Stochastic Perturbation Model for Optimal Position Transfer Characteristic

An analytic model describing the transfer properties of a discrete photosensitive element position detection system is developed. Improvement of the inherently nonlinear transfer characteristic is shown to be possible when the target is subject to perturbation in the form of Gaussian noise. Applying a spline function approximation approach, relationship between the element threshold, noise variance, and element displacement are obtained which achieve the best (Chebyschev) approximation to an ideal (linear) transfer characteristic. Effective smoothing is shown to be obtainable for relatively small noise variance.