Fourier ptychographic microscopy (FPM) is a high-throughput computational imaging technique, yet its depth-of-field (DOF) is often limited by the need for prior information in traditional models. While feature-domain FPM (FD-FPM) enables prior-free digital refocusing, its operating mechanisms and physical limits remain unclear. Furthermore, the profound impact of integrating physical prior information on reconstruction fidelity is not yet fully understood. Herein, this study establishes a theoretical framework to elucidate these mechanisms and define performance boundaries. We derive an analytical model that decouples optical diffraction from computational gain, predicting the maximum tolerable defocus across varied objectives with different numerical apertures. Experimentally, we achieve an extended DOF exceeding ten times the physical limit (e.g., extending the reliable imaging depth of a 0.4 NA objective from ∼4μm to ∼40μm), validating the model’s predictive accuracy (2% error). Using Zernike modal analysis, we verify that the recovered wavefront is dominated by defocus, enabling dual validation of reconstruction fidelity and defocus authenticity. Crucially, from an information-theoretic perspective, we explore a specific clarity-resolution trade-off between prior-based and prior-free approaches. We demonstrate that the introduction of ideal defocus prior reduces visual contrast, because its practical applications fail to adequately account for the physical geometric vignetting effect. This causes high-frequency attenuation, thereby sacrificing super-resolution details and artificially restricting the effective solution space. We demonstrate that the pure data-driven no-prior strategy retains broader high-frequency information. This work clarifies the principles and limits of prior-free refocusing in FPM and highlights specific trade-offs in prior-based approaches, guiding future adaptive imaging strategies.
Zhou et al. (Fri,) studied this question.