Abstract
The paper focuses on the moiré phenomenon as a tool of experimental mechanics.
The properties of moiré patterns are outlined. The application of these properties to the measurement of displacements of the points of a surface (intrinsic moiré), contours or deflections (projection moiré) and slopes (reflection moiré) is discussed. Observation methods, recording methods, data-processing techniques are outlined and practical aspects are stressed. Sensitivities and precisions that have been achieved are reviewed. Finally, some typical applications to problems in areas of interest are briefly described.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- a :
-
stereoscopic parallax measured in contour moiré technique
- d :
-
distance between grating and recording film
- I o ,I n :
-
background intensity andnth order harmonic component of transmitted intensity (n=1,2,3…)
- I(x), I(x,y) :
-
transmitted light intensity atx or (x,y) respectively
- ℓ/in., ℓ/mm:
-
lines per inch or lines per millimeter
- t :
-
gap introduced between two gratings
- u, v, w :
-
relative displacement measured alongx, y, z directions
- x :
-
coordinate of observed point
- X 1p ,X 2p :
-
horizontal projection at illumination and observation points in contour moiré technique
- Δx, Δy :
-
shift introduced to the plate inx andy directions
- Z :
-
distance between master grating and recording lens
- ΔZ :
-
distance between master and model gratings
- λ:
-
wavelength of light used
- α:
-
ratio of transparent rule width to the pitch of grating
- ϕ i , ϕ o :
-
angle subtended by illumination and observation directions in shadow-moiré techniques
- θ:
-
change of angle between initial and final positions in reflection-moiré techniques
- θ i , θ n :
-
angle of diffraction orderi andn
- ψ x , ψ y :
-
continuous fringe orders of the relative displacements inx andy directions
References
Sciammarella, C.A., Ross, B.E. andSturgeon, D., “Basic Optical Law In The Interpretation of Moiré Patterns Applied to the Analysis of Strains,” Parts 1 and 2,Experimental Mechanics,5 (5, 6),154–166 (1965).
Sciammarella, C.A., “Use of Gratings in Strain Analysis,”J. Physics E: Scientific Instruments,5,833–845 (1972).
Durelli, A.M., Sciammarella, C.A. andParks, V.J., “Interpretation of Moiré Patterns,”Proc. of the ASCE, J. Eng. Mech. Div.,89 (EM2)Part 1,71–88 (1963).
Sciammarella, C.A. andDurelli, A.J., “Moiré Fringes as a Means of Analyzing Strains,”Proc. of the ASCE, J. Eng. Mech. Div.,87 (EM1),51–74 (1961).
Chiang, F.P., “Determination of Signs in Moiré Method,”Proc. of the ASCE, J. Eng. Mech. Div.,95 (EM6),1379–1391 (1969).
Sciammarella, C.A. andDavis, D., “Gap Effect in Moiré Fringes Observed with Collimated Monochromatic Light,”Experimental Mechanics,8 (10),459–466 (1968).
Burch, J.M., “Photographic Production of Scales for Moiré Fringes Applications,”Brussels Colloquium On Optics in Metrology, London, Pergamon Press, 2–7 (May1958).
Burch, J.M. andPalmer, D.A., “Interferometric Methods For Photographic Production of Large Gratings,”Optica Acta,8,73–80 (1971).
Marchant, M. andBishop, S.M., “An Interference Technique For The Measurement of In-Plane Displacements of Opaque Surfaces,”J. Strain Analysis,9 (1),36–43 (1974).
Walker, C.A. andMcKelvíe, G., “A Practical Multiplied-moiré System,”Experimental Mechanics,10 (8),316–320 (Aug.1978).
Sciammarella, C.A. andSturgeon, D.S., “Thermal Stresses At High Temperatures In Stainless-steel Rings By the Moiré Method,”Experimental Mechanics,6 (5),235–243 (1966).
Holister, G.S. andLuxmoore, H.R., “The Production of High Density Moiré Grids,”Experimental Mechanics,8 (5),210–216 (May1968).
DeCaluwé, N., “Etching Moiré Test Grids in Steel,” Strain, 135–139 (July 1974).
Sciammarella, C.A. andChiang, F.P., “Gap Effect on Moiré Patterns,”Zeitschrift für Angewandte Mathematik und Physik,19,326–333 (1968).
Luxmoore, H.R., “The Moiré Effect Applied to Experimental Stress Analysis,”Strain,5 (3),164–170 (July1969).
Holister, G.S. andWatts, D. “Telecentric Systems For Moiré Analysis,”Experimental Mechanics,10 (1),31–38 (1970).
Kawakita, T., Shirota, Y. andMiyamoto, H., “Unique Application of the New Three-Dimensional Moiré Fringe Technique For Transient Analysis of High Speed Deformations,”Mech. Behavior of Matls., Proc. of the Inter. Conf. of Mech. Behaviour of Matls., Kyoto, Japan, 1971, The Soc. of Matls. Sci.,5,325–342 (1972).
Dechaene, R., DeCock, J. and DeCaluwé, N., “Measurement of Thermal Strains,” Rpt. of the Laboratorium voor Weerstand Van Materialen, Univ. of Ghents (1969).
Sciammarella, C.A., “Theoretical and Experimental Study on Moiré Fringes,” PhD Thesis, Ill. Instit. of Tech. (June 1960).
Theocaris, P.S., “The Moiré Method in Thermal Fields,”Experimental Mechanics,4 (8),223–231 (1964).
Sciammarella, C.A. and Sturgeon, D., “Substantial Improvement in the Processing of Moiré Data by Optical and Digital Filtering,” Proc. of the 3rd Inter. Cong. of Exper. Stress Analysis, West Berlin, 79–83 (1966).
Burch, J.M. andForno, C., “A High Sensitivity Moiré Grid Technique For Studying Deformations In Large Objects,”Optical Engrg.,14 (2),178–185 (1975).
Idesawa, M., Yagatai, T. andSoma, T., “Scanning Moiré Method and Automatic Measurement of 3-D Shapes,”Appl. Optics,16 (8),2152–2162 (1977).
Yokozeki, S. andMihira, S., “Moiré Interferometry,”Applied Optics,18 (8),1275–1280 (1979).
Sciammarella, C.A. and Lurowist, N., “Multiplication and Interpolation of Moiré Fringe Orders by Purely Optical Techniques,” Proc. of the 5th U.S. Natl. Cong. of Appl. Mech., June 1966, J. Appl. Mech., 425–430 (June 1967).
Holister, G.S., “Moiré Method of Surface Strain Measurement,” The Engineer, 149–152 (Jan. 1967).
Sciammarella, C.A., “Moiré-fringe Multiplication by Means of Filtering and Wave-reconstruction Process,”Experimental Mechanics,9 (4),179–185 (1969).
Guild, J., “The Interference Systems of Crossed Diffraction Gratings,” Oxford at the Clarendon Press (1956).
Post, D., “Analysis of Moiré Fringe Multiplication Phenomena,”Appl. Optics,6 (11),1938–1942 (1967).
Post, D., “New Optical Methods of Moiré-fringe Multiplication,”Experimental Mechanics,8 (2),63–68 (1968).
Post, D., “Moiré Fringe Multiplication With Non-Homogeneous Strain Fields,” JBCSA Conf., Recent Advances in Stress Analysis, 6.16–6.18, Roy. Aeronaut. Soc. (1969).
Sciammarella, C.A., DiChirico, G. and Chang, T.Y., “Moiré-holographic Technique For Three-Dimensional Analysis,” Proc. of the 12th Inter. Cong. of Appl. Mech., Aug.–Sept. 1968, J. Appl. Mech., 180–185 (March 1970).
Dantu, P., “Applications Rhéologiques de La Méthode des Réseaux,” Laboratoire Central des Ponts et Chausées (61.5) (1961).
Chiang, F.P., “A Method to Increase the Accuracy of the Moiré Method,”J. Eng. Mech. Div., Proc. of the ASCE,91 (EMI),137–149 (1965).
Sciammarella, C.A., “Elimination of the Effect of Lens Aberrations in Moiré Patterns Produced by Optically Projecting the Master Grid on the Model Grid,” J. Appl. Mech., 1038–1040 (Dec. 1967).
Sciammarella, C.A. andChiang, F.P., “Dynamical Stresses and Strains in Propellant Grains,”Proc. of the 6th Mig. of the Mech. Working Group, CPIA,1 (158),219–232 (Oct.1967).
Boone, P. andVan Beeck, W., “Moiré Fringe Multiplication Using a Spatially Filltered Projection System,”Strain,6,14–21 (1970).
Dantu, P., “Utilization des Réseaux Pour L'Etude des Déformations,”Laboratoire Central des Ponts et Chausees (57-6),26–47 (1957).
Parks, V.J. andDurelli, A.J., “Moiré Patterns of the Partial Derivatives of the Displacement Components,”J. Appl. Mech., Trans. of the ASME,33 Series E (4),901–906 (1966).
Sciammarella, C.A. andChang, T.Y., “Optical Differentiation of Displacement Patterns Using Shearing Interferometry by Wavefront Reconstruction,”Experimental Mechanics,11 (3),97–104 (1971).
Sciammarella, C.A. and Nyuko, H., “Determination of Strains by Applying Holographic Shearing Interferometry to Techniques That Provide Displacement Information,” Progress in Experimental Mechanics, Durelli Anniv. Vol., The Catholic University of America, 1–9 (May 1975).
Brutti, C., DiChirico, G. and Pighini, U., “Optical Differentiation of Moiré-Holographic Fringes by Wavefront Reconstruction With White Light Sources,” 1st European Cong. on Optics Appl. to Metrology, Paper 136-56, Strasbourg (Oct. 1977).
Sciammarella, C.A., “Technique of Fringe Interpolation in Moiré Patterns,”Experimental Mechanics,7 (11),19A-30A (1967).
Sciammarella, C.A. andSturgeon, D., “Digital Filtering Techniques Applied to the Interpolation of Moiré-fringe Data,”Experimental Mechanics,7 (11),468–475 (1967).
Sciammarella, C.A., andDoddington, C.W., “Effect of Photographic-film Nonlinearities on the Processing of Moiré-fringe Data,”Experimental Mechanics,7 (9),398–402 (1967).
Sciammarella, C.A., “A Numerical Technique of Data Retrieval From Moiré or Photoelastic Patterns,”Proc. SPIE, Seminar in Depth Pattern Recognition Studies,18,91–101 (1969).
Sciammarella, C.A. and Rowlands, E., “Numerical and Analog Techniques to Retrieve and Process Fringe Information,” Proc. of the 5th Inter. Conf. on Exper. Stress Analysis, Udine, Italy, 1.43–1.52 (1974).
Berghaus, D.G. andCannon, J.P., “Obtaining Derivatives From Experimental Data Using Smoothed Spline Functions,”Experimental Mechanics,13 (1),38–42 (1973).
Olson, D.L., “A Photomechanics System for Non-Destructive Three-Dimensional Stress Analysis,”PhD Thesis, Dept. of Agr. Engrg., Iowa State Univ., Ames, IA (1970).
Rowlands, R.E., Liber, T., Daniel, I.M. andRose, P.G., “Higher-order Numerical Differentiation of Experimental Information,”Experimental Mechanics,13 (3),105–113 (1973).
Bossaert, W., Dechaene, R. andVinckier, A., “Computation of Finite Strains From Moiré Displacement Patterns,”J. Strain Analysis,3 (1),65–75 (1968).
Ohta, A., Kosuge, M. andLasaki, E., “Measurement of Strain Distribution by the Moiré Fringe Multiplication Method at a Tip of Propagating Fatigue Crack,”Inter. J. of Fract.,13 (3),289–300 (1977).
Mulot, M., “Application of the Moiré to the Study of Mica Deformations,”Rev. D'Optique,4,252–259 (May1925).
Weller, R. andShephard, B.M., “Displacement Measurement by Mechanical Interferometry,”Proc. of the SESA,6 (1),35–38 (1948).
Kaezer, J. andKroupa, F., “The Determination of Strains by Mechanical Interference,”Czech. J. of Appl. Physics,1 (2),80–85 (1952).
Theocaris, P.S., “Moiré Method in Plates,” Non-Classical Shell Problems, Proc. of the IASS Symp., Warsaw, 877–889 (1964).
Pirodda, L., “Principi e Applicazione di un Metodo Fotogrammetrico Basatto Sull'impiego del Moiré,”Rivista di Ingegneria, (12),1–12 (1969).
Meadows, D.M., Johnson, W.O. andAllen, T.B., “Generation of Surface Contours by Moiré Patterns,”Appl. Optics,9 (4),942–947 (1970).
Takasaki, A., “Moiré Topology,”Appl. Optics,9 (6),1457–1472 (1970).
Chiang, C., “Moiré Patterns From the Surface and Their Application In Measuring Topography,”Brit. J. Appl. Physics (J. Phys D), Series 2,2,287–292 (1969).
Chiang, C., “Moiré Topography,”Appl. Optics,14 (1),177–179 (1975).
Heiniger, F. andTschudi, T., “Moiré Depth Contouring,”Appl. Optics,8 (10),1577–1581 (1979).
Roger, R., “Moiré Contouring—A re-Interpretation,” Univ. of Oxford, Dept. of Engrg. Sci., OUL Rpt., (1294) (1979).
Browne, A.L., “Fluid Film Thickness Measurement With Moiré Fringes,”Appl. Optics,11 (10),2269–2277 (1972).
Hovanesian, J.D. andHung, Y.Y., “Moiré Contour-Sum Contour-Difference and Vibration Analysis of Objects,”Appl. Optics,10 (12),2734–2738 (1971).
Perrin, J.C. andThomas, A., “Electronic Processing of Moiré Fringes: Application to Moiré Topography and Comparison With Photogrammetry,”Appl. Optics,18 (4),563–574 (1979).
Benoit, P., Mathieu, E., Hornière, J. andThomas, A., “Characterization and Control of Three Dimensional Objects Using Fringe Projection Techniques,”Nouvelle Review d'Optique,6 (2),65–73 (1975).
Pirodda, L., “Dimensional Metrology of Large Objects by Projection Moiré Techniques,” 1st European Cong. on Optics Appl. to Metrology,” Paper 136-60, Strasbourg (Oct. 1977).
Dessus, B. andLeBlanc, M., “Fringe Method and its Application to the Measurement of Deformations, Vibrations Contour Lines and Differences of Objects,”Opto. Electronics,5 (5),369–391 (Sept.1973).
Murakami, K. andMurakami, Y., “A Study of the Moiré Topography (An Accurate Theory and the Applicable Limit of the Divergent Light Ray Method),”Bul. of the JSME,21 (155),788–792 (1978).
Wasowski, J.J., “Moiré Surface Contouring by Addition Method,” Proc. of the 6th Inter. Conf. on Exper. Stress Analysis, Munich, 127–134 (1978).
Takasaki, H., “Moiré Topography,”Appl. Optics,12 (4),845–850 (April1973).
Keck, V.G., Windischbauer, G. andRanninger, G., “Ermittlung Von Mabzahlen Biologischer Objekte Mit Moiré-Topographie,”Optik,37 (3),310–315 (1973).
Murakami, K. andMurakami, Y., “A Study of the Moiré Topography. A Method for Discriminating Between the Concave and Convex Regions of an Object,”Bul. of the JSME,21 (152),196–202 (1978).
Livnat, A., Kapi, O. andErez, G., “Hills And Valleys In Optical Mapping and Its Application to Moiré Contouring,”Appl. Optics,19 (19),3396–3401 (1980).
Takasaki, H., “Moiré Topography Systems and Applications,” Handbook of Non-Topographic Photogrammetry, Amer. Soc. of Photogrammetry, 167–184 (1979).
Chiang, F.P., “A Shadow Moiré Method With Two Discrete Sensitivities,”Experimental Mechanics,15 (10),382–385 (1975).
Sciammarella, C.A., “Analysis of the Vibration of Plates by Means of the Moiré Method,” Metodi ed Applicazioni Dell'Analesi Sperimentale Delle Tensioni, Atti Del lo Convegno Nationale AIAS, Palermo, Italy, 15–21 (1972).
Hung, Y.Y., Liang, C.Y., Hovanesian, J.D. andDurelli, A.J., “Time-Averaged Shadow Moiré Method for Studying Vibrations,”Appl. Optics,16 (6),1717–1719 (1977).
Motycka, J., “A Grazing-incidence Moiré Interferometer For Displacement and Planeness Measurement,”Experimental Mechanics,15 (7),279–281 (1975).
Varner, J.R., “Holographic and Moiré Surface Contouring,” Holographic Non-Destructive Testing, Academic Press, 105–147 (1974).
Miles, C.A. andSpeight, B.S., “Recording the Shape of Animals by the Moiré Method,”J. of Physics E: Scientific Instruments,8,773–776 (1975).
Eppes, T.A., “Application of Moiré Techniques to Pictureless Gaging,” Tech. Spin Off Rpt., Contract AT (29-1)-613, U.S. Atomic Energy Commission (1975).
Ligtenberg, F.K., “Aver Een Methode Om Door Een Eenvoding Experiment de Momente in Styeve Platen te Palen,”Ingenieur (9),42–46 (1952).
Ligtenberg, F.K., “The Moiré Method, A New Experimental Method For the Determination of Moments in Small Slab Models,”Proc. of the SESA,12 (2),83–98 (1955).
Reider, G. andRitter, R., “Krummungsmessung an Beiasteten Platten nach dem Ligtenbergschen Moiré Verfaheren,”Forsch. Ing. Wes. Bd. 31 (3),33–34 (1965).
Bouwkamp, J.G., “The Moiré Method and the Evaluation of Principal Moments and Stress Directions,”Experimental Mechanics,4 (4),121–128 (1964).
Theocaris, P.S., “Moiré Patterns of Slope Contours in Flexed Plates,”Experimental Mechanics,6 (4),212–217 (1966).
Theocaris, P.S., “Slope Measurement by Means of Moiré Fringes,”J. Sci. Instr.,42,607–610 (1965).
Heise, U., “A Moiré Method For Measuring Plate Curvature,”Experimental Mechanics,7 (1),47–48 (1967).
Chiang, F.P. andJaisingh, G., “A New Optical System For Moiré Methods,Experimental Mechanics,14 (11),459–462 (1974).
Ritter, R. andHerbst, M., “Ein Optisches System Zur Aufnahme von Verformungsgrossen Dynamisch Belasteter Platten,”Forsch. Eng. Wes.,42 (3),82–85 (1976).
Ritter, R. andGonska, W., “Experimentelle Bestimmung der Krummungs Grossen Dynamisch Belasteter Platten Nach der Moiré Prinzip,”Forsch., Eng. Wes.,43 (5),141–145 (1977).
Pedretti, M., “Nouvelle Méthode de Moiré Pour L'Analyse Des Plaques Flechies,” Doctoral Thesis, Ecole Polytechnique Federale de Lausanne (1974).
Ranganayakamma, B. andChiang, F.P., “Mismatches Applied to Ligtenberg's Reflective Moiré Methods,”J. of Strain Analysis,8 (1),24–29 (1973).
Duncan, J.P., “The Optical Survey of Curve Surfaces,” Rpt.—Dept. of Mech. Engrg., The Univ. of Brit. Columbia (1966).
Osgerby, C., “Application of the Moiré Method for Use with Cylindrical Surfaces,”Experimental Mechanics,7 (7),313–320 (1967).
Sciammarella, C.A. andDurelli, A.J., “Elasto-Plastic Stress and Strain Distribution in a Finite Plate With a Circular Hole Subjected to Unidimensional Load,”J. of Appl. Mech.,30 (1),115–121 (1963).
Theocaris, P.S., “The Moiré Method in Thermal Fields,”Experimental Mechanics,4 (8),223–231 (1964).
Theocaris, P.S. andHazell, C.R., “Experimental Investigation of Subsequent Yield Surfaces Using the Moiré Method,”J. Mech. Phys. Solids,13,281–294 (1965).
Ullmann, K., “Anwendung des Moireefektes Zur Experimentellen Dehnungsanalyse,”Beiträge Zur Spannungsund Dehnungsanalyse, Berlin, Akademie-Verlag (1970).
Sampson, R.C. andCampbell, D.M., “The Grid Shift Technique For Moiré Analysis of Strain in Solid Propellants,”Experimental Mechanics,7 (11),449–457 (1967).
Theocaris, P.S. andHadjijoseph, Chr., “Transient Lateral Contraction Ratio of Polymers in Creep and Relaxation,”Kolloid-Zeitschrift Zeitschrift Für Polymere,202 (2),133–139 (1965).
Cloud, G., Radke, R. andPeiffer, J., “Moiré Gratings For High Temperatures and Long Times,”Experimental Mechanics,19 (10),19N-21N (1979).
Sciammarella, C.A. andRao, M.P.K., “Failure Analysis of Stainless Steel at Elevated Temperatures,”Experimental Mechanics,19 (11),389–398 (1979).
Liu, H.W. and Ke, J.S., “Moiré Method,” Experimental Techniques in Fracture Mechanics, ed. by A.S. Kobayashi,2,SESA, 111–165 (1975).
Armenakas, A.E. andSciammarella, C.A., “Experimental Investigation of the Failure Mechanism of Fiber-reinforced Composites Subjected to Uniaxial Tension,”Experimental Mechanics,13 (2),49–58 (1973).
Armenakas, A.E. andSciammarella, C.A., “Response of Glass-fiber-reinforced Epoxy Specimens at High Rates of Tensile Loading,”Experimental Mechanics,13 (10),433–440 (1973).
Daniel, I.M., Rowlands, R.E. andPost, D., “Moiré Methods for Strain Analysis of Composites,”Experimental Mechanics,13 (6),246–252 (1973).
Dykes, B.C., “Analysis of Displacements in Large Plates by the Grid-Shadow Moiré Technique,” Experimental Stress Analysis and its Influence on Design, Proc. of the 4th Inter. Conf. on Exper. Stress Analysis, Cambridge (1970).
Beynet, P. andPlunkett, R., “Plate Impact and Plastic Deformation by Projectiles,”Experimental Mechanics,11 (2),64–73 (1971).
Takasaki, H., “Moiré Topography,” Proc. of the ISP Biostereometrics, 74 Symp. (1974).
Padlog, T. andGallagher, H., “Measurement of Angular Displacements of Practical Wing Structures by the Moiré Fringe Technique,”Tech. Rpt. No. FDL TDR 64 92, AF Flight Dynamics Lab., Wright-Patterson AFB (1964).
Laermann, K.H., “On the Experimental Analysis of Plates With Large Deflections Including Plates on Yielding Subgrade,” Proc. of the IUTAM Symp. on “Optical Methods in Mechanics of Solids,” ed. by A. Lagarde, Sijthoff and Noordhoff, 187–193 (1981).
Chiang, F.P. andJaising, G., “Dynamic Moiré Method For the Bending of Plates,”Experimental Mechanics 13 (11),459–462 (1974).
Schiewiger, H. andStreubel, R., “Die Vermungsanalyse Schalagartig Belasteter Glasplatten Mit Hilfe des Moireverfahrens,”Forch. Ing. Wess.,44 (6),169–176 (1978).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sciammarella, C.A. The moiré method—A review. Experimental Mechanics 22, 418–433 (1982). https://doi.org/10.1007/BF02326823
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02326823