Graphical display of the spatial distribution of elements in a specimen has been recognized as a powerful technique since the earliest days of electron-beam x-ray microanalysis. With recent advances in computing power and mass storage, it has become practical to save complete spectra at each pixel rather than simple window counts, providing great flexibility for analytical post-processing. The term "spectrum imaging" has been coined to describe such a data structure.Hunt and Williams give a concise summary of the advantages of spectrum imaging, including the ability to map an element which was not known to be present when the data were acquired, and the ability to integrate spectra from image regions of arbitrary shape to improve statistical precision. Quantitative analysis may also be applied at each pixel to produce a concentration map, which is more informative than the raw or perhaps background-subtracted window counts usually displayed. Sensitive discrimination of phases is possible using various fitting techniques on the pixel spectra, matching them against each other or against standards.

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X-rays are emitted from a relatively large volume in bulk samples, limiting the smallest features which are visible in X-ray maps. Beam spreading also hampers attempts to make geometric measurements of features based on their boundaries in X-ray maps. This has prompted recent interest in using low voltages, and consequently mapping L or M lines, in order to minimize the blurring of the maps.An alternative strategy draws on the extensive work in image restoration (deblurring) developed in space science and astronomy since the 1960s. A recent example is the restoration of images from the Hubble Space Telescope prior to its new optics. Extensive literature exists on the theory of image restoration. The simplest case and its correspondence with X-ray mapping parameters is shown in Figures 1 and 2.Using pixels much smaller than the X-ray volume, a small object of differing composition from the matrix generates a broad, low response. This shape corresponds to the point spread function (PSF). The observed X-ray map can be modeled as an “ideal” map, with an X-ray volume of zero, convolved with the PSF. Figure 2a shows the 1-dimensional case of a line profile across a thin layer. Figure 2b shows an idealized noise-free profile which is then convolved with the PSF to give the blurred profile of Figure 2c.