X-ray images of small blood vessels in angiography: question of isoplanatism.

The basic theory of x-ray image formation of blood vessels, which is related to isoplanatism, is discussed. The x-ray intensity distributions of the blood vessel images are derived first for the actual case, which gives "correct" x-ray images obtained by the ray-tracing method. Secondly, as an approximation of the actual case, the image distributions are derived by the convolution method, which corresponds to an isoplanatic case. It is concluded that, under practical conditions, x-ray images of blood vessels are given approximately by a convolution integral of the object distribution, that is, the input x-ray pattern of the vessel exposed with a parallel x-ray beam, with the line spread function of geometric unsharpness. Therefore, this theory provides support for the experimental procedure commonly used in obtaining blood vessel images, and for the validity of applying in angiography the concept of the line spread function and the modulation transfer function of geometric unsharpness.