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This paper considers the design of a detection system to optimally detect known spatially invariant signal fields corrupted by an additive, zero-mean, covariance-separable, and spatially isotropic noise field. The detection system has as its input samples (in a plane) of the signal-plus-noise field; each spatial sample is the output of a point detector. In an earlier paper , optimal processing of the point detector outputs and the design of circular arrays were considered. This paper is concerned with the design of several other array configurations. Some of the results, which are related to singular detection problems, dramatically point out the need for proper modeling of covariance functions. These results also indicate that the use of derivatives in detection is extremely unreliable when there is any nonzero instrument noise.