In the fields of radar imaging and detection, the use of optical components appears as an attractive solution to overcome limitations of current technologies. This paper focuses on the development of a new class of microwave-photonic radar imaging systems enabling volumetric image reconstruction. These operations are made possible using a multiple-input multiple-output antenna array architecture combined with the conception of a dedicated optical multiplexing technology to limit the complexity of the whole reception chain. Particular emphasis is placed on the development of mathematical formalisms specifically adapted to these microwave-photonic radar architectures, making it possible to model the measurements carried out and to reconstruct three-dimensional radar images. These solutions are validated by the reconstruction of complex scenes with a multiple-input multiple-output radar made of up to 16 transmitters and 16 receivers.