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Possible effects caused by the presence of classical thermal field fluctuations and inherent absorption of the non-linear crystal at THz frequencies were investigated using the theoretical approach based on generalized Klyshko-Kirchhoff law. The huge angular diversity of SPDC-generated THz photons was studied both theoretically and experimentally. Comparatively greater progress has been achieved in detecting optical photons, which are emitted at small Stokes shifts, correlate with their THz counterparts, and can provide information on THz properties of matter without direct detection of THz waves. However, for a vast majority of attracting applications (ghost imaging without THz cameras, absolute calibration of quantum efficiency of THz detectors, and other tasks), the direct measurement of optical-terahertz correlation function g(2) is important. The solution to this problem is significantly complicated by the lack of current THz receivers capable of operating in the single-photon mode and high-speed coincidence circuits. First results of g(2) measurement using analog readings of an idler THz receiver (a superconducting NbN bolometer) and a signal optical detector (a photo multiple tube) are discussed.