Abstract

A common-path radial-shearing interferometer is examined for its ability to measure the power spectrum of an object's intensity transmittance. For an object illuminated with spatially incoherent light, it is shown that the contrast of the intensity distribution observed at the interferometer's output contains a cosine transform of the object's intensity transmittance. From a coherence theory point of view, this manifestation is shown to be the result of a direct mapping between the object's frequency spectrum and the coherence properties of the interfering beams. Alternatively, when one considers the system impulse response, each point in the object is found to produce a set of cosinusoidal fringes whose frequency is directly related to that object point. The subsequent incoherent summation over the object results in an interference pattern that contains a bias term plus the transform of the object's intensity transmittance. Experimental results obtained for standard objects such as circular apertures and Ronchi rulings compare favorably with theoretical predictions.

© 1990 Optical Society of America