Lensless imagers can make cameras far thinner than conventional optics and can compress rich scene information into a single measurement. But the same optical multiplexing that enables those advantages can also scramble a scene so strongly that reconstruction loses the information it needs. We address this design problem by evaluating lensless encoders through mutual information estimated directly from noisy measurements. By combining a probabilistic model of measurement distributions with a detector-noise model, we compare encoders without tying performance to any one reconstruction algorithm and quantify how object sparsity, encoder multiplexing, and noise interact. Across simulations, we show that dense objects are best matched to low-multiplexing encoders, whereas progressively sparser objects benefit from higher multiplexing. We then optimize phase-mask encoders for specific object classes, and these information-optimal designs outperform heuristic masks in mutual information while also improving downstream reconstruction quality. Experiments with a conventional lens, a random multi-focal lenslet array, and a diffuser reinforce the same lesson for dense natural images: more multiplexing can reduce recoverable information. By making information capture itself the design target, our work offers decoder-independent engineering rules for lensless imaging and other multiplexed computational imaging systems. Because the best encoder depends on the assumed object distribution and mutual information does not guarantee every task-specific outcome, the next step is to test robustness under distribution shift, alternate noise models, and specialized downstream tasks.
