Tools for assessing the accuracy of Monte Carlo tolerancing

Monte Carlo simulations predict an optical system’s as-built performance, such as wavefront, MTF, or focal length. High accuracy is achieved by running many cases, while a time-limited analysis runs a small number of cases at ‘reduced accuracy’. This paper investigates the relationship between accuracy and number of cases. The error for a Monte Carlo’s Cumulative Probability Distribution (CPD) at the mean, mean plus/minus one standard deviation, and mean plus/minus two standard deviations are reported. These apply to normal and non-normal distributions. In practice, the performance and error are tabularly reported. For a case in which the histogram is a Gaussian function, the CPD is an ERF function and is fully determined by the mean and standard deviation of the histogram. In most real cases, the histogram is not Gaussian and typically has a longer tail toward worse results. A similar effect appears in the CPD. In the paper, we show how the CPD is affected by the error in the mean as well as by the error in the standard deviation of the histogram, for Gaussian as well as non-Gaussian distributions.