Nonlinear programming is used to design a non-contact high resolution optical system capable of sensing all six degrees of freedom of an object. This system uses two wide-beam lasers to illuminate two reflective fiducial markers placed on the object's surface. Light rays reflected from these markers are incident on three position sensitive detectors, which measure the x-y coordinates of the centroids of the incident light spots. The mathematical model of the system, which maps object coordinates into light spot coordinates, is very complex and highly nonlinear. The purpose of the study is to find designs that optimize three objectives: linearity error, range, and sensitivity, both singly and in combination, and to gain insight into the design tradeoffs among them. The design variables include the angular orientation of the laser beams, the positions of each of the fiducial markers, and the distance between sensor and object planes. Analysis of the model shows how these variables must be changed to improve each objective. Computational results obtained using a generalized reduced gradient (GRG) algorithm show how geometric constraints on system area and component overlap limit the attainment of each objective. Tradeoff studies show the strong tradeoffs among these objectives, and indicate that the most important design variables are the orientations of the light sources. The methodology shows great promise for reducing the development time of sensors with specific requirements, and for improving sensor performance.
