The angular properties of sensor, implemented in Kretschmann?s scheme, where the optimized for oblique incidence of light thin-film reflection interferometer acts as a sensing element, are described in the paper. Analytical equations, defining the sensor?s properties for S and P polarization states at working wavelength in vicinity of working angle of incidence, are provided, as well as approximate equations for main parameters of sensor: sensitivity, angular full width at half maximum, contrast and figure of merit. The possibility to vary the named parameters by choosing appropriate metal and dielectric layers of the structure is shown. For an example, the numerical calculations are made for one of special cases, optimized for S polarization state, as having larger figures of merit. The dependencies of angular properties on number of layers and base thickness are demonstrated. It is shown, that angular measurements with this method are theoretically capable of infinite figures of merit, and in practice they are only limited by losses in layered structure and beam divergency. The recommendations for experimental realization of method are given. Keywords: reflection interferometer, total internal reflection, refractive index sensor.

Experimental study of the sensor in the Kretschmann optical scheme, in which the sensitive element is a reflection interferometer (RI) for the oblique incidence of light, is presented for the first time. A brief theory of RI is given. The experimental sample was used to measure the refractive index of the residual atmosphere in a vacuum chamber during its pumping. The high Q-factor of the RI resonator made it possible to obtain a fairly narrow spectral maximum with a width of 1.7 nm. The spectral sensitivity of the sensor was 1000 nm/RIU and the quality parameter was 529 RIU-1, it was also demonstrated that resolution of 6.5·10-8 RIU can be achieved. Proposals for further improvement of the sensor characteristics are formulated. Keywords: reflection interferometer, total internal reflection, refractive index sensor.