For non-coplanar arrays, the integrals can be inverted analytically using a three-dimensional Fourier transform Eric Weisstein's World of Math to obtain the sky brightness
The result, given by Perley, is that
where I is the actual sky brightness.
References
Perley, R. A. "Wide Field Imaging II: Imaging with Noncoplanar Arrays." Ch. 14 in Synthesis Imaging in Radio Astronomy: Third NRAO Summer School, 1988 (Ed. R. A. Perley, F. R. Schwab, and A. H. Bridle). San Francisco, CA: Astronomical Society of the Pacific, 1989.
