Estimation of methods for calculating the phase shift of wave fronts of own modes of a confocal resonator

Background: The redefinition of a unit of length - a meter - through a unit of time and a fundamental constant - the speed of light in vacuum - has opened up the fundamental possibility of a significant reduction in the uncertainty of its reproduction. Now progress in areas such as absolute ballistic gravimetry, control of large-sized aspherical optics, laser interferometry, and the production of electronic components in the semiconductor industry have made this feature extremely relevant. It is known that the measuring scale of laser interferometers used for precision distance measurement is non-linear, since the common-mode surfaces of any real radiation beam are located irregularly in space. To compensate for the effect of this irregularity on the measurement result, it is necessary to know the precision phase structure of real laser beams. Objectives of the work is comparing existing methods for studying the phase structure of optical radiation beams and estimating the distribution of the topological phase shift of a relatively uniform plane wave. Materials and methods:. The well-known theoretical methods for calculating the topological phase shift of in-phase surfaces of an optical beam are considered and compared - the Lommel-Debye method based on the Fresnel-Kirchhoff integral, the modified method based on the Rayleigh-Sommerfeld integral and the Gaussian beam method based on a parabolic equation. Results: Each method performed calculations of the accumulated phase lag of the focused radiation beam when moving the observation plane relative to the focal point. The distribution of the relative change in the distance between the in-phase surfaces in the range of displacements from λ to 106•λ was also calculated. The most adequate physical picture of the phenomenon was obtained by the Gaussian beam method based on a parabolic equation. Conclusion: The results will be used to reduce the systematic error of laser interferometers.