  The improvement of the calibration relation for determining the size of the
broad-line region from the observed optical luminosity of active galactic
nuclei (AGN) is a necessary task to study fundamental parameters of distant
AGNs such as mass of the central supermassive black hole. The most popular
method of the BLR size estimation is the reverberation mapping based on
measuring the time delay between the continuum flux and the flux in the
emission lines. In our work, we apply the method of photometric reverberation
mapping in medium-band filters, adapted for observations at the Zeiss-1000
telescope of the SAO RAS, for the study of AGN with broad lines in the range of
redshifts $0.1 < z < 0.8$. This paper describes the technique of observations
and data processing, provides a sample of objects and demonstrates the
stability of the used method. As a preliminary result for 2MASX
J08535955+7700543 at $z=0.1$ we have obtained time delay estimates of $\tau
(ICCF)=32.2^{\pm10.6}$ days and $\tau(JAVELIN)=39.5_{-15.8}^{+23.0}$ days that
are consistent with each other and also within the accuracy of the existing
calibration relations.
