On quantitativeness of diffraction-limited quantitative phase imaging

Quantitative phase imaging (QPI) has advanced by accurately quantifying phase shifts caused by weakly absorbing biological and artificial structures. Despite extensive research, the diffraction limits of QPI have not been established and examined. Hence, it remains unclear whether diffraction-affected QPI provides reliable quantification or merely visualizes phase objects, similar to phase contrast methods. Here, we develop a general diffraction phase imaging theory and show that it is intrinsically connected with Rayleigh's resolution theory. Our approach reveals the entanglement of phases under restoration, imposing diffraction bounds on spatial phase resolution and, unexpectedly, on phase accuracy. We prove that the phase accuracy depends on the size, shape, and absorption of objects forming the sample and significantly declines if the object size approaches the Rayleigh limit (a relative phase error of -16% for an Airy disk-sized object with low phase shift). We show that the phase accuracy limits can be enhanced at the cost of deteriorated phase resolution by attenuating the sample background light. The QPI diffraction limits are thoroughly examined in experiments with certified phase targets and biological cells. The study's relevance is underscored by results showing that the phase accuracy of some structures is lost (a relative phase error of -40%) even though they are spatially resolved (a phase visibility of 0.5). A reliable procedure is used to estimate phase errors in given experimental conditions, opening the way to mitigate errors' impact through data post-processing. Finally, the phase accuracy enhancement in super-resolution QPI is discovered, which has not been previously reported.