Estimating uncertainty in resolution tests

Abstract

Resolution testing of imaging optical equipment is still commonly performed using the USAF 1951 target. The limiting resolution is normally calculated from the group and element that can just be resolved by an observer. Although resolution testing has limitations, its appeal lies in the fact that it is a quick test with low complexity. Resolution uncertainty can serve as a diagnostic tool, aid in understanding observer variability, and assist in planning experiments. It may also be necessary to satisfy a customer requirement or international standard. This paper derives theoretical results for estimating resolution and calculating its uncertainty, based on observer measurements, while taking the target spatial-frequency quantization into account. It is shown that estimating the resolution by simply averaging the target spatial frequencies yields a biased estimate, and thus an improved estimator is provided. An application illustrates how the results derived can be incorporated into a larger uncertainty analysis.