When optical fibres are made by first constructing optical-fibre preforms, the fibre which is pulled from the heated preform is simply a scaled down version of the original preform structure. The expansion coefficient profile α(r) of the preform, which relates directly to the fabrication variables, can be determined from non-destructive optical retardation measurements δ(r) performed on the preform. In addition, the residual elastic stress distributions in a fabricated preform, which can be used to compare different fabrication procedures, have simple definitions as linear functionals of the expansion coefficients α(r). Thus, through the use of optical retardation data, an examination of different manufacturing procedures for preform fabrication is reduced to a problem in non-destructive manufacturing procedures for preform fabrication is reduced to a problem in non-destructive testing and analysis. The underlying numerical problem of evaluating the stres distributions reduces to solving and Abel-type integral equation for α(r), which involves an indeterminacy, followed by the evaluation of linear functionals defined on α(r). It is shown how the known inversion formulae for the Abel-type integral equation can be used formally to reduce the numerical problem of evaluating the radial stress to the evaluation of a linear functional defined on the data δ(r) which bypasses the indeterminacy. When only the radial stress is required, the problem of actually solving the Abel-type integral equation is avoided. Methods for evaluating the non-radial stresses, which avoid the indeterminacy, are also derived.