In this paper, we present a new interference scheme with transverse shift of beams for remote monitoring of parameters of optical elements. The results of studying the measurement accuracy are given and the main noise sources of the presented scheme are considered. The advantages of this scheme are the high accuracy (the experimentally realized accuracy is higher than λ/3000, where λ is the wavelength of the sounding radiation), high speed allowing us to study nonstationary processes, and selectivity ensuring the study of a given surface by using other optical elements of the scheme.