International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.5, pp. 128-129

Section 2.5.3.3.1. Nonuniform response correction

B. B. Hea*

aBruker AXS Inc., 5465 E. Cheryl Parkway, Madison, WI 53711, USA
Correspondence e-mail: bob.he@bruker.com

2.5.3.3.1. Nonuniform response correction

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A 2D detector can be considered as an array of point detectors. Each pixel may have its own response, and thus a 2D detector may exhibit some nonuniformity in intensity measurement when exposed to an isotropic source. The nonuniform response can be caused by manufacturing defects, inadequate design or limitations of the detector technology. For instance, a nonuniform phosphor screen or coupling fibre optic for a CCD detector may cause nonuniformity in quantum efficiency (Tate et al., 1995[link]). A gas-filled detector may have a different intensity response between the detector edge and centre due to the variation in the electric field from the centre to the edge. A thorough correction to the nonuniformity of the intensity response can be performed if the detector counting curves of all pixels are given. In practice, this is extremely difficult or impossible, because the behaviour of a pixel may be affected by the condition of the adjacent pixels and the whole detector. The practical way to correct the non­uniformity of the intensity response is to collect an X-ray image from an isotropic point source at the instrument centre and use the image data frame to generate a correction table for the future diffraction frames. The frame collected with the isotropic source is commonly referred to as a `flood-field' frame or a flat-field image, and the correction is also called a flood-field correction or flat-field correction (Stanton et al., 1992[link]). Another type of correction for a nonuniform response is background correction. Background correction is done by subtracting a background frame from the data frame. The background frame is collected without X-ray exposure. Integrating detectors, such as image plates or CCDs, have a strong background which must be considered in nonuniform response correction. Photon-counting detectors, such as MWPC and microgap detectors, have negligible background, so background correction is not necessary.

The X-ray source for calibration for flood-field correction should be a uniform, spherically radiating point source. Identical brightness should be observed at any pixel on the detector. The radiation strength of the source should match the intensity of the diffraction data to be collected. The photon energy of the source should be the same as or close to the X-ray beam used for diffraction-data collection so that the detector behaves the same way during calibration and data collection.

There are many choices of calibration sources, including X-ray tubes, radioactive sources, diffuse scattering or X-ray fluorescence. The radioactive source Fe-55 (55Fe) is the most commonly used calibration source for a diffraction system because of its major photon energy level of 5.9 keV. X-ray fluorescence is an alternative to a radioactive source. Fluorescence emission is generated by placing a fluorescent material into the X-ray beam. Fluorescence radiation is an isotopic point source if the irradiated area is a small point-like area. For example, Cu Kα can produce intense fluorescence from materials containing significant amounts of iron or cobalt and Mo Kα can produce intense fluorescence from materials containing yttrium. In order to avoid a high localized intensity contribution from X-ray diffraction, the fluorescent material should be amorphous, such as a glassy iron foil. An alternative to a glassy alloy foil is amorphous lithium borate glass doped with the selected fluorescent element up to a 10% concentration (Moy et al., 1996[link]).

There are many algorithms available for flood-field correction depending on the nature of the 2D detector. The correction is based on the flood-field frame collected from the calibration source. The simplest flood-field correction is to normalize the counts of all pixels to the same level assuming that all pixels have the same response curve. The corrected frame from an isotropic source is not flat, but maintains the cos3 [\phi] falloff effect, which will be considered in the frame integration. For gas-filled detectors, such as MWPC and microgap detectors, the pixel intensity response is not independent, but is affected by X-ray exposure to surrounding pixels and the whole detector. Flood-field correction is carried out by applying a normalization factor to each pixel in which a `rubber-sheet' kind of stretching and shrinking in regions along the x and y detector axes slightly alters the size of each pixel (He, 2009[link]). The total number of counts remains the same after the correction but is redistributed throughout the pixels so that the image from an isotropic source is uniformly distributed across the detector. The flood-field calibration must be done with the same sample-to-detector distance as for the diffraction-data collection.

References

He, B. B. (2009). Two-dimensional X-ray Diffraction. New York: John Wiley & Sons.Google Scholar
Moy, J. P., Hammersley, A. P., Svensson, S. O., Thompson, A., Brown, K., Claustre, L., Gonzalez, A. & McSweeney, S. (1996). A novel technique for accurate intensity calibration of area X-ray detectors at almost arbitrary energy. J. Synchrotron Rad. 3, 1–5.Google Scholar
Stanton, M., Phillips, W. C., Li, Y. & Kalata, K. (1992). Correcting spatial distortions and nonuniform response in area detectors. J. Appl. Cryst. 25, 549–558.Google Scholar
Tate, M. W., Eikenberry, E. F., Barna, S. L., Wall, M. E., Lowrance, J. L. & Gruner, S. M. (1995). A large-format high-resolution area X-ray detector based on a fiber-optically bonded charge-coupled device (CCD). J. Appl. Cryst. 28, 196–205.Google Scholar








































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