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The non-orthogonality of algebraic polynomials of field coordinatestraditionally used to model field-dependent corrections to astrometricmeasurements, gives rise to subtle adverse effects. In particular, certainfield dependent perturbations in the observational data propagate into theadjusted coefficients with considerable magnification. We explain how the worstperturbation, resulting in the largest solution error, can be computed for agiven non-orthogonal distortion model. An algebraic distortion model of fullrank can be converted into a fully orthonormal model based on the Zernikepolynomials for a circular field of view, or a basis of functions constructedfrom the original model by a variant of the Gram-Schmidt orthogonalizationprocess for a rectangular field of view. The relative significance oforthonormal distortion terms is assessed simply by the numerical values of thecorresponding coefficients. Orthonormal distortion models are easily extendablewhen the distribution of residuals indicate the presence of higher order terms.

The Worst Distortions of Astrometric Instruments and Orthonormal Models for Rectangular Fields of View