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foc the the lso 1 2 1 2 D. G. Fischer and T. D. Visser Vol. 21, No. 11 /November 2004 /J. Opt. Soc. Am. A 2097coherent, it is of prime importance to explore the correla-tion properties of such focused wave fields. In the present paper an important class of partially co-herent fields, namely, Gaussian-Schell model fields, is ex-amined. In particular, the spectral degree of coherence of the field in the focal region is analyzed. It is shown that, depending on the effective coherence length of the field in the aperture, the coherence length in the focal region can be either greater or smaller than the width of the inten-sity distribution. Also, the spectral degree of coherence is found to possess phase singularities. This implies that the fields at certain pairs of points are completely uncor-related. 2. PARTIALLY COHERENT FOCUSED FIELDS Consider a converging, monochromatic field of frequency v that is exiting a circular aperture with radius a in a plane screen (see Fig. 1). The origin O of the coordinate Here the angle brackets denote the average, taken over a statistical ensemble of monochromatic realizations $U (0)(r8)exp(2ivt) % (Ref. 6, Sec. 4.7), and the asterisk de-notes the complex conjugate. The cross-spectral density of the focused field W~r1, r2, v! 5 ^U*~r1, v!U~r2, v! & (3) is given by the formula W~r1, r2, v! 5 1 l