An Analysis of Focus Sweep for Improved 2D Motion Invariance

Recent research on computational cameras has shown that it is possible to make motion blur nearly invariant to object speed and 2D (i.e., in-plane) motion direction, with a method called focus sweep that moves the plane of focus through a range of scene depth during exposure. Nevertheless, the focus sweep point-spread function (PSF) slightly changes its shape for different object speeds, deviating from perfect 2D motion invariance. In this paper we perform a time-varying light field analysis of the focus sweep PSF to derive a uniform frequency power assignment for varying motions, leading to a finding that perfect 2D motion invariance is possible in theory, in the limit of infinite exposure time, by designing a custom lens bokeh used for focus sweep. With simulation experiments, we verify that the use of the custom lens bokeh improves motion invariance also in practice, and show that it produces better worst-case performance than the conventional focus sweep method.