Image defocus provides a useful depth cue in computer vision, and can also be used to recover phase information in coherent microscopy. In a differential setting, both problems can be addressed by solving simple equations, known as Depth from Differential Defocus and the Transport of Intensity Equation. Relating these governing equations requires putting them on equal footing, so we'll look at the assumptions common to photography and microscopy applications, and go through a gentle introduction to coherence, light fields and Wigner Distribution Functions, and generalized phase. We'll show that depth from defocus can be seen as a special case of phase recovery, with a new interpretation of phase for incoherent settings.

Emma Alexander is a postdoc in the Vision Science department at UC Berkeley, and will be joining the Computer Science department at Northwestern University as an assistant professor in 2022. She received a B.S. in Physics and in Computer Science from Yale in 2013 and an M.S. (2016) and PhD (2019) in Computer Science from Harvard under the advisement of Professor Todd Zickler. She has received the NSF Graduate Research Fellowship, ECCV Best Student Paper, ICCP Best Demo, and the Berkeley CIVO Postdoctoral Fellowship.