Differential methods are shown to reveal inherent phase in light, corresponding to either the structure of the scattering object, or to aberrations in the imaging medium. Intensity measurements of scattered electromagnetic fields are related to the phase structure of the underlying coherent wavefronts. For an ideal imaging system, intensity differentials with varying focus encode the phase and hence optical density distribution of a scattering object. This is used to characterize diffraction due to thick absorber topography in deep UV lithography (193nm wavelength) using a focus stack from a mask imaging tool. The imaging methods thus developed enable feature-specific process window calibration during lithography, while supplementing mask design capabilities from experimental data. Switching from strongly absorbing , patterned lithography masks to weakly scattering phase diffusers allows probing the imaging system as well, much like audio system characterization using wide spectrum noise. This enables in-situ characterization of optical-system transfer functions using the speckle generated from the rough diffuser. Under a linear approximation between the diffuser phase and speckle intensity, system aberrations are shown to be encoded in the power spectrum of the speckle. This proves to be an effective way of probing the imaging system in extreme UV lithography (13.5nm wavelength), where mask roughness naturally creates weak speckle in the image intensity. A new theoretical formulation demonstrates that the phase of the pupil can be completely recovered in a band-limited imaging system by computing image intensity differentials created by tilting the illumination angle on the EUV mask. Experiments on a synchrotron EUV imaging tool validate the method, showing real time recovery of imaging system aberrations, simply from differentials of speckle images from a blank mask.