Method for determining deformations of wavefront of light beam caused by waviness of surfaces of optical system

TLDR: In this article, the wavefront deformations of the light beam caused by the waviness of the surfaces of the optical system were determined by a variational method under free boundary conditions, approximating w(x,y) by a trigonometric polynomial.

Abstract: FIELD: optics.SUBSTANCE: invention relates to the field of optics and can be used to determine the deformations of the wave front of a light beam that has passed through an optical system, caused by the waviness of the surfaces of the optical system. In the inventive method, an incoherent homocentric light beam with a wavelength λ is directed to the optical system. Position of the plane Pis determined, in which the peak intensity of the light beam in the image of the cross-section of the light beam passing the optical system and focused in the image space has a maximum value of Iamong the experimentally recorded peak intensities in the images of the cross sections of the light beam. Diameter D of the light beam in the plane P is measured, perpendicular to the axis of the light beam and in contact with the last surface of the optical system, and the distance Lto it from the plane P. Intensity distribution I(u,v) of the light beam in the coordinates (u,v) of the plane Pis registered, function ψ(u,v)=ln[I(u,v)/I(u,v)] is determined and decomposed in a two-dimensional trigonometric Fourier series, the sequence number μof the highest harmonic of the Fourier series is found, the square of the amplitude of which is not less than 0.02 from the square of the maximum amplitude value in the spectrum of harmonics. Intensity distribution I(ξ,η) of light beam in the coordinates of the plane Pis registered, the position of the planes Pand Pis chosen away from the plane Paccording to the introduced ratios, taking into account the values of λ, D, μ, L. Wavefront deformations of the light beam w(x,y) caused by the waviness of the surfaces of the optical system are determined from the equation connecting w(x,y) in the coordinates (x,y) of the plane P with the intensity distribution of the light beam in the plane P, the intensity distribution of the light beam I(x,y) is used, expressed in the coordinates of the plane P by replacing the variables in the distribution I(ξ,η):Equation is solved by a variational method under free boundary conditions, approximating w(x,y) by a trigonometric polynomial.EFFECT: determination of wavefront deformations of the light beam caused by the waviness of the surfaces of the optical system, with high accuracy while greatly simplifying the measurement process and reducing its labor intensity.1 cl, 5 dwg