Inverse analysis for the recovery of forces applied to photoelastic tactile transducers

Abstract

In this paper, the forward and inverse analyses of one‐ and two‐layer photoelastic tactile transducers are presented. For such transducers, an applied force profile generates stresses in the photoelastic layer, making it birefringent. Consequently, circularly polarized light input to the transducer becomes elliptically polarized at the output because of the introduction of a phase‐lead distribution. Herein, the forward and inverse analyses of a one‐layer photoelastic tactile transducer, under ideal conditions, are first presented. The transducer is modeled using closed form equations based on the theories of elasticity and photoelasticity, which allow the calculation of the light intensity distribution corresponding to an applied force profile. However, to recover the force profile from a light intensity distribution (i.e., the inverse problem), the phase‐lead distribution must be determined first. A novel technique is described for this purpose. In the second part of the paper, we consider the forward and inverse analyses of a two‐layer transducer, under nonideal conditions, where the light‐intensity distribution is no longer noise‐free. In the forward analysis, the calculation of the stress distribution in the transducer is implemented by finite‐element analysis. The recovery of the phase‐lead distribution under noisy conditions, however, constitutes an ill‐posed inverse problem. A novel algorithm that accurately and effectively determines the phase‐lead distribution from a noisy light‐intensity distribution is presented. © 1998 John Wiley & Sons, Inc.