Volume 49, number 5 OPTICS COMMUNICATIONS 1 April 1984 MULTIAPERTURE SPECKLE SHEARING ARRANGEMENTS FOR STRESS ANALYSIS D.K. SHARMA, R.S. SIROHI and M.P. KOTHIYAL Engineering Design Centre, Indian Institute of Technology, Madras 600 036, India Received 6 December 1983 Revised manuscript received 24 January 1984 The investigations are made on two, four-aperture speckle shearing arrangements designed with custom built shearing elements. The first arrangement allows the measurement of inplane displacement along with the slope and curvature requir- ed for the evaluation of bending moments. The second arrangement is specifically designed for the measurement of second order cross derivatives that are needed for the evaluation of twisting moment for flexural members. It also yields slope in- formation in two other orthogonal directions inclined at 45° to x or y directions. The main advantage of the two arrange- ments is that only two exposures are necessary and there is no shift of recording plate or repetition of loading conditions involved in the process. 1. Introduction The determination of strain, stress and bending mo- ments requires differentiation of the measured distri- bution of surface displacement. This can be convenient- ly done with the help of speckle shear interferometry. Here the wavefront from a diffuse object surface is first divided into two or more wavefronts using an op- tical arrangement and then recombined at the record- ing plane with a relative lateral displacement (shear) between them. This results in any point on the image plane receiving contributions from two or more points on the object. The first derivative of displacement or slope can be obtained once the contributions from two adjacent object points are reaching the same point on the image. Several authors [1-6] have reportedly obtained the slope information using (a) defocussing technique [1,2] and (b)use of discrete optical ele- ments for introduction of necessary shear [3,4,6]. As far as the evaluation of second derivatives is con- cerned the various techniques have been variation of the moir6 method. In one case two transparencies con- taining the same slope information are superposed and sheared in a particular direction. The resultant moir6 pattern yields the curvature in that direction [9]. In the second approach the two slope patterns are record- ed on the same photographic plate with plate being displaced in between the two recordings [5]. The meth- 0 030-4018/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) od is cumbersome in that it involves four exposures, replication of loading conditions and a displacement of the recording plate. Besides, the information extrac- tion involves a Fourier filtering stage. Recent work of Krishnamurthy et al. [7] has led to the conclusion that only three sheared fields are nec- essary for obtaining the curvature (d 2 w/dx 2) informa- tion. They obtained curvature with the help of a three segment lens. We have recently reported [8] a three aperture speckle shearing interferometer making use of two small angle wedges as shearing elements. This arrangement was shown to yield not only curvature information with a two exposure shear specklegram but also pure slope information. Here we are reporting two, four-aperture speckle shearing arrangements. The first one yields slope and curvature information and simultaneously senses any inplane displacement occuring during the experiment. The second is specifically designed for evaluation of second order cross derivatives needed for evaluating twisting moment. It however, also yields slope infor- mation in two other orthogonal directions inclined at 45 ° to x or y directions. 2. The four-aperture speckle shearing interferometer This arrangement is designed for obtaining slope 313