Abstract: Methods and apparatus for imaging a phase or amplitude that characterizes a scattered field emanating from a physical medium. A local probe is stepped to a plurality of successive probe positions and illuminated with an illuminating beam, while a specified phase function is imposed on a reference beam relative to the illuminating beam. A field associated with the scattered field is superimposed with the reference beam and the detection of both yields a detected signal which is recorded as a function of probe position in order to obtain a hologram. The holograph is transformed, filtered, and retransformed to generate an image. Alternatively, the illuminating beam may directly illuminate successive positions of the physical medium.