In interferometric radiometry, the correlations between all pairs of radio-frequency (RF) receivers must be performed in order to obtain the scene visibilities. This represents a cumbersome problem in passive imaging where large signal bandwidths are typically required to achieve fast-acquisition times and improve the radiometric resolution of the image. In this case, the signal distribution and the correlation at intermediate frequencies require very fast signal acquisition and processing subsystems. This paper presents a technique to perform correlations of millimeter-wave signals produced by thermal emission in the optical domain as a solution to the aforementioned problem. The proposed method is based on converting the RF signal to the optical domain by modulating a laser beam with the RF signal using a {\rm LiNbO}3 phase modulator. This conversion allows to perform the signal distribution in the optical domain to obtain the combination of the receiver pairs. The correlation is obtained by measuring the power of the photocurrent produced by photodetecting the combined signal. The results of an experimental validation consisting on the acquisition of passive images using a linear interferometric array are presented to support the feasibility of the method. In addition, performance considerations of the system have been developed and validated by calculating the standard deviation of a visibility measurement.