Continuing improvements in the fabrication of super-smooth spherical and aspheric optical surfaces for applications such as extreme-ultraviolet lithography have given rise to the need to characterize the surface roughness of these optics to the sub-Angstrom level. Phase-shifting interference microscopes are well suited to acquire high-precision, three-dimensional surface structure rapidly, without contact, and over a wide range of spatial frequencies. This paper describes a new phase-shifting interference microscope by ADE Phase Shift, together with exemplary measurements of Angstrom-level surface roughness. The microscope was designed to measure large diameter (up to 500 mm) convex, concave and aspheric optics. To access all areas of the test surface, samples are placed symmetrically at the center of an R-theta stage. The phase-shifting microscope head pivots in the direction of the translation stage travel by ±20 degrees to match the major component of surface slope, while a second tilt control nulls minor tilt in the orthogonal direction. A 1K by 1K high-resolution, digital camera reduces random noise in the system to below 0.15 Angstrom rms for 16 averaged maps of nulled interferograms. When testing non-planar surfaces, the interference fringes cannot be nulled out, and special care has to be taken to minimize phase-dependent errors, commonly known as fringe print-through. A print-through level of less than 0.2 Angstrom rms has been achieved with a careful opto-mechanical system design in combination with an advanced phase algorithm whose filtering action suppresses higher-order harmonics caused by phase-shifter and detector non-linearity, as well as vibrations.