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Imaging systems have traditionally been designed to mimic the human eye and produce visually interpretable measurements. Modern imaging systems, however, process raw measurements computationally before or instead of human viewing. As a result, the information content of raw measurements matters more than their visual interpretability. Despite the importance of measurement information content, current approaches for evaluating imaging system performance do not quantify it: they instead either use alternative metrics that assess specific aspects of measurement quality or assess measurements indirectly with performance on secondary tasks. We developed the theoretical foundations and a practical method to directly quantify mutual information between noisy measurements and unknown objects. By fitting probabilistic models to measurements and their noise characteristics, our method estimates information by upper bounding its true value. By applying gradient-based optimization to these estimates, we also developed a technique for designing imaging systems called Information-Driven Encoder Analysis Learning (IDEAL). Our information estimates accurately captured system performance differences across four imaging domains (color photography, radio astronomy, lensless imaging, and microscopy). Systems designed with IDEAL matched the performance of those designed with end-to-end optimization, the prevailing approach that jointly optimizes hardware and image processing algorithms. These results establish mutual information as a universal performance metric for imaging systems that enables both computationally efficient design optimization and evaluation in real-world conditions. A video summarizing this work can be found at: https://waller-lab.github.io/EncodingInformationWebsite/

Recent work has demonstrated that imaging systems can be evaluated through the information content of their measurements alone, enabling application-agnostic optical design that avoids computational decoding challenges. Information-Driven Encoder Analysis Learning (IDEAL) was proposed to automate this process through gradient-based optimization. In this work, we study IDEAL across diverse imaging systems and find that it suffers from high memory usage, long runtimes, and a potentially mismatched objective function due to end-to-end differentiability requirements. We introduce IDEAL with Interchanging Optimization (IDEAL-IO), a method that decouples density estimation from optical parameter optimization by alternating between fitting models to current measurements and updating optical parameters using fixed models for information estimation. This approach reduces runtime and memory usage by up to 6x while enabling more expressive density models that guide optimization toward superior designs. We validate our method on diffractive optics, lensless imaging, and snapshot 3D microscopy applications, establishing information-theoretic optimization as a practical, scalable strategy for real-world imaging system design.