Experimental Mechanics

, Volume 12, Issue 2, pp 57–66 | Cite as

Techniques for the determination of absolute retardation in photoelasticity

The different patterns of fringes that can be obtained in holographic interferometry and in conventional interferometry are analyzed by the authors
  • C. A. Sciammarella
  • G. Quintanilla


The purpose of this paper is to give an interpretation to the fringes observed in holographic interferometry when plane-polarized light or circularly polarized light is utilized. It is shown that, when plane-polarized light is utilized and both the loaded and the unloaded states are considered, the obtained patterns are formed by the superposition of three families of fringes: the two families of absolute optical retardation and the family of relative retardation. The intensity distribution is also a function of the orientation of the plane of polarization, and along the points where the plane of polarization is parallel to one of the principal directions, only one of the families of absolute retardation is observed. By utilizing circularly polarized light, the dependence on the orientation of the principal axis is eliminated and patterns consisting of the superposition of the three above-mentioned families are obtained. If only the loaded state is considered, the holographic interferometer behaves as an ordinary polariscope with the reference beam playing the role of the analyzer. The relationships between the observed families are discussed. Examples of application to the disk and ring under diametral compression are also given.


Mechanical Engineer Fluid Dynamics Loaded State Intensity Distribution Principal Axis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols


stress-optical constant

\(\bar a\)

\(stress - optical constant = \frac{a}{{(a^2 - b^2 )h}}\)


complex representation of the reconstructed first order wavefront (scalar wave)


stress-optical constant

\(\bar b\)

\(stress - optical constant = \frac{b}{{(a^2 - b^2 )h}}\)


cos β


exposure=I·t, first exposure


same, second exposure


thickness of the unloaded model


thickness of the loaded model


light intensity, first exposure


light intensity of the first order in the reconstruction


light intensity in the reconstructed image, plane-polarized light, bright background


light intensity in the reconstructed image, plane-polarized light, dark background


light intensity in the reconstructed image, circularly polarized light, bright background


light intensity in the reconstructed image, circularly polarized light, dark background


\(\frac{{2\pi }}{\lambda }\)


\(ratio of the exposure times = \frac{{t_1 }}{{t_2 }}\)




constant of proportionality


index of refraction of the model in the unloaded condition


principal indexes of refraction


complex representation of the reconstruction wavefront


amplitude modulus of the reconstruction wavefront


sin β


\(R^2 \in 1^2 \in R^2\)


exposure times, first and second exposures respectively


transmission function of the holographic plate


slope of the straight-line portion of the plot density vs. the logarithm of the exposure

\(\delta _1\)

absolute variation of the optical path of the polarized component vibrating parallel to the principal direction 1

\(\delta _2\)

same, with respect to the direction 2

\(\delta _3\)

difference between the absolute variation of the optical paths 1 and 2

\(\varepsilon 1\)

object wavefront during the first exposure (vector wave) primed →x′,y′,z′ unprimed →x,y,z;

\(\varepsilon 2\)

same, during the second exposure

\(\varepsilon R\)

reference wavefront

\(\varepsilon 1T,\varepsilon 2T\)

total light vectors, first and second exposure respectively

\(\bar \varepsilon\)
complex amplitude vectors primed →x′, y′, z′ unprimed →x, y, z
\(\varepsilon _x ,\varepsilon _y\)

scalar components of the complex amplitude vectors

\(\varepsilon R, \varepsilon 1, \varepsilon 2\)

modulus of the reference wavefront, the object wavefront (first exposure), the object wavefront (second exposure).\(\varepsilon = \sqrt {\varepsilon _{x^2 } + \varepsilon _{y^2 } }\)

\(\psi x, \psi y\)

phases of the components of the amplitude vector


angle of inclination of the reference and object wavefronts with respect to the plane of the hologram


wavelength of the light

\(\sigma _1 ,\sigma _2\)

principal stresses


phase change introduced by the unloaded model

\(\psi _1\)

change of phase introduced by the loaded model in the principal direction 1

\(\psi _2\)

same, in the principal direction 2


angular frequency of the light


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rodgers, G. L., “Polarization Effects in Holography,” Jnl. of the Optical Society of America (1966).Google Scholar
  2. 2.
    Hovanesian, J. D., Brcic, V. and Powell, R., “A New Stress-Optic Method, Stress-Holo-Interferometry,” Tehnika (November 1967).Google Scholar
  3. 3.
    Fourney, M. E.Application of Holography to Photoelasticity,”Experimental Mechanics,8 (1),33–38 (1968).CrossRefGoogle Scholar
  4. 4.
    Manojaran, D. and Sevigny, L., “Polarization Holography,” Jnl. of the Optical Society of America,56 (1967).Google Scholar
  5. 5.
    Bryngdahl, O., “Polarizing Holography,” Jnl. of the Optical Society of America,57 (1967).Google Scholar
  6. 6.
    Fourney, M. E., Waggoner, A. P. and Mate, K. V., “Recording Polarization Effects via Holography,” Jnl. of the Optical Society of America,58 (1968).Google Scholar
  7. 7.
    Lohman, A. W., “Reconstruction of Vectorial Wavefronts,” Applied Optics,4 (1965).Google Scholar
  8. 8.
    Nicolas, J., “Sur la Déterminatior. de la Somme des Contraintes Principales au Moyen de L’Interferometrie Holographique,” Comptes Rendus de L’Academie des Sciences, t. 267, Serie A (1968).Google Scholar
  9. 9.
    Hovanesian, J. D., Brcic, V. andPowell, R. L., “A New Experimental Stress-Optic Method: Stress-Holo-Interferometry,”Experimental Mechanics,8 (8),362–368 (1968).CrossRefGoogle Scholar
  10. 10.
    Powell, R. L., Hovanesian, J. D. and V. Brcic, “Hologram Interferometry with Birefringent Objects.” The Engineering Uses of Holography. Proceedings of the Conference held at the University of Strathclyde (September 1968).Google Scholar
  11. 11.
    Hovanesian, J. D., “Interference of Two and Three Reconstructed Waves in Photoelasticity,”U. S. Navy Journal of Underwater Acoustics,18 (4) (October 1968).Google Scholar
  12. 12.
    Kezin, G. L., Sakharov and Zhavozonov, “The Use of Holography in Investigations of Hydraulic Equipment by the Photoelastic Method,” Ency. Stroit 7 (97) (1969).Google Scholar
  13. 13.
    Holoway, D. C., “Holography and its Application to Photoelasticity,”T and M Report No. 329, University of Illinois, Urbana, Ill. (June 1969).Google Scholar
  14. 14.
    Fourney, M. E. andMate, K. V.Further Applications of Holography to Photoelasticity,”Experimental Mechanics,10 (5),177–186 (1970).CrossRefGoogle Scholar
  15. 15.
    Hosp, V. E. andWutze, G.The Application of Holography in Plane Photoelasticity,”Materialprüfung Bd. 11 (12)S. 409–415 (1969).Google Scholar
  16. 16.
    Hosp, V. E. andWutze, G., “Holographic Determination of the Principal Stresses in Plane Models,”Materialprüfung Bd. 12 (1)S. 13–22 (1970).Google Scholar
  17. 17.
    Sanford, R. J. andDurelli, A. J., “The Interpretation of Fringes in Stress-Holo-Interferometry,”Experimental Mechanics,11 (4),161–166 (1971).CrossRefGoogle Scholar
  18. 18.
    Post, D.The Generic Nature of the Absolute-retardation Method in Photoelasticity,”Experimental Mechanics,7 (6),233–241 (1967).CrossRefGoogle Scholar
  19. 19.
    Nisida, M. andSaito, H., “A New Interferomatic Method of Two-dimensional Stress Analysis,”Experimental Mechanics,4 (12),366–376 (1964).CrossRefGoogle Scholar
  20. 20.
    Favre, H., “Sur une Nouvelle Méthode Optique de Détermination des Tensions Interieures,”Tesis, Polytechnic Institute of Zurich, Revue Opt.,8,193,241, 289 (1929).Google Scholar
  21. 21.
    Sciammarella, C. A., Doddington, C. W., “Effect of Photographic Film Nonlinearities on the Processing of Moiré Fringe Data,”Experimental Mechanics,7 (9),398–402 (1967).CrossRefGoogle Scholar
  22. 22.
    Sciammarella, C. A. and Palacio, M., “Photoelastic Test of a Deep Beam,”Ciecia y Tecnica 113 (569) (1949).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1972

Authors and Affiliations

  • C. A. Sciammarella
    • 1
  • G. Quintanilla
    • 1
  1. 1.Dept. of Aerospace Engineering and Applied MechanicsPolytechnic Institute of BrooklynBrooklyn

Personalised recommendations