MULTIMERIDIONAL REFRACTION - DEPENDENCE OF THE MEASUREMENT ACCURACY ON THE NUMBER OF MERIDIANS REFRACTED

A Monte Carlo simulation of multimeridional refraction measurements wa s used to investigate the dependence of the accuracy of the measuremen t on the number of meridians refracted, N, and on the standard deviati on of a measurement in a single meridian, sigma. For the description o f the measurement errors, the residual refraction values were used, i. e., the parameters of the refraction remaining after application of th e measured correction. The distributions of the residual refraction va lues were found to be independent of the ''true'' refraction values; i n addition, by means of a factor root N/sigma, reduced residual refrac tion values could be defined which also were independent of N and sigm a. A vector space proposed by Lakshminarayanan and Varadharajan (based on Long's power matrix) was used to represent the joint distribution of the residual refraction values in three-dimensional space. It was f ound to be a three-variate Gaussian distribution with zero mean and di agonal covariance matrix. It could further be shown that the vector sp ace proposed by Harris is identical to the one used, up to a linear tr ansformation. Several criteria, based on the one- and three-dimensiona l distributions and corresponding to different levels of accuracy, are discussed resulting in a wide range of answers about the number of me ridians to be refracted.