<title>Optical heterodyne polarimeter with spatiotemporal carrier frequencies for studying dynamic photoelastic stresses</title>

Abstract

An optical heterodyne polarimeter operating with spatiotemporal carrier frequencies is presented for contour mapping of dynamic principal stress distributions in an epoxy photoelastic sample. Introducing of the spatiotemporad carrier frequencies causes the temporal and spatial resolutions to be fairly improved in the mapping of the stress distributions. The major functional scheme of the polarimeter is illustrated in Fig. 1. A circularly polarized beam of light transmitted by the loaded photoelastic sample turns into an elliptically polarized signal beam, which is photomixed with a local oscillator beam consisting of orthogonal linearly polarized two-frequency components. At every pixel of the arrayed photodetector, the elliptically polarized signal beam is decomposed into orthogonal linearly polarized components to be interfered, respectively, with the counterpart v1 and UT components of the local oscillator beam. Since both the z' and z'2' components are tilted in wavefront at different angles to the signal beam, the resultant photourrentgenerated at every pixel involves two beat-components at different spatiotemporal carrier frequencies. The two beat-components can be filtered in the spatiotemporal frequency domain to irovicle significant information for mapping the principal stress distribution. The combination of the spatial and temporal carrier frequencies is capable of broadening the bandwidths in the spatial and temporal frequency domain compared with.those using only the spatial or temporal carrier frequencies [1]. The spatial and temporal bandwidths of the present polarimeter are found to be both approximately three times as wide as those of the previously reported optical heterodyne polarimeters [2,3]. Experimental demonstration was carried out using a Mach-Zehnder type optical heterodyne interferometer. The temporal and spatial bandwidths of the MOS type arrayed photodetector were set at 1033 Hz and 10 mm1 ,respectively, and.the temporal and spatial bandwidths for filtering were set at 500 Hz and 5 mm1, respectively. Under these conditions, the temporal and spatial bandwidths were 1 ms and 0.1 mm for mapping of the stress distributions. A sample plate of epoxy with a circular hole of 1.5 mm in diameter was used for the experiment. The top and bottom ends of the plate were supported, and an increasing force was applied from the left to the hole. The contour mapped resuits of the spatiotemporal stress distributions ar shown in Fig. 2. The first trace is the azimuth x ofthe principal stress a, and the second and third traces are the magnitudes of the orthogonal principal stresses o and a, respectively. The spacing of two successive contours of the azimuth is 15°, and that of the magnitudes is 2.0 x iO N/rn2. The tensile and compressive stresses are indicated, respectively, by positive and negative signs. As can be seen froth the figure, o. is tensile at the left of the hole, whereas 0qiscompressive at the right of the hole. The gradients of the principal stresses increase with time.