Optical EngineeringUse of Mueller matrices in the photoelastic determination of the stress distribution in a model for a solid propellant rocket grain
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We introduce some basic optical rules dealing with Mueller matrices as phenomenological descriptors of optical devices. Specific simple examples illustrate how all the Stokes parameters of a beam passing through a system of several devices can be determined by the multiplication of the individual Mueller matrices of the respective system components and the Stokes vector of the incident beam. Two resulting families of interference fringes in the (visible) emerging field of the devices considered are separated from each other by the introduction of suitable additional system components. The "isochromatic" family of fringes can thus be isolated from the "isoclinic" family, and a natural application to photoelastic problems becomes evident. Thus, a second purpose is to use this technique and these fringes to photoelastically determine the stress distribution in a disk with a square perforation, when the disk is subjected to a uniformly distributed pressure, acting at its outside or at its inside periphery. This enables the visualization and quantification of the stresses developed during the burning of the grain. The size of the square hole and the radii of the fillets at the corners of the square are variables of the study. Results are given as stress concentration factors, in dimensionless form, and are of use to the designer of solid propellant rocket grains. An analogy is given to suggest another application at longer wavelengths to calibrate or discriminate between some radar signals in the microwave region.