Abstract
An instantaneous phase-stepping and subsequent phase analysis method, using a CCD camera with a form-birefringent micro-retarder array, is proposed for interferometry. An optical setup of a polarization interferometry using a Twyman-Green interferometer with two polarizers is constructed to analyze the distribution of out-of-plane displacement. Light emerging from the interferometer is recorded using a CCD camera that has micro-retarder array on the CCD plane. This micro-retarder array has four different principal directions. That is, an image obtained by the CCD camera contains four types of data corresponding to four different optical axes of the retarder. The four images separated from the image recorded by the CCD camera are reconstructed using gray-level interpolation. Then, the distributions of the Stokes parameters that represent the state of polarization are calculated from the four images. The phase distribution of the interference fringe pattern produced by the Twyman-Green interferometer is then obtained from these Stokes parameters. This method is applicable to time-dependent phenomena because multiple exposures are unnecessary for sufficient data acquisition in the completion of phase analysis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Han, B., “Thermal Stresses in Microelectronics Subassemblies: Quantitative Characterization Using Photomechanics Method,” Journal of Thermal Stresses,26(6),583–613 (2003).
McKelvie, J., “Moiré Strain Analysis: An Introduction, Review and Critique, Including Related Techniques and Future Potential,” Journal of Strain Analysis for Engineering, Design,33(2),137–151 (1998).
Gong, X.L. andToyooka, S., “Investigation Mechanism of Plastic Deformation by Digital Speckle Pattern Interferometry,” EXPERIMENTAL MECHANICS,39(1),25–29 (1999).
Pfaff, R.D., Washabaugh, P.D., andKnauss, W.G., “An Interpretation of Twyman-Green Interferograms from Static and Dynamic Fracture Experiments,” International Journal of Solids and Structures,32(6–7)939–955 (1995).
Smith, C.W. andKobayashi, A.S., “Experimental Fracture Mechanics,”Handbook on Experimental Mechanics, 2nd Edn., Kobayashi, A.S., ed., VCH Publishers, New York, 905–968 (1993).
Huntley, J.M., “Automated Fringe Pattern Analysis in Experimental Mechanics: A Review,” Journal of Strain Analysis for Engineering Design,33(2),105–125 (1998).
Malacara, D., “Methods of Interferogram Analysis,”, Trends in Optical Non-destructive Testing and Inspection, Rastogi, P.K. and Inaudi, D., eds., Elsevier, Oxford, 15–35 (2000).
Surrel, Y., “Fringe Analysis,” Photomechanics, Rastogi, P.K., ed., Springer, Berlin, 55–102 (2000).
Patil, A. andRastogi, P., “Approaches in Generalized Phase Shifting Interferometry,” Optics and Lasers in Engineering,43(3–5),475–490 (2005).
Morimoto, Y. andFujigaki, M., “Real-time Phase Distribution Analysis in Moiré”, Trends in Optical Non-destructive Testing and Inspection, Rastogi, P.K. and Inaudi, D., eds., Elsevier, Oxford, 415–432 (2000).
Fujigaki, M., Morimoto, Y., andYabe, M., “Real-time Measurement of Nanometer Displacement Distribution by Integrated Phase-shifting Method,” JSME International Journal, Series A,45(3),448–452 (2002).
Yamamoto, Y., Morimoto, Y., Fujigaki, M., and Yoneyama, S., “Two-directional Phase-shifting Moiré Interferometry and Its Application to Thermal Deformation Measurement of Electromic Device”, Proceedings of the 6th Far-East Conference on Non-Destructive Testing, Japanese Society for Non-Destructive Inspection, Tokyo, 445–450 (2002).
Yoneyama, S., Morimoto, Y., Nomura, T., Fujigaki, M. andMatsui, R., Real-time Analysis of Isochromatics and Isoclinics Using the Phaseshifting Method”, EXPERIMENTAL MECHANICS,43(1),83–89 (2003).
Yoneyama, S., Morimoto, Y., andMatsui, R., “Photoelastic Fringe Pattern Analysis by Real-time Phase-shifting Method”, Optics and Lasers in Engineering,39(1),1–13 (2003).
Smythe, R. andMoore, R., “Instantaneous Phase Measuring Interferometry,” Optical Engineering,23(4),361–364 (1984).
Koliopoulos, C.L., “Simultaneous Phase Shift Interferometer”, Advanced Optical Manufacturing and Testing II, Victor, J. and Doherty, D.V.M., eds. Proceedings of SPIE,1531,119–127 (1991).
Van Haasteren, A.J.P. andFrankena, H.J., “Real-time Displacement Measurement Using a Multicamera Phase-stepping Speckle Interferometer,” Applied Optics,33(19),4137–4142 (1994).
Ngoi, B.K.A., Venkatakrishnan, K., Sivakumar, N.R., andBo, T., “Instantaneous Phase Shifting Arrangement for Microsurface Profiling of Flat Surfaces,” Optical Communications,190(1–6),109–116 (2001).
Sivakumar, N.R., Hui, W., Venkatakrishman, K., andNgoi, B.K.A., “Large Surface Profile Measurement with Instantaneous Phase-shifting Interferometry,” Optical Engineering,42(2),367–372 (2003).
Onuma, K., Nakamura, T., andKuwashima, S., “Development of New Real-time Phase-shift Interferometry for the Investigation of Crystal Growth Kinetics,” Journal of Crystal Growth,167(1–2),387–390 (1996).
Astrakharchik-Farrimond, E., Shekunov, B.Y., York, P., Sawyer, N.B.E., Morgan, S.P., Somekh, M.G., andSee, C.W., “Dynamic Measurements in Supercritical Flow Using Instantaneous Phase-shift Interferometry,” Experiments in Fluids,33(2),307–314 (2002).
Azzam, R.M.A. andBashara, N.M., Ellipsometry and Polarized Light, Elsevier, Amsterdam (1977).
Barter, J.D., Thompson, H.R. Jr., andChristine, L.R., “Visible-regime Polarimetric Imager: A Fully Polarimetric Real-time Imaging System,” Applied Optics,42(9),1620–1628 (2003).
Kikuta, H., Toyota, H., andYu, W., “Optical Elements with Subwavelength Structured Surfaces,” Optical Review,10(2),63–73 (2003).
Kikuta, H., Haccho, H., Iwata, K., Hamamoto, T., Toyota, H., andYotsuya, T., “Real-time Polarimeter with a Form-birefringent Micro Retarder Array,” Optical Engineering for Sensing and Nanotechnology, Iwata, K., ed., Proceedings of SPIE4416,19–22 (2001).
Gonzaler, R.C. andWoods, R.E., Digital Image Processing, 2nd Edn., Prentice-Hall, Englewood Cliffs, NJ (2002).
Theocaris, P.S. andGdoutos, E.E., Matrix Theory of Photoelasticity, Springer, New York (1979).
Sabatke, D.S., Descour, M.R., Dereniak, E.L., Sweatt, W.G., Kemme, S.A., andPhipps, G.S., “Optimization of Retardance for a Complete Stokes Polarimeter,” Optics Letters,25(11),802–804 (2000).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yoneyama, S., Kikuta, H. & Moriwaki, K. Instantaneous phase-stepping interferometry using polarization imaging with a micro-retarder array. Experimental Mechanics 45, 451–456 (2005). https://doi.org/10.1007/BF02427994
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02427994