The flutter shutter paradox

Photography is the art of acquiring as many photons as possible of a given scene. In classic cameras, the aperture time is irremediably limited by the risk of a motion blur when the camera and the scene are in relative motion. Nevertheless, two recent camera concepts, the Agrawal et al. flutter shutter and the Levin et al. motion-invariant photography permit one to extend indefinitely the exposure time while guaranteeing an invertible motion blur. In this paper, a complete mathematical theory of these new technologies is proposed. Modeling the capture noise, the theory furnishes explicit formulas for the signal to noise ratio (SNR) of the final image after deconvolution when the motion is uniform. It puts in evidence the existence of two variants, the analog flutter shutter and the numerical flutter shutter. The results of the resulting quantitative comparison are slightly paradoxical. First, it is shown that the best camera aperture strategies are always flutter shutters, even when the aperture time is a priori fixed. Second, it is shown that the SNR increase obtained by using a flutter shutter in the presence of a known motion remains bounded, even with an infinite exposure time. Incidentally, the theory gives the formula of the optimal classic snapshot in the presence of motion and compares its performance to the optimal flutter shutter. © 2013 Society for Industrial and Applied Mathematics.