Slope and curvature measurement by a double-frequency-grating shearing interferometer
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This paper describes a shearing interferometer capable of the direct measurement of the slopes and curvatures of reflecting plates. The wavefront shear is produced by a double-frequency grating which is simply a grating containing two closely spaced frequencies. The first-order waves associated with each frequency form the interferogram, the contours of which are related to the model's slope or curvature depending upon system arrangement and recording procedure.
Four arrangements are described: two for slope and two for curvature. In one, the slope contours are obtained directly and in real time. In the second slope arrangement, an extra spatial-filtering step is necessary to obtain the slope contours. However, this arrangement, as opposed to the first, measures the slope only due to the loading, compensating for initial model slope and optical-system aberrations.
The two curvature techniques can be described as double-shearing interferometers having a primary and secondary shear. The primary shear for both arrangements is provided by the double-frequency grating. In one technique, the secondary shear is provided by a translation of the recording film between two exposures during the recording step. A subsequent spatialfiltering step displays the curvature fringes. The second technique requires only a single exposure and places a beam splitter at the location of one of the first-order diffraction spectra during the filtering step. The field equations defining the fringe values are derived for all four arrangements with experimental results also being given.
- Baruch, M., “Integral Equations for Nondestructive Determination of Buckling Loads of Elastic Plates and Bars,”Israel J. of Tech.,11 (1–2),1–8 (1973).
- Ligtenberg, F.K., “The Moiré Method: A New Experimental Method for the Determination of Moments in Small Slab Models,”Proc. SESA 12 (2),83–98 (1954).
- Duncan, J.P. andBrown, C.J.E., “Slope Contours in Flexed Elastic Plates by the Salet-Ikeda Technique,”Proc. of First Int. Cong. on Exp. Mech., Editor B.E. Rossi, Pergamon Press, New York, 149–176 (1963).
- Theocaris, P.S. andKoutsambessis, A., “The Multisource and the Slit Source and Grating Methods for Recording Slope Contours in Plates,”Acta Technika Czech.,18 (6,176–184 (1967).
- Boone, P.M., “Determination of Slope and Strain Contours by Double-exposure Shearing Interferometry,”Experimental Mechanics,15 (8),295–302 (1975).
- Saito, H., Yamaguchi, I. andHachimine, K., “An Application of Holographic Interferometry to Stress Analysis of Elastic Bending Plate,”Scientific Papers of Inst. of Phys. and Chem. Res.,64 (4),104–111 (1970).
- Hung, Y.Y. andTaylor, C.E., “Measurement of Slopes of Structural Deflections by Speckle-shearing Interferometry,”Experimental Mechanics,14 (7),281–285 (1974). CrossRef
- Assa, A., Betser, A.A. andPolitch, J., “The Recording of Slope and Curvature Contours of Flexed Plates Using a Grating Shearing Interferometer,”Applied Optics,16 (9),2504–2513 (1977).
- Assa, A., “Some New Optical Methods for Use in Experimental Stress Analysis,” D.Sc. Thesis, Dept. of Aeronautical Engineering, Technion, Israel Institute of Technology (1975).
- Duncan, J.P. andSabin, P.G., “Determination of Curvatures in Flexed Elastic Plates by the Martinelli-Ronchi Technique,”Experimental Mechanics,3 (12),285–293 (1963).
- Stetson, K., “Moiré Method for Determining Bending Moments from Hologram Interferometry,”Optics Tech.,2 (2),80–84 (1970). CrossRef
- Chiang, F.P. andBailangadi, M., “A Method for Direct Determination of Small Curvatures,”Trans. ASME, Series E, J. Appl. Mech.,42 (1),29–31 (1975).
- Heise, V., “A Moiré Method for Measuring Plate Curvatures,”Experimental Mechanics,7 (1),47–48 (1967).
- Wyant, J.C., “Double Frequency Grating Lateral Shear Interferometer,”Applied Optics,12 (9),2057–2060 (1973).
- Francon, M. andMallick, S., “Polarization Interferometers,”John Wiley and Sons, New York (1971).
- Slope and curvature measurement by a double-frequency-grating shearing interferometer
Volume 19, Issue 4 , pp 129-137
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- 1. General Electric Co., 12345, Schenectady, NY
- 2. Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel
- 3. Department of Aeronautical Engineering, Technion, Israel Institute of Technology, Haifa, Israel