Optical Noncontact Dual-Angle Linear Displacement Measurements of Large Structures by P.L. Fuhr, D. Huston, J.G. Beliveau, P.J. Kajenski and W.B. Spillman ABSTRACT--An optical technique has been developed whereby two angles and linear displacement can be simul- taneously measured in a noncontact fashion. The method depends upon the properties of diffraction gratings with linear variation of period along their length and photodetection using CCD arrays. The grating is attached to a structure at a point of interest while all other system components are placed at a remote location. Experimental results obtained using this technique are presented and compared with theory. Introduction In order to be able to properly characterize the static and dynamic properties of large structures, one often wishes to measure the structural deformation under constant load conditions and the structural damping characteristics following impulse loading. Over many years considerable work dealing with different ways to measure structural parameters has been reported in the literature; J-~ most of these efforts have involved developing methods to measure single structural parameters. Ideally, a single-measurement technique would provide measure- ment information pertaining to a number of structural parameters, and could provide these multiple measurands simultaneously. In particular, knowledge of the linear displacement of the structure dtle to loading is of para- mount importance, along with the ability to distinguish such displacement from the rotary displacements caused by torsional twisting and total beam flexing, both of which may be occurring at the same time. In addition, certain modal-modification algorithms require the simul- taneous measurement of displacement and rotation at a point? Accelerometers, which are generally used to deter- mine dynamic response of structures, cannot, by a single measurement, determine separate linear and rotary displacements. While an analogous fiber-optic technique for measur- ing only linear displacement has been described in the literature, 7 we have extended that work by developing a simple noncontact optical method whereby such separa- P.L. Fuhr and D. Huston are Assistant Professors, J.-G. Befiveau is Professor and P. Kajenski is Graduate Student, College of Engineering and Mathematics, University of Vermont, Burlington, l i t 05405. W.B. Spillman is Research Head, Simmonds Precision, Aircraft Systems Division, Vergennes, leT 05491. Original manuscript submitted: July 1990. Final manuscript received: February 2L 1991. tion can be achieved. Such separation allows simultaneous measurement of linear displacement and dual angular rotary displacement. The measurement system com- ponents are simply a laser, a variable period grating attached to the structure of interest, and some mechanism (mechanical or optical) for determining the angles of the various diffracted orders, configured as shown in Fig. 1. Data obtained with this system can be used to calculate all three displacements in a straightforward manner, In this paper, the basic implementation of reflective chirped grating sensors for displacement measurements is des- cribed. A simple theoretical analysis of the concept is provided and experimental results are presented and discussed. Theory When illuminated by a collimated beam of light of narrowband wavelength X at a constant angle, O~, the diffraction of light from a traditional constant-spacing reflection grating with alternating reflective and absorbing stripes depends upon the grating period, d (the center to center separation between reflective stripes), and the collection angle, 0,,, as shown in Fig. 2, i.e., d (sin 0,- sin 0m) = mX (1) where all angles are measured in the plane containing the incident angle and the normal to the grating. The quantity m is the order of the diffraction and is an integer. The grating stripes are normal to this plane of incidence. The reference axis is normal to the plane of the grating and its origin is at the grating. The angle of incidence is always taken as positive and the sign of the diffraction angle is also positive when the diffracted beam is on the same side of the reference axis as the incident beam, negative when on the other side. Linear Displacement 'Chirped' diffraction gratings differ from traditional gratings by having the grating period, d, increase linearly across the diffraction grating. Thus, at any position y ', along the grating, the grating period d is given by the 'chirping equation' d - do +dl y '; y' can be inferred from a knowledge of d by use of eq (1): mX do y'= --- (2) dl (sin 0..- sin 0~) d, Experimental Mechanics * 185