Taking a sequence of photographs using multiple illumination sources or settings is central to many computer vision and graphics problems. A growing number of recent methods use multiple sources rather than single point sources in each frame of the sequence. Potential benefits include increased signal-to-noise ratio and accommodation of scene dynamic range. However, existing multiplexing schemes, including Hadamard-based codes, are inhibited by fundamental limits set by Poisson distributed photon noise and by sensor saturation. The prior schemes may actually be counterproductive due to these effects. We derive multiplexing codes that are optimal under these fundamental effects. Thus, the novel codes generalize the prior schemes and have a much broader applicability. Our approach is based on formulating the problem as a constrained optimization. We further suggest an algorithm to solve this optimization problem. The superiority and effectiveness of the method is demonstrated in experiments involving object illumination.