Phase function of spatial coherence from second-, third-, and fourth order intensity correlations

It is well known that the intensity interferometry of Hanbury Brown and Twiss measures the square of the absolute value of the normalized coherence function and that the phase of the function is lost. We show that the cosine and the sine of the phase can be determined using triple- and quadruple-intensity correlations. This information is used to derive the intensity distribution of the object. The procedure for the phase reconstruction described depends on the starting values of the phase function for the least separation of the mirrors or for the nearest neighbors in the two perpendicular directions of the array of mirrors. These starting values are determined by means of an amplitude correlation experiment, such as the Young's two-slit type. The procedure of intensity correlations is then used for all other separations throughout the array. Computer simulation of the proposed procedure and a simple example of reconstruction of object intensity distribution are shown.