Abstract

It is shown that three optical parameters that are necessary for stress computation in integrated photoelasticity can be measured with high accuracy by use of a Fourier polarimetry method. Inasmuch as a photoelastic sample, which is an object of investigation in integrated photoelasticity, is a kind of an elliptic retarder, the technique presented here measures relative retardation δ, azimuth angle θ, and ellipticity angle ∊ instead of the characteristic parameters that traditionally have been used in integrated photoelasticity. The ability of the new technique to provide better accuracy with a simpler setup has been proved experimentally. Furthermore, the technique is self-contained as for phase measurement; i.e., it automatically performs phase unwrapping at the points where phase data exceed the value of π. The full value of a phase at a certain point is retrieved by processing of π-modulo phase data that have been precisely measured at several wavelengths. The usefulness of the new method for integrated photoelasticity has been demonstrated through measurement of a diametrically compressed disk viewed at oblique light incidence.

© 2001 Optical Society of America

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References

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  1. H. Aben, Integrated Photoelasticity (McGraw-Hill, New York, 1979).
  2. J. F. Doyle, H. T. Danyluk, “Integrated photoelasticity for axisymmetric problems,” Exp. Mech. 18, 215–220 (1978).
    [CrossRef]
  3. H. Kubo, R. Nagata, “Determination of dielectric tensor field in weakly inhomogeneous anisotropic media,” J. Opt. Soc. Am. 69, 604–610 (1979).
    [CrossRef]
  4. H. Aben, “Integrated photoelasticity as tensor field tomography,” in Proceedings of the International Symposium on Photoelasticity (Japan Society of Mechanical Engineering, Tokyo, 1986), pp. 243–250.
  5. Y. A. Andrienko, M. S. Dubovikov, A. D. Gladun, “Optical tomography of a birefringent medium,” J. Opt. Soc. Am. A 9, 1761–1764 (1992).
    [CrossRef]
  6. Y. A. Andrienko, M. S. Dubovikov, A. D. Gladun, “Optical tensor field tomography: the Kerr effect and axisymmetric integrated photoelasticity,” J. Opt. Soc. Am. A 9, 1765–1768 (1992).
    [CrossRef]
  7. Y. A. Andrienko, M. S. Dubovikov, “Optical tomography of tensor fields: the general case,” J. Opt. Soc. Am. A 11, 1628–1631 (1994).
    [CrossRef]
  8. R. A. Tomlinson, E. A. Patterson, “Determination of characteristic parameters for integrated photoelasticity using phase stepping,” in Proceedings of the SEM Annual Meeting on Theoretical Experimental, and Computer Mechanics (Society for Experimental Mechanics, Bethel, Conn., 1998), pp. 118–121.
  9. R. A. Tomlinson, E. A. Patterson, “Evaluating characteristic parameters in integrated photoelasticity,” in Proceedings of the Eleventh International Conference on Experimental Mechanics (Balkema, Rotterdam, The Netherlands, 1998), pp. 495–500.
  10. S. K. Mangal, K. Ramesh, “Determination of characteristic parameters in integrated photoelasticity by phase-shifting technique,” Opt. Lasers Eng. 31, 263–278 (1999).
    [CrossRef]
  11. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1997).
  12. A. S. Voloshin, A. S. Redner, “Automated measurement of birefringence: development and experimental evaluation of the technique,” Exp. Mech. 28, 252–257 (1989).
    [CrossRef]
  13. R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
    [CrossRef]
  14. J. L. Pezanniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
    [CrossRef]
  15. R. W. Collins, J. Koh, “Dual rotating-compensator multichannel ellipsometer: instrument design for real-time Mueller matrix spectroscopy or surfaces and films,” J. Opt. Soc. Am. A 16, 1997–2006 (1999).
    [CrossRef]
  16. S. Yu Berezhna, I. V. Berezhnyi, M. Takashi, “Photoelastic analysis through Jones matrix imaging Fourier polarimetry,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics (Japan Society of Mechanical Engineering, Tokyo, (1999), Vol. 2, pp. 635–640.
  17. C. Buckberry, D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
    [CrossRef]
  18. A. D. Nurse, “Full-field automated photoelasticity by use of a three-wavelength approach to phase stepping,” Appl. Opt. 36, 5781–5786 (1997).
    [CrossRef] [PubMed]
  19. S. Yu. Berezhna, I. V. Berezhnyy, M. Takashi, “Stress tensor field tomography through polarimetry: accuracy of optical data,” in Proceedings of the Fourth International Workshop on Advances in Experimental Mechanics (University of Ljubljana, Ljubljana, Slovenia, 1999), pp. 117–131.
  20. A. S. Kobayashi, ed., Handbook on Experimental Mechanics (Society for Experimental Mechanics, Bethel, Conn., 1993).

1999 (2)

S. K. Mangal, K. Ramesh, “Determination of characteristic parameters in integrated photoelasticity by phase-shifting technique,” Opt. Lasers Eng. 31, 263–278 (1999).
[CrossRef]

R. W. Collins, J. Koh, “Dual rotating-compensator multichannel ellipsometer: instrument design for real-time Mueller matrix spectroscopy or surfaces and films,” J. Opt. Soc. Am. A 16, 1997–2006 (1999).
[CrossRef]

1997 (1)

1996 (1)

C. Buckberry, D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
[CrossRef]

1995 (1)

J. L. Pezanniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

1994 (1)

1992 (2)

1989 (1)

A. S. Voloshin, A. S. Redner, “Automated measurement of birefringence: development and experimental evaluation of the technique,” Exp. Mech. 28, 252–257 (1989).
[CrossRef]

1979 (1)

1978 (2)

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
[CrossRef]

J. F. Doyle, H. T. Danyluk, “Integrated photoelasticity for axisymmetric problems,” Exp. Mech. 18, 215–220 (1978).
[CrossRef]

Aben, H.

H. Aben, Integrated Photoelasticity (McGraw-Hill, New York, 1979).

H. Aben, “Integrated photoelasticity as tensor field tomography,” in Proceedings of the International Symposium on Photoelasticity (Japan Society of Mechanical Engineering, Tokyo, 1986), pp. 243–250.

Andrienko, Y. A.

Azzam, R. M. A.

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1997).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1997).

Berezhna, S. Yu

S. Yu Berezhna, I. V. Berezhnyi, M. Takashi, “Photoelastic analysis through Jones matrix imaging Fourier polarimetry,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics (Japan Society of Mechanical Engineering, Tokyo, (1999), Vol. 2, pp. 635–640.

Berezhna, S. Yu.

S. Yu. Berezhna, I. V. Berezhnyy, M. Takashi, “Stress tensor field tomography through polarimetry: accuracy of optical data,” in Proceedings of the Fourth International Workshop on Advances in Experimental Mechanics (University of Ljubljana, Ljubljana, Slovenia, 1999), pp. 117–131.

Berezhnyi, I. V.

S. Yu Berezhna, I. V. Berezhnyi, M. Takashi, “Photoelastic analysis through Jones matrix imaging Fourier polarimetry,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics (Japan Society of Mechanical Engineering, Tokyo, (1999), Vol. 2, pp. 635–640.

Berezhnyy, I. V.

S. Yu. Berezhna, I. V. Berezhnyy, M. Takashi, “Stress tensor field tomography through polarimetry: accuracy of optical data,” in Proceedings of the Fourth International Workshop on Advances in Experimental Mechanics (University of Ljubljana, Ljubljana, Slovenia, 1999), pp. 117–131.

Buckberry, C.

C. Buckberry, D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
[CrossRef]

Chipman, R. A.

J. L. Pezanniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Collins, R. W.

Danyluk, H. T.

J. F. Doyle, H. T. Danyluk, “Integrated photoelasticity for axisymmetric problems,” Exp. Mech. 18, 215–220 (1978).
[CrossRef]

Doyle, J. F.

J. F. Doyle, H. T. Danyluk, “Integrated photoelasticity for axisymmetric problems,” Exp. Mech. 18, 215–220 (1978).
[CrossRef]

Dubovikov, M. S.

Gladun, A. D.

Koh, J.

Kubo, H.

Mangal, S. K.

S. K. Mangal, K. Ramesh, “Determination of characteristic parameters in integrated photoelasticity by phase-shifting technique,” Opt. Lasers Eng. 31, 263–278 (1999).
[CrossRef]

Nagata, R.

Nurse, A. D.

Patterson, E. A.

R. A. Tomlinson, E. A. Patterson, “Evaluating characteristic parameters in integrated photoelasticity,” in Proceedings of the Eleventh International Conference on Experimental Mechanics (Balkema, Rotterdam, The Netherlands, 1998), pp. 495–500.

R. A. Tomlinson, E. A. Patterson, “Determination of characteristic parameters for integrated photoelasticity using phase stepping,” in Proceedings of the SEM Annual Meeting on Theoretical Experimental, and Computer Mechanics (Society for Experimental Mechanics, Bethel, Conn., 1998), pp. 118–121.

Pezanniti, J. L.

J. L. Pezanniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Ramesh, K.

S. K. Mangal, K. Ramesh, “Determination of characteristic parameters in integrated photoelasticity by phase-shifting technique,” Opt. Lasers Eng. 31, 263–278 (1999).
[CrossRef]

Redner, A. S.

A. S. Voloshin, A. S. Redner, “Automated measurement of birefringence: development and experimental evaluation of the technique,” Exp. Mech. 28, 252–257 (1989).
[CrossRef]

Takashi, M.

S. Yu. Berezhna, I. V. Berezhnyy, M. Takashi, “Stress tensor field tomography through polarimetry: accuracy of optical data,” in Proceedings of the Fourth International Workshop on Advances in Experimental Mechanics (University of Ljubljana, Ljubljana, Slovenia, 1999), pp. 117–131.

S. Yu Berezhna, I. V. Berezhnyi, M. Takashi, “Photoelastic analysis through Jones matrix imaging Fourier polarimetry,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics (Japan Society of Mechanical Engineering, Tokyo, (1999), Vol. 2, pp. 635–640.

Tomlinson, R. A.

R. A. Tomlinson, E. A. Patterson, “Evaluating characteristic parameters in integrated photoelasticity,” in Proceedings of the Eleventh International Conference on Experimental Mechanics (Balkema, Rotterdam, The Netherlands, 1998), pp. 495–500.

R. A. Tomlinson, E. A. Patterson, “Determination of characteristic parameters for integrated photoelasticity using phase stepping,” in Proceedings of the SEM Annual Meeting on Theoretical Experimental, and Computer Mechanics (Society for Experimental Mechanics, Bethel, Conn., 1998), pp. 118–121.

Towers, D.

C. Buckberry, D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
[CrossRef]

Voloshin, A. S.

A. S. Voloshin, A. S. Redner, “Automated measurement of birefringence: development and experimental evaluation of the technique,” Exp. Mech. 28, 252–257 (1989).
[CrossRef]

Appl. Opt. (1)

Exp. Mech. (2)

A. S. Voloshin, A. S. Redner, “Automated measurement of birefringence: development and experimental evaluation of the technique,” Exp. Mech. 28, 252–257 (1989).
[CrossRef]

J. F. Doyle, H. T. Danyluk, “Integrated photoelasticity for axisymmetric problems,” Exp. Mech. 18, 215–220 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
[CrossRef]

Opt. Eng. (1)

J. L. Pezanniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Opt. Lasers Eng. (2)

S. K. Mangal, K. Ramesh, “Determination of characteristic parameters in integrated photoelasticity by phase-shifting technique,” Opt. Lasers Eng. 31, 263–278 (1999).
[CrossRef]

C. Buckberry, D. Towers, “New approaches to the full-field analysis of photoelastic stress patterns,” Opt. Lasers Eng. 24, 415–428 (1996).
[CrossRef]

Other (8)

S. Yu. Berezhna, I. V. Berezhnyy, M. Takashi, “Stress tensor field tomography through polarimetry: accuracy of optical data,” in Proceedings of the Fourth International Workshop on Advances in Experimental Mechanics (University of Ljubljana, Ljubljana, Slovenia, 1999), pp. 117–131.

A. S. Kobayashi, ed., Handbook on Experimental Mechanics (Society for Experimental Mechanics, Bethel, Conn., 1993).

H. Aben, “Integrated photoelasticity as tensor field tomography,” in Proceedings of the International Symposium on Photoelasticity (Japan Society of Mechanical Engineering, Tokyo, 1986), pp. 243–250.

S. Yu Berezhna, I. V. Berezhnyi, M. Takashi, “Photoelastic analysis through Jones matrix imaging Fourier polarimetry,” in Proceedings of the International Conference on Advanced Technology in Experimental Mechanics (Japan Society of Mechanical Engineering, Tokyo, (1999), Vol. 2, pp. 635–640.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1997).

R. A. Tomlinson, E. A. Patterson, “Determination of characteristic parameters for integrated photoelasticity using phase stepping,” in Proceedings of the SEM Annual Meeting on Theoretical Experimental, and Computer Mechanics (Society for Experimental Mechanics, Bethel, Conn., 1998), pp. 118–121.

R. A. Tomlinson, E. A. Patterson, “Evaluating characteristic parameters in integrated photoelasticity,” in Proceedings of the Eleventh International Conference on Experimental Mechanics (Balkema, Rotterdam, The Netherlands, 1998), pp. 495–500.

H. Aben, Integrated Photoelasticity (McGraw-Hill, New York, 1979).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the PSA Fourier polarimeter: 1, light source; 2, spatial filter; 3, collimator; 4, rotating polarizer; 5, 8, rotatory devices; 6, sample; 7, rotating analyzer; 9, objective; 10, CCD camera; 11, computer; 12, camera controller; 13, rotatory stage controller.

Fig. 2
Fig. 2

Mean absolute measurement error for phase, azimuth, and ellipticity angles versus phase. The crystallographic axes of the Babinet–Soleil compensator were set at 0° orientation in a laboratory coordinate system during phase measurement and at 25° orientation when an azimuth angle was measured. Accuracy for the ellipticity angle was investigated with a test sample created from two quarter-wave plates. The data for the ellipticity angle were computed with Eq. (5) if the phase values were within [0; 175°] and with Eq. (6) if the phase values reached [175°; 180°].

Fig. 3
Fig. 3

Schematic illustration of the light path in a disk immersed in liquid. N is the number of intervals at which the light path is sampled in theoretical computations, a is the angle of incidence, and d is the sample’s thickness.

Fig. 4
Fig. 4

Distribution of the retardation in the disk along the scan, chosen at y = 0.5R. A theoretical plot was generated by the suggested computational algorithm. The light path was sampled in N = 100 equidistant increments. The angle of light incidence was a = 30°.

Fig. 5
Fig. 5

Theoretically generated and experimentally obtained azimuth angle distributions at y = ±0.5R and a = 30°.

Fig. 6
Fig. 6

Theoretically generated and measured ellipticity angle profiles in the disk along the scan at y = ±0.5R for a = 30°.

Fig. 7
Fig. 7

Theoretically predicted and experimentally obtained ellipticity angle values at point (0;0.5R) for several angles of incidence of light into the disk.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

ID=a0+n=14an cos 2nα+bn sin 2nα,
δw=cos-1(2a2/a0-a4/a02+b4/a021/2),
θ=1/4 cos-1a4/a0/a4/a02+b4/a021/2,
θ=14sin-1b4/a0a4/a02+b4/a021/2
=12sin-1-2b2/a0sinδ
=±1/2 sin-11-4a4/a02+b4/a021/2/1-cos δ1/2,
σpbr= Alpbflr,
t12×=-ν11-expiCμd1-ν1/ν2expiCμd,
t21×=1ν21-expiCμd1-ν1/ν2expiCμd,
t22×=expiCμd-ν1/ν21-ν1/ν2expiCμd,
ν1,2=21222-11±μ,
μ=11-222+41221/2,
pp-0=C1σpp+C2σbb+σmm,
bb-0=C1σbb+C2σpp+σmm,
mm-0=C1σmmC2σpp+σbb,
T=s=1N ts,

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