, in Applications of Lasers to Photography and Information Handling, R. D. Murray, Ed. (Society of Photographic Scientists and Engineers, Inc., Washington, D.C., 1968), pp. 197–215.
  5. D. Finkelstein, H. M. Presby, Rev. Sci. Instrum. 38, 1563 (1967).
    [CrossRef]
  6. H. M. Presby, “Laser Phasography of Jets, Shocks and Plasmas” Thesis, Belfer Graduate School of Science, Yeshiva University, 1966.
  7. C. Veret, “Low Density Visualization” 30th Reunion of AGARD on the New Experimental Techniques, Munich, 1967 (Translation NASA TTF-11, p. 509, 1968).
  8. J. Dyson, J. Opt. Soc. Amer. 47, 386 (1957).
    [CrossRef]
  9. A. L. Besse, J. G. Kelley, Rev. Sci. Instrum. 37, 1497 (1966).
    [CrossRef]
  10. W. D. Burnett, Laser Eye and Skin Hazard Evaluation, Sandia Corp., May1968 (Available from Div. of Tech. Inf. USAEC as SC-RR-68-174*).

1967 (1)

D. Finkelstein, H. M. Presby, Rev. Sci. Instrum. 38, 1563 (1967).
[CrossRef]

1966 (1)

A. L. Besse, J. G. Kelley, Rev. Sci. Instrum. 37, 1497 (1966).
[CrossRef]

1964 (1)

1957 (1)

J. Dyson, J. Opt. Soc. Amer. 47, 386 (1957).
[CrossRef]

1947 (1)

W. J. Bates, Proc. Phys. Soc. (London) 59, 940 (1947).
[CrossRef]

Bates, W. J.

W. J. Bates, Proc. Phys. Soc. (London) 59, 940 (1947).
[CrossRef]

Besse, A. L.

A. L. Besse, J. G. Kelley, Rev. Sci. Instrum. 37, 1497 (1966).
[CrossRef]

Burnett, W. D.

W. D. Burnett, Laser Eye and Skin Hazard Evaluation, Sandia Corp., May1968 (Available from Div. of Tech. Inf. USAEC as SC-RR-68-174*).

Dyson, J.

J. Dyson, J. Opt. Soc. Amer. 47, 386 (1957).
[CrossRef]

Finkelstein, D.

D. Finkelstein, H. M. Presby, Rev. Sci. Instrum. 38, 1563 (1967).
[CrossRef]

Kelley, J. G.

A. L. Besse, J. G. Kelley, Rev. Sci. Instrum. 37, 1497 (1966).
[CrossRef]

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics (John Wiley & Sons, Inc., New York, 1967), p. 155.

Murty, M. V. R. K.

Presby, H. M.

D. Finkelstein, H. M. Presby, Rev. Sci. Instrum. 38, 1563 (1967).
[CrossRef]

H. M. Presby, “Laser Phasography of Jets, Shocks and Plasmas” Thesis, Belfer Graduate School of Science, Yeshiva University, 1966.

Rowe, R. L.

R. L. Rowe, in Applications of Lasers to Photography and Information Handling, R. D. Murray, Ed. (Society of Photographic Scientists and Engineers, Inc., Washington, D.C., 1968), pp. 197–215.

Veret, C.

C. Veret, “Low Density Visualization” 30th Reunion of AGARD on the New Experimental Techniques, Munich, 1967 (Translation NASA TTF-11, p. 509, 1968).

Appl. Opt. (1)

J. Opt. Soc. Amer. (1)

J. Dyson, J. Opt. Soc. Amer. 47, 386 (1957).
[CrossRef]

Proc. Phys. Soc. (London) (1)

W. J. Bates, Proc. Phys. Soc. (London) 59, 940 (1947).
[CrossRef]

Rev. Sci. Instrum. (2)

D. Finkelstein, H. M. Presby, Rev. Sci. Instrum. 38, 1563 (1967).
[CrossRef]

A. L. Besse, J. G. Kelley, Rev. Sci. Instrum. 37, 1497 (1966).
[CrossRef]

Other (5)

W. D. Burnett, Laser Eye and Skin Hazard Evaluation, Sandia Corp., May1968 (Available from Div. of Tech. Inf. USAEC as SC-RR-68-174*).

R. S. Longhurst, Geometrical and Physical Optics (John Wiley & Sons, Inc., New York, 1967), p. 155.

H. M. Presby, “Laser Phasography of Jets, Shocks and Plasmas” Thesis, Belfer Graduate School of Science, Yeshiva University, 1966.

C. Veret, “Low Density Visualization” 30th Reunion of AGARD on the New Experimental Techniques, Munich, 1967 (Translation NASA TTF-11, p. 509, 1968).

R. L. Rowe, in Applications of Lasers to Photography and Information Handling, R. D. Murray, Ed. (Society of Photographic Scientists and Engineers, Inc., Washington, D.C., 1968), pp. 197–215.

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Figures (3)

Fig. 1
Fig. 1

Multiple reflections from second surface mirror. A plane wave is incident at angle β to the normal. Portions of rays from (x + w), (x), (xw), (x − 2w), …, reach (x) after 0, 1, 2, 3 … reflections from the seond surface. Sizes and angles have been distorted to emphasize significant factors.

Fig. 2
Fig. 2

Interferogram of helium flow over a suspended electrode (0.03 m × 0.03 m). The flow is successively increased from (a) no flow to (g) full flow. (h) A combined interferogram and shadowgraph is shown which is described more fully in the text. The pictures were taken on Polaroid Type 57 (ASA 3000) film at 10−3-sec exposure with a 1.0 neutral density filter at the laser.

Fig. 3
Fig. 3

(a) Interferogram of alcohol evaporating from a warm spark plug. The two broad fringes at the lower right are due to radius of curvature of the wavefronts. These are also seen in (b) an interferogram of an alcohol flame. (c) Same as (b) but with an intentionally superposed fringe pattern. (d) Shadowgraph of an alcohol flame. P/N 55 film at 1/250 sec.

Equations (10)

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A ( x , y ) exp { i k [ r + p ( x , y ) ] } ,
A = exp [ 1 2 a b α ( x , y , r ) d r ] ,
I = { B A + exp [ i k ( R + + P + ) ] + ( 1 B 2 ) C A 0 exp [ i k ( R 0 + P 0 ) ] + B ( 1 B 2 ) C 2 A exp [ i k ( R + P ) ] + B 2 ( 1 B 2 ) C 3 A 2 exp [ i k ( R 2 + P 2 ) ] + } 2 .
I = C 2 A 0 2 + 2 B A 0 { C A + cos [ k ( R + R 0 + P + P 0 ) ] + C 3 A cos [ k ( R 0 R + P 0 P ) ] } + B 2 { A + 2 2 C 2 A 0 2 + C 4 A 2 + 2 C 2 A A + cos [ k ( R + R + P + P ) ] + 2 C 4 A 0 A 2 cos [ k ( R 0 R 2 + P 0 P 2 ) ] } + .
R 0 = ( z 0 2 + x 2 + y 2 ) 1 2 z 0 + x 2 / ( 2 z 0 ) + y 2 / ( 2 z 0 ) , R + = [ z 0 2 + ( x + w ) 2 + y 2 ] 1 2 2 d R 0 + ( w 2 + 2 x w ) / ( 2 R 0 ) 2 d , R R 0 + ( w 2 2 x w ) / ( 2 B 0 ) + 2 d , R 2 R 0 + ( 4 w 2 4 x w ) / ( 2 R 0 ) + 4 d , etc .
I = C 2 A 0 2 + B 2 ( A + 2 2 C 2 A 0 2 + C 4 A 2 2 C 4 A 0 A 2 2 C 2 A A + ) + B 2 ( C A + A 0 + 2 C 3 A A 0 ) cos ( k δ ) + 4 C 2 B 2 ( A A + + C 2 A 0 A 2 ) cos 2 ( k δ ) + ,
I = A 0 2 + 2 B A 0 ( A + + A ) cos ( k δ ) .
[ A 0 2 + B A 0 ( A + + A ) ] / [ A 0 2 2 B A 0 ( A + + A ) ] 9.
I = B 2 ( A 0 2 + A + 2 ) 2 B 4 ( A 0 2 + A A + ) + 2 B 2 A + A 0 cos ( k δ ) + B 4 [ 2 A A 0 cos ( k δ ) + 4 A A + cos 2 ( k δ ) ] + .
I = B 2 [ A + 2 + ( 1 2 B 2 ) A 0 2 2 B 2 A A + + 2 A + A 0 cos k δ ] .

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