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.
Modified QPSK partition algorithm based on MAP estimation for probabilistically-shaped 16-QAM