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We report on the results of the experimental simultaneous observation of all the parametric optical signals related to terahertz-wave detection in a continuously pumped nonlinear-optical crystal [3]: signals due to up-conversion of the incident THz radiation to the Stokes and anti-Stokes optical ranges, due to up-conversion of the thermal noise to the both ranges and due to SPDC in the Stokes part of the optical signal spectrum (Fig.). To avoid the different influence of the idle absorption effects, we have detected THz radiation in the frequency range 0.120-0.300 THz where Mg:LiNbO3 crystals used for parametric frequency conversion can be considered as practically transparent. Nevertheless, it became clear that this is not enough for estimating the SPDC-calibration as an absolute procedure in the THz range. In case of strongly non-degenerate SPDC one has to take special care for the single-mode character of the parametric interaction. Transverse spatial limitation of the nonlinear interaction volume in a crystal (mostly due to a pump beam focusing) leads to increase of a number of idle modes which can contribute to a single mode of an output signal. This number grows considerably when the frequency relation / i s is going down. All the idle modes are well-filled by classical and quantum fluctuations forming the background signals of the thermal up-conversion and SPDC, but cannot be filled uniformly by an incident THz radiation. The filling factor has to be taken into account in the SPDC calibration of any energy characteristic of the input radiation. Results of theoretical calculations of the filling factor, made for differently focused Gaussian pump beams and different geometries of the parametric THz up-conversion schemes, will be discussed.