Effects of focal spot intensity distribution and collimator width in reconstructive x-ray tomography

In computed tomography the finite width of the collimator aperture implies that the image is reconstructed from scans having finite strip width. This blurs the image and limits scanner resolution. Bracewell has discussed the nature of the blurring produced and suggested a method to partially restore the image under the assumption that the x-ray focal spot has a uniform intensity distribution. However, pinhole radiographs of x-ray focal spots reveal intensity distribution in the scanning plane which peaks at the edges of the focal spot with a reduced intensity in the center. A model is presented which simulates this intensity distribution as the sum of two point sources of x rays separated by a uniform line source. This results in a point absorber response function which is a superposition of two rectangular distributions and the one discussed by Bracewell. The corresponding tranfer function is derived which shows that the intensity distribution of the focal spot influences the high spatial frequency components of the reconstructed image more than the low frequency components.