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

TL;DR

This paper discusses how non-orthogonal polynomial models in astrometry can cause magnified errors, and proposes converting them into orthonormal models for improved accuracy and interpretability.

Contribution

It introduces a method to transform non-orthogonal distortion models into orthonormal ones, enhancing the robustness and clarity of astrometric corrections.

Findings

Orthogonal models reduce error magnification.

Conversion to orthonormal basis is feasible for rectangular fields.

Orthonormal coefficients directly indicate term significance.

Abstract

The non-orthogonality of algebraic polynomials of field coordinates traditionally used to model field-dependent corrections to astrometric measurements, gives rise to subtle adverse effects. In particular, certain field dependent perturbations in the observational data propagate into the adjusted coefficients with considerable magnification. We explain how the worst perturbation, resulting in the largest solution error, can be computed for a given non-orthogonal distortion model. An algebraic distortion model of full rank can be converted into a fully orthonormal model based on the Zernike polynomials for a circular field of view, or a basis of functions constructed from the original model by a variant of the Gram-Schmidt orthogonalization process for a rectangular field of view. The relative significance of orthonormal distortion terms is assessed simply by the numerical values of the corresponding coefficients. Orthonormal distortion models are easily extendable when the distribution of residuals indicate the presence of higher order terms.