Determination of the orientation distribution function for collagen fibrils in a connective tissue site from a high-angle X-ray diffraction pattern

Improved techniques are described for determining the orientation distribution function, g(φ), for collagen fibrils in a connective tissue site from a single high-angle X-ray diffraction pattern. Such patterns are dominated by equatorial diffraction from the collagen fibrils. An interactive computing method is described for measuring the angular intensity distribution through the intensity maxima of this equatorial pattern. The distribution can be represented as a sum of even-ordered Legendre polynomials multiplied by appropriate coefficients. This procedure is also applied to elastoidin spicules in which the collagen is perfectly oriented. Division of one set of coefficients by the other then yields a set of coefficients which allows g(φ) to be calculated by summation of a series of even-ordered Legendre polynomials; a method is described which allows the number of terms required to be determined.