Transport of Event Equation: Phase Retrieval from Defocus Events

To time-efficiently and stably acquire the intensity information for phase retrieval under a coherent illumination, we leverage an event-based vision sensor (EVS) that can detect changes in logarithmic intensity at the pixel level with a wide dynamic range. In our optical system, we translate the EVS along the optical axis, where the EVS records the intensity changes induced by defocus as events. To recover phase distributions, we formulate a partial differential equation, referred to as the transport of event equation, which presents a linear relationship between the defocus events and the phase distribution. We demonstrate through experiments that the EVS is more advantageous than the conventional image sensor for rapidly and stably detecting the intensity information, defocus events, which enables accurate phase retrieval, particularly under low-lighting conditions.