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The van Cittert-Zernike theorem describes the Fourier transform relationship between an extended source and its visibility function. Developments in classical optics texts use scalar field formulations for the theorem. Here, we develop a polarimetric extension to the van Cittert-Zernike theorem with applications to passive microwave earth remote sensing. The development provides insight into the mechanics of two-dimensional inteferometric imaging, particularly the effects of polarization basis differences between the scene and the observer.