We demonstrate the capability of laboratory-based x-ray microscopes, using intensity-modulation masks, to access the sub-micron length scale in the dark field contrast channel while maintaining micron resolution in the resolved (refraction and attenuation) channels. The dark field contrast channel reveals the presence of ensembles of samples' features below the system resolution. Resolved refraction and attenuation channels provide multi-modal high-resolution imaging down to the micron scale. We investigate the regimes of modulated and un-modulated dark field as well as refraction, quantifying their dependence on the relationship between feature size in the imaged object and aperture size in the intensity-modulation mask. We propose an analytical model to link the measured signal with the sample's microscopic properties. Finally, we demonstrate the relevance of the microscopic dark field contrast channel in applications from both the life and physical sciences, providing proof of concept results for imaging collagen bundles in cartilage and dendritic growth in lithium batteries.