Error Metrics for Partially Coherent Wavefields

Lensless imaging methods that account for partial coherence have become very common in the past decade. However, there are no metrics in use for comparing partially coherent light fields, despite the widespread use of such metrics to compare fully coherent objects and wavefields. Here, we show how reformulating the mean squared error and Fourier ring correlation in terms of quantum state fidelity naturally generalizes them to partially coherent wavefields. These results fill an important gap in the lensless imaging literature and will enable quantitative assessments of the reliability and resolution of reconstructed partially coherent wavefields.