“Point-diffraction” ptychographic methods use small-area illumination of relatively simple diffracting objects, e.g. in the context of point-diffraction interferometry or spot-scanning microscopy. The resulting interferograms can be adequately sampled with relatively few detector pixels, and the reduced data volume enables the use of faster or more accurate reconstruction algorithms that might not be usable in conventional wide-field ptychography. In one algorithmic approach, “first-principles ptychography”, the diffraction object’s optical transfer function and the illumination field are simultaneously reconstructed without relying on any assumptions about the internal structure or diffraction mechanisms within the object or illumination optics. This capability would be useful for applications such as interferometric testing of optics for EUV lithography and inspection/metrology.