Early two-dimensional reconstruction and recent topics stemming from it.

In 1955 I was a Lecturer in Physics at the University of Cape Town when the Hospital Physicist at the Groote Schuur Hospital resigned. South African law required that a properly qualified physicist supervise the use of any radioactive isotopes, and since I was the only nuclear physicist in Cape Town, I was asked to spend 1 1/2 days a week at the hospital attending to the use of isotopes, and I did so for the first half of 1956. I was placed in the Radiology Department under Dr. J. Muir Grieve, and in the course of my work I observed the planning of radiotherapy treatments. A girl would superpose isodose charts and come up with isodose contours which the physician would then examine and adjust, and the process would be repeated until a satisfactory dose-distribution was found. The isodose charts were for homogeneous materials, and it occurred to me that since the human body is quite inhomogeneous these results would be quite distorted by the inhomogeneities a fact that physicians were, of course, well aware of. It occurred to me that in order to improve treatment planning one had to know the distribution of the attenuation coefficient of tissues in the body, and that this distribution had to be found by measurements made external to the body. It soon occurred to me that this information would be useful for diagnostic purposes and would constitute a tomogram or series of tomograms, though I did not learn the word “tomogram” for many years. At that time the exponential attenuation of Xand gamma-rays had been known and used for over sixty years with parallel sided homogeneous slabs of material. I assumed that the generalization to inhomogeneous materials had been made in those sixty years, but a search of the pertinent literature did not reveal that it had been done, so I was forced to look at the problem ab initio. It was immediately evident that the problem was a mathematical one which can be seen from Fig. 1. If a fine beam of gamma-rays of intensity I, is incident on the body and the emerging intensity is I, then the measurable quantity g = In(I0/I) = SLfds, where f is the variable absorption coefficient along the line L. Hence if f is a function in two dimensions, and g is known for all lines intersecting the body, the question is: “Can f be determined if g is known ?“. Again this seemed like a problem which would