There is growing interest in the use of coded aperture imaging systems for a variety of applications. Using an analysis framework based on mutual information, we examine the fundamental limits of such systems—and the associated optimum aperture coding—under simple but meaningful propagation and sensor models. Among other results, we show that when SNR is high and thermal noise dominates shot noise, spectrally-flat masks, which have 50% transmissivity, are optimal, but that when shot noise dominates thermal noise, randomly generated masks with lower transmissivity offer greater performance. We also provide comparisons to classical pinhole and lens-based cameras.