In the recent years, the theory and technologies of electromagnetic computational imaging have been well developed and several novel imaging methods have been proposed, one of which is known as the microwave imaging under random field illumination. In order to solve the matrix equation of imaging model, the key of such an imaging system is to generate the random electromagnetic radiation field distribution, implementing the independent measurements under random field illuminations. In this work, an optimal microwave imaging system for the desired imaging region and resolution is theoretically analyzed and experimentally implemented. In the randomness analysis, the correlation between different measurements is evaluated by the singular value decomposition, which is also adopted as a criterion for choosing the optimal parameters of the imaging system. Based on random field illuminations generated by the least number of antenna elements, a full-rank matrix equation can be used to reconstruct the object by direct matrix inversion, which can be completed in nearly real-time once the system calibration is implemented in advance. The numerical simulation and experimental investigation are performed, and the results prove the effectiveness of the proposed optimal imaging system. By using the traditional array theory, it is found that for an N-element phase array, Nilluminations with each element excited by a single frequency, equal amplitude and randomized 0 or ${\text{π}}$ phase signal will result in Nindependent measurements. Theoretically, any additional measurement under random illumination will be correlated with the previous Nmeasurements. Since the random field illumination is obtained by array antennas with 1-bit random phase modulation, the power radiated by each transmitting element is not sacrificed, resulting in an optimal power efficiency of the imaging system compared with those of earlier metasurface-based imaging systems. Besides, a single frequency signal source is used in the system, which also realizes the optimal spectrum efficiency. In conclusion, there are two major innovations of the proposed imaging system: 1) the completely random field illuminations based on 1-bit phase modulation; 2) the approach to optimizing the system on desired demand. The compact and low-cost imaging system promises to have various imaging applications, such as public security and indoor localization.