First, the degree of monochromaticity and collimation of the incident and detected beams is addressed. As µ is a function of atomic density, n, incident energy, E, and atomic number, Z, it is important to use both a monochromatic incident beam and to detect only those transmitted photons that do not interact further with the object. Perfect silicon crystal monochromators have been used to retain only those transmitted photons with energy E and have also been used to reduce the detection of low angle scattered radiation. Some representative images of osteoporotic bone using polychromatic and monochromatic incident beams, with and without the silicon monochromators and collimators illustrate the improvement in image quality.

Second, a program is underway to examine the parameterisation of µ [1] in order to allow three mono-energy CT scans to more accurately determine specimen characterisation. The additivity rule for the linear attenuation coefficient may be expressed as

where the three cross-sections are the coherent, incoherent and photo-electric terms respectively. Using a synchrotron radiation source a series of uniform, low atomic number and low density specimens have been investigated over the energy range 8 to 20.5 keV. The results indicate that a correction factor, arising from an expansion of Z/Z, is required in materials containing hydrogen, while the results for CO₂ indicate that no additional correction term is required.

The third aspect of this work to improve CT image quality has involved a study of the effect of the accuracy of the reconstructed image using phantoms and simple test objects, as a function of the reconstruction filter used in the summation- convolution-back-projection (SCBP) method. A projection p (x_r) at the angel is composed of a set of ray sums at the translation position x_r. The "best" image that is possible, assuming low noise data, is obtained using the Ram-Laks [2], or ramp, filter as used in the expression.

where P(X_R) is the 1D Fourier transform of p(x_r), and the is the ramp filter referred to above. In many instances the data is noisy and the filter is augmented by multiplying with a low- pass term W(X_R), with W(X_R=0) =1. It has been found that the departure from the true value of µ after using this form of smoothing can be determined at each pixel position and is proportional to the second derivative of the smoothing term evaluated at the DC spatial frequency, W"(0). Typical results will be presented to support these findings. REFERENCES

1. D. F. Jackson and D. J. Hawkes, "X-ray Attenuation Coefficients of Elements and Mixtures", Physics Reports, Vol. 70, No. 3, pp. 169-233, 1981
2. G. N. Ramachandran and A. V. Lakshminarayanan, "Three Dimensional Reconstruction from Radiographs and Electron micrographs: Applications of Convolutions Instead of Fourier Transforms", Proc. Natl. Acad. Sci. U. S. A., Vol. 68, pp. 2236- 2240, 1971