A gold film is the microscope's ruler. This page reads it, ring by ring, and writes the calibration down.
Load the ring pattern of an evaporated gold film or another standard, refine the centre, integrate the pattern into a radial profile, find the rings and let the page assign them to the standard and fit the camera constant. The camera length follows from the pixel size and the wavelength, the elliptical distortion from the ring radius against azimuth, and the image-to-pattern rotation from two directions you click. The calibration can be saved for the diffraction indexer.
Click the pattern near its centre, then refine: the page moves the centre until the radial profiles of opposite sectors agree. A beam stop or a saturated centre does not matter as long as two or more rings are complete.
The physical pixel of the camera times the binning gives the pixel of the pattern; with the wavelength this turns the camera constant (Å·px) into the camera length (mm) and, if the nominal value is entered, into the correction factor.
Load the image of the same specimen (a straight edge, a lattice-fringe direction, a needle) and click two points along it; then, with the pattern loaded, click the two points of the corresponding direction in the pattern (a spot pair, or the streak of the edge). The rotation from image to pattern is reported with its 180° ambiguity.
Every measurement made from a diffraction pattern rests on the camera constant λL, the product of the wavelength and the effective camera length, which converts a distance on the pattern to a reciprocal spacing: r·d = λL. The nominal camera length read from the microscope is rarely better than a few percent, it changes with the objective-lens current, the specimen height and the projector settings, and it must be measured with a standard whose spacings are known. The polycrystalline ring pattern of an evaporated gold or aluminium film is the standard of choice because every ring of the fcc lattice is present at once, and the same pattern gives the elliptical distortion of the projector system and, with an image of the same field, the rotation between image and pattern that a magnification change introduces.
The page refines the centre by requiring the radial profiles of opposite sectors of the pattern to agree, integrates the pattern azimuthally into a profile of intensity against radius, removes a rolling-minimum background and finds the ring peaks by prominence with parabolic interpolation to a fraction of a pixel. The rings are then assigned to the standard's d-spacings: the innermost measured ring is tried as the first, second, third or fourth allowed reflection of the standard, each hypothesis is fitted by least squares to r = K/d, and the assignment that explains the most rings with the smallest residual wins, so a missing first ring or a spurious inner peak does not spoil the fit. The camera constant K in Å·px, the camera length from the pixel size and the wavelength, the residual of each ring and the correction factor to the nominal value are reported. The ellipticity of a chosen ring is measured from its radius in 24 azimuthal sectors as the amplitude of the 2φ harmonic, and its axis, which is what a distortion correction needs. The rotation calibration takes two points along a direction in the image and two along the corresponding direction in the pattern.
The standards are cubic metals and salts whose lattice parameters are well known at room temperature; the d-spacings come from the parameters and the reflection rules of the structure type, and a specimen that is strained, alloyed or at another temperature has different spacings. The accuracy of K is limited by the ring positions, typically a few tenths of a pixel on a sharp ring, so a pattern with rings out to a large radius and a well-refined centre gives a camera constant good to about 0.2 percent; a diffuse film, a beam stop that cuts the inner rings, or a pattern recorded at a different objective-lens setting from the specimen of interest all degrade it. The ellipticity measured here is the distortion at one radius; a full distortion map varies with radius and needs several rings. The page reads uncompressed 8-bit and 16-bit TIFF, PNG and JPEG images; a saturated centre is tolerated because the profile is only used beyond the smallest ring radius.
@misc{tripathy2026ringpatterncalibration,
author = {Tripathy, Manisha},
title = {Ring Pattern Calibration},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tem/ring-calibration}},
note = {Interactive web tool}
}