Abstract: The absolute interferometric measurement of the shape of either flat, or spherical surfaces is achieved by incorporating a Fizeau-interferometer and a test piece holder capable of several degrees of freedom of movement relative to the reference position in the interferometer. A data acquisition and processing technique inter-compares three test parts in various combinations. Full surface absolute maps for each of the test pieces are determined using at least two different rotational positions of one test-piece to yield rotationally sheared maps of that surface. An optimized numerical reconstruction algorithm employing linear filtering and superposition of different angular shear spectra in the angular frequency domain is employed. The method does not require any assumptions about the surfaces under test; and it has low error propagation, even in the case of high spatial resolution.