Revealing and optimizing coherence-driven trade-offs in partially coherent differential imaging

Optical analog computing under partially coherent illumination offers a promising route toward high-speed, low-noise, and interference-robust information processing. However, the role of spatial coherence in optical differentiation has not been fully explored. Here, we demonstrate spatial differential imaging under Gaussian–Schell model illumination and show that the output intensity comprises three distinct contributions: object differentiation, mode differentiation, and cross terms. This decomposition reveals a fundamental coherence-driven trade-off: while reduced coherence suppresses speckle noise to improve edge smoothness, mode differentiation and cross terms introduce an object-dependent structured background that degrades contrast. By quantifying this interplay through theory and experiment, we identify an optimal coherence window (0.6 < μ < 1) that balances edge smoothness and contrast. These results establish a practical guideline for spatial optical differentiation under partially coherent light, advancing robust optical analog computing and imaging applications.