Abstract

A method of determining stress at a point is suggested here. The effect of bending of a wave front that is due to variations of the refractive index is used to measure different aspects of stresses. A Fourier lens with a cross slit at its front focal plane is used to form interference fringes at planes near its back focal plane. The sample, illuminated by a plane-parallel coherent beam of light, is placed close to a cross slit, and the change in fringe pattern due to axial shift of the spectrum planes of the slits is measured to relate it to the state of stress.

© 1997 Optical Society of America

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References

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  1. J. W. Dally and W. F. Riley, Experimental Stress Analysis (McGraw-Hill, New York, 1978), Chap. 1, pp. 16–17.
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, p. 62.
  3. J. C. Maxwell, in The Scientific Papers of James Clerk Maxwell, W. D. Niven, ed. (Dover, New York, 1965), Vol. 1, p. 68.
  4. R. J. Standford, J. Exp. Mechan. 20, 427 (1980).
    [CrossRef]
  5. L. Pirodda, in Optical Metrology, O. D. D. Soares, ed., Vol. 131 of Applied Sciences: Series E (Martinus Nijhoff, Dordrecht, The Netherlands, 1987), pp. 223–241.
    [CrossRef]
  6. S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, J. Opt. Eng. 33, 3359 (1994).
    [CrossRef]
  7. S. K. Bhadra, R. N. Chakraborty, K. Sengupta, S. K. Sarkar, and A. Basuray, J. Mod. Opt. 43, 2009 (1996).
    [CrossRef]

1996 (1)

S. K. Bhadra, R. N. Chakraborty, K. Sengupta, S. K. Sarkar, and A. Basuray, J. Mod. Opt. 43, 2009 (1996).
[CrossRef]

1994 (1)

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, J. Opt. Eng. 33, 3359 (1994).
[CrossRef]

1980 (1)

R. J. Standford, J. Exp. Mechan. 20, 427 (1980).
[CrossRef]

Basuray, A.

S. K. Bhadra, R. N. Chakraborty, K. Sengupta, S. K. Sarkar, and A. Basuray, J. Mod. Opt. 43, 2009 (1996).
[CrossRef]

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, J. Opt. Eng. 33, 3359 (1994).
[CrossRef]

Bhadra, S. K.

S. K. Bhadra, R. N. Chakraborty, K. Sengupta, S. K. Sarkar, and A. Basuray, J. Mod. Opt. 43, 2009 (1996).
[CrossRef]

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, J. Opt. Eng. 33, 3359 (1994).
[CrossRef]

Chakraborty, R. N.

S. K. Bhadra, R. N. Chakraborty, K. Sengupta, S. K. Sarkar, and A. Basuray, J. Mod. Opt. 43, 2009 (1996).
[CrossRef]

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, J. Opt. Eng. 33, 3359 (1994).
[CrossRef]

Dally, J. W.

J. W. Dally and W. F. Riley, Experimental Stress Analysis (McGraw-Hill, New York, 1978), Chap. 1, pp. 16–17.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, p. 62.

Maxwell, J. C.

J. C. Maxwell, in The Scientific Papers of James Clerk Maxwell, W. D. Niven, ed. (Dover, New York, 1965), Vol. 1, p. 68.

Pirodda, L.

L. Pirodda, in Optical Metrology, O. D. D. Soares, ed., Vol. 131 of Applied Sciences: Series E (Martinus Nijhoff, Dordrecht, The Netherlands, 1987), pp. 223–241.
[CrossRef]

Riley, W. F.

J. W. Dally and W. F. Riley, Experimental Stress Analysis (McGraw-Hill, New York, 1978), Chap. 1, pp. 16–17.

Sarkar, S. K.

S. K. Bhadra, R. N. Chakraborty, K. Sengupta, S. K. Sarkar, and A. Basuray, J. Mod. Opt. 43, 2009 (1996).
[CrossRef]

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, J. Opt. Eng. 33, 3359 (1994).
[CrossRef]

Sengupta, K.

S. K. Bhadra, R. N. Chakraborty, K. Sengupta, S. K. Sarkar, and A. Basuray, J. Mod. Opt. 43, 2009 (1996).
[CrossRef]

Standford, R. J.

R. J. Standford, J. Exp. Mechan. 20, 427 (1980).
[CrossRef]

J. Exp. Mechan. (1)

R. J. Standford, J. Exp. Mechan. 20, 427 (1980).
[CrossRef]

J. Mod. Opt. (1)

S. K. Bhadra, R. N. Chakraborty, K. Sengupta, S. K. Sarkar, and A. Basuray, J. Mod. Opt. 43, 2009 (1996).
[CrossRef]

J. Opt. Eng. (1)

S. K. Bhadra, S. K. Sarkar, R. N. Chakraborty, and A. Basuray, J. Opt. Eng. 33, 3359 (1994).
[CrossRef]

Other (4)

L. Pirodda, in Optical Metrology, O. D. D. Soares, ed., Vol. 131 of Applied Sciences: Series E (Martinus Nijhoff, Dordrecht, The Netherlands, 1987), pp. 223–241.
[CrossRef]

J. W. Dally and W. F. Riley, Experimental Stress Analysis (McGraw-Hill, New York, 1978), Chap. 1, pp. 16–17.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, p. 62.

J. C. Maxwell, in The Scientific Papers of James Clerk Maxwell, W. D. Niven, ed. (Dover, New York, 1965), Vol. 1, p. 68.

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Figures (2)

Fig. 1
Fig. 1

Schematic drawing of the experimental arrangement under a typical test condition is shown. The spectra of the horizontal and the vertical slits are shown to be focused at different planes on the z axis. L, Laser source; MO, microscope objective; PH, pinhole; C, collimating lens; S, sample under load; FL, Fourier lens of focal length f; SPx and SPy, spectrum planes of the vertical and the horizontal slits at distances z1 and z2 from the observation plane (OP), respectively.

Fig. 2
Fig. 2

Photographs of the fringes, with schematic drawings representing experimental conditions and the equivalent state of stresses. SP’s, spectrum planes.

Equations (7)

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Au,v=Rectu/2p+Rectv/2p,
ax,y=K-+-+Au,vexp-2πiux+vydudv,
ax,y=K1sinc2πpxδy+sinc2πpyδx.
Ux1,y1=A/z1 sinc2πpx1exp-iky12/2z1+A/z2 sinc2πpy1exp-ikx12/2z2,
I=UU*=A2/z12sinc22πpx1+A2/z22sinc22πpy1+2A2 sinc2πpx1sinc2πpy1×cosky12/2z1-kx12/2z2.
cosky12/2z1-kx12/2z2=1.
y12/m2-x12/l2=1,

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