Correction for collimator width (restoration) in reconstructive X-ray tomography

Abstract

X-ray measurements made by scanning in a plane, in successive position angles, involve a degradation (smoothing, or blurring) associated with the nonzero width of the strip occupied by the X-ray beam. The collimating holes that define the X-ray beam cannot be made indefinitely small without increasing the X-ray source power indefinitely. However, making a tomogram from the strip integrals is usually handled as though the data consisted of line integrals. The result is that each infinitesimal element of the tomogram is spread out into a density distribution resembling a cone with a central crater. Restoration of the tomogram to correct for the blurring associated with the strip width is warranted and will receive greater attention as the precision of measurements increases and as demand for resolution approaching that of conventional radiography begins to push instrumental design against various limits. Restoration is a well-developed subject, but in each field of application has its own peculiarities. Systematic and statistical properties of tomograms, the character of their errors, and the desired information will influence the future development of restoration in tomography. X-ray tomography is also special in that diffraction of the rays is negligible and that sharp shadow edges may be formed.