An Inverse-Analysis Method for the Recovery of Applied Forces on a Photoelastic Transducer

In this paper, a novel tactile photoelastic transducer for normal forces is presented. When a normal input force profile is applied to the transduction medium, stress is generated in the photoelastic layer making it birefringent. Consequently, circularly-polarized input light becomes elliptically polarized at the output due to the introduction of a phase-lead distribution. If a circular-reflection polaridoscope is used, the output light-intensity is a circular function of the total phaselead distribution. The first part of the paper describes the forward analysis of the transducer using finite-element analysis to determine the stress distribution in the transducer. Then, the phase-lead distribution is determined using the theory of photoelasticity. The second part of the paper describes a technique for the recovery of the phase-lead distribution from the ideal noise-free light-intensity distribution. Also, a verification method is proposed to determine whether a recovered phase-lead distribution is the correct one or not. In the third part of the paper, we consider the non-ideal situation, where the light-intensity distribution is no longer noise-free. Quantization errors added to the detected light-intensity distribution are also considered. Recovering the phaselead distribution under noisy conditions constitutes an ill-posed inverse problem. An algorithm that accurately and effectively determines the phase-lead distribution from a noisy light-intensity distribution is presented. The inverse-tactile problem is solved using an optimization function.