Method of precision calibration of magnification of scanning microscopes with the use of test diffraction grating

A method of precision calibration of magnification of a scanning microscope with the use of test diffraction grating, comprising the steps of positioning and orientation of a test object on a microscope stage so that strips of a test diffraction grating are perpendicular to a direction on 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 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:
• separation from it of a one-dimensional array-line S(u) which contains a profile of an image of periodically repeating strips of a test-object;
• multiplication of the line S(u) by shifting of its copy relative to an original by an integer number of periods, adjustment of a value of the shift by the method of least squares in accordance with a criterion of the best coincidence of the overlapping portions of the original and the copy of the line S(u), calculation of average values S(u) in the zone of overlapping as a semisum of values of the original and copy S(u) in each point of the zone;
• transformation of the multiplied array S(u) into an array P(w) in accordance with the formula P ⁡ ( w ) = ∑ j = 1 N / 2 ⁢ ⁢ [ S ⁡ ( j ) * S ⁡ ( j + w ) ]
• where N is a number of members in the multiplied array S(u);
• determination of coordinates w1, w2, w3, w4 . . . of successive maximums of the function P(w) wherein w4>w3>w2>w1>0;
• determination of an average period T′ of the test grating in pixels for the selected line S(u) in accordance with the formula T ′ = 1 n - 1 ⁢ ∑ i = 1 n - 1 ⁢ ⁢ ( w i + 1 - w i )
• where n is a number of maxima in the function P(w);
• moving to a next line S(u) with a new value of coordinates v and performing for it the same line-by-line mathematical processing;
• performing statistic processing of obtained set of values T′ corresponding to various lines v with calculation of an average period Tav for all lines and calculating a magnification Mu along the selected direction u in accordance with the formula M u = T av · L T o · N
• wherein L is width of a medium of the image in direction of calibration, T0 is an independently attested value of a pitch of the test object, N is a number of pixels on a line along the direction u.