Aiming to understand the ultimate limit of the measuring uncertainty of optical instruments, and the origins of these limits, we found that virtually all limits come as uncertainty products. Nature never give presents. But these uncertainty products offer to bargain with nature: by sacrificing some knowledge about one parameter, we increase our knowledge about another parameter. this is not just theoretical consideration: there is a wide range of opportunities.
It is emphasized that it is not only physics which brings limits. Limits and products of limits are as well introduced via information theory.
Exploring and exploiting the limits is FUN! And limits are a never ending source of interesting novel problems.
Caption:
δx, δz = ultimate lateral / longitudinal measuring uncertainty,
sin u = observation aperture, θ = triangulation angle,
δα = uncertainty of the slope angle,
C = Channel capacity, SBP = space-bandwidth-product
Here a comprehensive paper: I 310 pdf “Discover better Optical Sensors by Exploring and Exploiting Nature’s Limits”, OSA Imaging and Applied Optics Congress, Computational Senssing and Imaging (COSI), Munich, June 24-27. 2019
An early paper: T 66. pdf Gerd Häusler, „Fundamental limits of three-dimensional sensing (or: nature makes no presents),“ Proc. SPIE 1319, Optics in Complex Systems, (1 July 1990) 352-353, doi: 10.1117/12.34739. Event: 15th International Optics in Complex Systems, 1990, Garmisch, Germany