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Time Average Geometric Moiré—Back to the Basics

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Abstract

Applicability of time average geometric moiré for elastic oscillating structures is analysed in this paper. Mathematical and numerical models describing the formation of time averaged fringes are carefully constructed without the assumption that dynamic deflections are described by a slowly varying function. Though time average geometric moiré is considered as a classical optical experimental technique, we show that well known relationship between the fringe order, amplitude of oscillation and pitch of the grating in state of equilibrium can be used only when the amplitude is small. Otherwise the inverse problem of fringe interpretation becomes much more complicated and is the object of analysis in this paper. We describe the interpretation of fringes produced by time average geometric moiré in detail and illustrate the complexity of the problem by numerical examples.

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References

  1. Shang H, Xie H, Wang X, Jiang S, Dai F, Wang W et al (2005) Thermal properties measurement of micro-electromechanical system sensors by digital moiré method. Strain 41:157–162. doi:10.1111/j.1475-1305.2005.00226.x.

    Article  Google Scholar 

  2. Han A (1998) Recent advancements of moiré and microscopic moiré interferometry for thermal deformation analyses of microelectronics devices. Exp Mech 38:278–288.

    Google Scholar 

  3. Sciammarella CA, Sciammarella FM, Kim T (2003) Strain measurements in the nanometer range in a particulate composite using computer-aided moiré. Exp Mech 43:341–347. doi:10.1007/BF02410533.

    Article  Google Scholar 

  4. Kobayashi AS (1993) Handbook on experimental mechanics, 2nd edn. SEM, Bethel.

    Google Scholar 

  5. Patorski K, Kujawinska M (1993) Handbook of the moiré fringe technique. Elsevier, Oxford.

    Google Scholar 

  6. Field JE, Walley SM, Proud WG, Goldrein HT, Siviour CR (2004) Review of experimental techniques for high rate deformation and shock studies. Int J Impact Eng 30:725–775. doi:10.1016/j.ijimpeng.2004.03.005.

    Article  Google Scholar 

  7. Post D, Han B, Ifju P (1997) High sensitivity moiré: experimental analysis for mechanics and materials. Springer, Berlin.

    Google Scholar 

  8. Dai FL, Wang ZY (1999) Geometric micron moiré. Opt Lasers Eng 31:191–198. doi:10.1016/S0143-8166(99)00020-2.

    Article  Google Scholar 

  9. Liang CY, Hung YY, Durelli AJ, Hovanesian JD (1979) Time-averaged moiré method for in-plane vibration analysis. J Sound Vib 62:267–275. doi:10.1016/0022-460X(79)90026-9.

    Article  Google Scholar 

  10. Lin CJ, Chiang FP (1982) Time-average in-plane moiré method for the analysis of nonsinusoidal cyclic loading. Exp Mech 22:64–68. doi:10.1007/BF02326078.

    Article  Google Scholar 

  11. Mitchell AK (2005) Optical modal analysis using white-light projected fringes. Exp Mech 45:250–258. doi:10.1007/BF02427949.

    Article  Google Scholar 

  12. Asundi A (1994) Novel techniques in reflection moiré. Exp Mech 34:230–242. doi:10.1007/BF02319760.

    Article  Google Scholar 

  13. Ragulskis M, Maskeliunas R, Ragulskis L, Turla V (2005) Investigation of dynamic displacements of lithographic rubber roller by time average geometric moiré. Opt Lasers Eng 43:951–962. doi:10.1016/j.optlaseng.2004.10.004.

    Article  Google Scholar 

  14. Sciammarella CA (2003) Overview of optical techniques that measure displacements: Murray lecture. Exp Mech 43:1–19. doi:10.1007/BF02410478.

    Article  Google Scholar 

  15. Munoz-Rodriguez JA, Rodriguez-Vera R (2004) Image encryption based on moiré pattern performed by computational algorithms. Opt Commun 236:295–301. doi:10.1016/j.optcom.2004.03.089.

    Article  Google Scholar 

  16. Sciammarella CA (1965) Basic optical law in the interpretation of moiré patterns applied to the analysis of strains—part 1. Exp Mech 5:154–160. doi:10.1007/BF02324049.

    Article  Google Scholar 

  17. Voloshin AS, Burger CP, Rowlands RE, Richard TG (1986) Fractional moiré strain analysis using digital imaging techniques. Exp Mech 26:254–258. doi:10.1007/BF02320050.

    Article  Google Scholar 

  18. Ning PT, Peng WL (1988) Automatic analysis of moiré fringe patterns by using an image-processing system. Exp Mech 28:350–354. doi:10.1007/BF02325175.

    Article  Google Scholar 

  19. Riordan J (1968) Combinatorial identities. Wiley, New York.

    MATH  Google Scholar 

  20. Watson GN (1995) A treatise on the theory of Bessel functions. Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  21. Ragulskis M, Saunoriene L (2006) Applicability of optical geometric differentiation for time average geometric moiré. Strain 42:173–179. doi:10.1111/j.1475-1305.2006.00273.x.

    Article  Google Scholar 

  22. Vest CM (1979) Holographic interferometry. Wiley, Ontario.

    Google Scholar 

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Authors and Affiliations

  1. Department of Fundamental Sciences, Kaunas University of Technology, Studentu 50-222, Kaunas, 51638, Lithuania

    M. Ragulskis (SEM Member) & Z. Navickas

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  1. M. Ragulskis
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  2. Z. Navickas
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Correspondence to M. Ragulskis.

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Ragulskis, M., Navickas, Z. Time Average Geometric Moiré—Back to the Basics. Exp Mech 49, 439–450 (2009). https://doi.org/10.1007/s11340-008-9167-8

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  • DOI: https://doi.org/10.1007/s11340-008-9167-8

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