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Generation and detection of terahertz (THz) waves has attracted considerable interest due to promising applications of the THz waves in various areas including spectroscopy, imaging, non-destructive evaluation and others. Among different approaches for compact table-top THz sources and detectors, nonlinear-optical frequency-conversion schemes are in the forefront. They produce conversion of optical energy of visible and NIR lasers into the THz gap under THz generation, and also can be applied for THz detection using advanced optical technologies via up-conversion of the THz radiation into the optical range. Nevertheless, the problem of absolute measurement of terahertz fields is very important for such devices, as well as for other THz schemes, but still remains as not properly solved. We propose to use the quantum-optical effect of spontaneous parametric down-conversion (SPDC) for calibration of the spectral brightness of THz radiation in the course of its non-linear-optical detection [1]. Idea of the calibration is close to the Klyshko method [2] for absolute measurement of the spectral brightness of optical radiation. As it was shown by D.N. Klyshko [3], generation of signal photons of frequency under SPDC in an optically transparent crystal can be formally treated as parametric conversion of the zero-vacuum electromagnetic field fluctuations at the idler frequency ( being a pump frequency). For self-consistency of this analogy, the effective spectral brightness of idler-field quantum fluctuations should be taken as exactly photon per mode (in quantum units), that is in radiometric units. Radiation of the optical source is involved into the frequency conversion process together with the quantum fluctuations; its brightness is calibrated in terms of Nvac by measuring the total output signal intensity and intensity of the pure SPDC signal. The SPDC signal radiation at THz-shifted optical frequencies always persists under non-linear-optical THz detection as well, and can be used as a reference-type background. However, the thermal fluctuations are also considerable in the terahertz range. We have studied experimentally relative contributions of thermal fluctuations into the SPDC signals, at Stokes frequencies , and into the sum-frequency signals, at anti-Stokes frequencies . Results of this study, the way to separate contributions of thermal and quantum fluctuations, and the whole procedure of the SPDC-based calibration of THz radiation brightness will be reported.