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This paper presents a mathematical analysis of the compound intensity interferometer (a generalization of the interferometer of Hanbury Brown and Twiss) which measures the complex spatial frequency spectrum of remote incoherent radio sources. The system has three elements, two of which are a fixed short distance apart while the third moves along the common baseline. The received signals from the two adjacent elements are multiplied together while the third element's signal is simply square-law detected. This produces two voltages (intensity fluctuations) which are fed through low-frequency band-pass filters to remove the dc value and then are brought together, multiplied, and time-averaged. The interferometer output has two values (a complex output) corresponding to an in-phase and a phase-quadrature multiplication of the RF signals from the two adjacent elements. From a series of measured outputs one can deduce the radio source distribution's spatial frequency spectrum and hence synthesize a radio map of the sources. This fourth-order correlation system has no RF transmission link between its widely separated elements, i.e., between the two fixed elements and the variable third element. Consequently, it is not affected by phase-instability in the interferometer transmission link nor by fluctuations in the atmosphere. However, in common with all intensity interferometers, it is relatively insensitive to weak radio sources.