Estimating uncertainty in resolution tests

Resolution testing of imaging optical equipment is still com- monly 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 uncer- tainty can serve as a diagnostic tool, aid in understanding observer vari- ability, and assist in planning experiments. It may also be necessary to satisfy a customer requirement or international standard. This paper de- rives theoretical results for estimating resolution and calculating its un- certainty, based on observer measurements, while taking the target spatial-frequency quantization into account. We show that estimating the resolution by simply averaging the target spatial frequencies yields a biased estimate, and we provide an improved estimator. An application illustrates how the results derived can be incorporated into a larger un-