This paper proposes a novel technique for estimating the signal power spectral density to be used in the transfer function of a microphone array post-filter. The technique is a modification of the existing Zelinski post-filter, which uses the auto- and cross-spectral densities of the array inputs to estimate the signal and noise spectral densities. The Zelinski technique, however, assumes zero cross-correlation between noise on different sensors. This assumption is inaccurate in real conditions, particularly at low frequencies and for arrays with closely spaced sensors. In this paper we replace this with an assumption of a theoretically diffuse noise field, which is more appropriate in a variety of realistic noise environments. In experiments using noise recordings from an office of computer workstations, the modified post-filter results in significant improvement in terms of objective speech quality measures and speech recognition performance.