Optical-information method of sub-diffraction angular measurement

Subject of study . This study investigates an optical-information method for measuring the angle between a laser beam and the normal to a flat surface, with an error on the order of 1% of the diffraction limit or less. Aim of study. The objective is to determine the achievable metrological characteristics of the optical-information method for sub-diffraction angular measurements and to evaluate their dependence on the number of processed images, spatial resolution, signal level discretization, and signal-to-noise ratio. Method. The research involved mathematical modeling of interference patterns, development of a prototype processing algorithm, and both numerical and analytical solutions to the equations defining the angular deviations of laser beams. Main results. A method is proposed for measuring the angular position of a laser beam relative to the normal to a flat surface, achieving, in principle, an error level of 1/10–1/100 of the diffraction limit. The method relies on specially developed algorithms for the mathematical processing of arrays of two-dimensional interference patterns generated by a Michelson interferometer with a moving retro-reflector. Unlike the autocollimation method, this optical configuration does not require large longitudinal dimensions and is, in principle, insensitive to vibration. The proposed method is categorized as an optical-information method, as it requires intensive computational processing based on a mathematical model of the measurement process. The optical layout and data processing algorithm are described. Numerical simulation results of the measurement process are presented. It is shown that, through mathematical processing of the interference pattern array created by the Michelson interferometer with a corner reflector under optical path difference modulation, beam deflection angles can be measured with an error significantly below the diffraction limit. An adaptive data processing algorithm is described. A comprehensive mathematical and numerical model of the measurement process is developed, and numerical simulations are conducted. Key quantitative parameters characterizing the metrological performance and potential of the method are established. Specifically, for a laser beam with a 1/ e 2 diameter of 2 mm and a wavelength of 0.63 µm, the minimum measurable angular deviation from the nominal position is estimated at 0.5 ′′ . The algorithm is shown to be effective even with highly noisy data and provides a substantial gain in accuracy even at low spatial resolution. This improvement is achieved by increasing the number of processed interference patterns, thereby narrowing the bandwidth of the measuring system. Practical significance. The relationships derived in this study enable the practical implementation of a sub-diffraction angle meter and a corresponding measurement methodology.