Simple method of precision calibration of magnification of a scanning microscopes with the use of test diffraction grating

A method of precision calibration of magnification of scanning microscopes with the use of a test diffraction grating, comprising the steps of positioning and orientation of a test object on a stage of microscope so that strips of a test diffraction grating are perpendicular to a direction along which a calibration is performed;

• scanning of a selected portion of the test object along axes X and Y;
• measuring values of a signal S versus coordinates x and y in a plane of scanning and storing of said values S (x, y) in a digital form as a two-dimensional digital array;
• transforming the two-dimensional array of signals S(x, y) into a two-dimensional array S (u, v) by turning of the axes so that a direction of a new axis u is perpendicular to the strips of the grating and a direction of a new axis v coincides with the strips of the grating;
• line-by-line mathematical processing of the array S (u, v) including for each line S(u) approximating of an array of discrete values S (u, v) with a periodical analytical function
• y(x)=A*sin(B*x−c)+D,
• wherein A, B,C, D are empiric constants whose values are selected in accordance with a best correspondence between an analytical curve and the one dimensional array of S(u), determining a pitch T of the analytical function Y(x) for a line v in accordance with a formula:
• Tv=2*π/B,
• wherein T is a value of the pitch in pixels, B is a value of the empirical constant B obtained in a previous step and corresponding to a best approximation of the array S(u) to the analytical function;
• performing standard statistical processing of sets of values Tv corresponding to various lines v by calculating of an average value of the pitch T for all lines;
• and calculating a magnification Mu in accordance with the selected direction u in correspondence with the formula:
• M U = T · L T 0 · N ,
• wherein L is a width of a medium of the image in a direction of calibration, To is an independently attested value of a pitch of the test object in absolute units, N is a number of pixels on a line along the direction u.