Application of Young–Michelson and Brown–Twiss interferometers for determining geometric parameters of nonplanar rough objects

The possibility of using Young–Michelson and Brown–Twiss interferometers for measuring the angular dimensions and parameters of the surface shape of remote passively scattering and self-luminous nonplanar rough objects by optical radiation propagating from them is substantiated. The analysis is based on the properties of approximate transverse functions of field coherence B_t and B_t' and intensity coherence B_ti and B_ti' formed by the time averaging of the products of fields and intensities taken at two points of a receiving aperture (the prime denotes self-luminous objects). The averaging time is set to be much longer than the coherence time of radiation propagating from an object. It is shown that for the radiation coherence length much smaller than the depth of the visible region of the object, the functions B_t and B_t' are proportional to the Fourier transform of the intensity distribution in the image of a remote object, which is the generalisation of the Van Cittert–Zernicke theorem to the case of a nonplanar object, while functions B_ti and B_ti' are proportional to the squares of the modulus of the Fourier transform of this distribution. It is also shown that the recording of functions B_t and B_t' with a Young–Michelson interferometer gives only the angular dimensions of the visible region of objects, whereas the recording of functions B_ti and B_ti' with a Brown–Twiss interferometer allows one to find these dimensions and the radius of curvature of the object surface.