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.
Try this: click near the centre of the pattern to move it, then press refine in the Standard card and watch the centre, the fitted rings and the residuals update.
Every measurement from a pattern uses λL: r·d = λL. The nominal camera length is rarely better than a few percent, so measure it with a standard.
Every ring of the fcc lattice is present at once. The same pattern also gives the elliptical distortion of the projector system.
Each ring found is tried in turn as the first to fourth reflection of the standard. The fit to r = K/d that explains the most ring strength wins (a strong ring counts more than a faint one), then the smallest residual.
Ellipticity comes from one ring’s radius in 24 sectors. The rotation uses two points in the image and two in the pattern.
Click the pattern near its centre (within 15% of the image size), then refine: the page first finds a rough centre, where the pattern best matches itself turned half a turn, then searches around that point and moves the centre until the radial profiles of opposite sectors agree, then until the strongest clear ring is the same distance from it all the way round. The beam stop is left out, and a clipped centre is skipped.
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.
The cards beside the pattern summarise the method. The full description is here.
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 (from a start far off, first a rough centre within 15% of the image size, the point about which a reduced copy of the pattern best matches itself turned by 180 degrees; then a coarse search within 24 px and a fine one, over the whole profile range). It then measures the radius of the strongest ring that is clear of its neighbours in 24 sectors, fits the radius against angle with a mean, an off-centre term and an elliptical term, and moves the centre until that ring is equally far from it all the way round. It integrates the pattern azimuthally into a profile of intensity against radius, removes a rolling-minimum background and finds the ring peaks by prominence (the height of a peak above the dips on either side of it) with parabolic interpolation to a fraction of a pixel. The rings are then assigned to the standard's d-spacings: each measured ring in turn 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 ring strength with the smallest residual wins, so a missing first ring or a spurious peak does not spoil the fit. Two peaks on the same ring of the standard, such as the two edges of an elliptical ring, count as one ring. When the ellipticity is known (measured below, or found by refine on the ring it centres on), each pixel’s radius is first divided by 1 + ε cos 2(φ − axis). Every ring is then a circle at its mean radius before the profile is taken. Without this step, a 2% distortion smeared neighbouring rings into each other and moved K by about 0.5%. A ring that lies within two half widths of another ring of the standard is a blend: its peak is pulled toward the other ring, so it is listed but K is fitted without it.
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.
Cubic metals and salts with well-known room-temperature lattice parameters. A strained, alloyed or heated specimen has different spacings.
Ring positions are good to a few tenths of a pixel on a sharp ring. With rings out to a large radius and a well-refined centre, K is good to about 0.2 percent.
A diffuse film, a beam stop that cuts the inner rings, or a pattern taken at a different objective-lens setting from your specimen.
The ellipticity here is the distortion at one radius. A full distortion map varies with radius and needs several rings.
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 8-bit and 16-bit TIFF (uncompressed, LZW, Deflate or JPEG inside the TIFF), PNG and JPEG images. The beam stop (the darkest part of the pattern, joined to the middle) is left out, and rings are only looked for beyond the circles that are more than half beam stop or clipped, so a beam stop or a saturated centre does not pull the centre or add false rings; the readout says how much was left out. A negative (dark rings on a light background) is read with the “dark rings on light bkgd” box, which inverts the grey levels before any of this.
The page checks the pattern you load and says so next to the result when:
Checked (October 2026). The ring positions follow from the lattice parameters in the table: gold with a = 4.0786 Å (NBS Circular 539) gives d111 = 2.3548 Å, d200 = 2.0393 Å, d220 = 1.4420 Å and d311 = 1.2297 Å, with radius ratios √(4/3), √(8/3) and √(11/3) to the 111 ring, as the page computes. The electron wavelengths it uses are 3.701, 2.508 and 1.969 pm at 100, 200 and 300 kV (Williams and Carter, Table 1.2).
@misc{tripathy2026ringpatterncalibration,
author = {Tripathy, Manisha},
title = {Ring Pattern Calibration},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tem/ring-calibration}},
note = {Interactive web tool}
}