Wave-front measurement errors from restricted concentric subdomains

In interferometry and optical testing, system wave-front measurements that are analyzed on a restricted subdomain of the full pupil can include predictable systematic errors. In nearly all cases, the measured rms wave-front error and the magnitudes of the individual aberration polynomial coefficients underestimate the wave-front error magnitudes present in the full-pupil domain. We present an analytic method to determine the relationships between the coefficients of aberration polynomials defined on the full-pupil domain and those defined on a restricted concentric subdomain. In this way, systematic wave-front measurement errors introduced by subregion selection are investigated. Using vector and matrix representations for the wave-front aberration coefficients, we generalize the method to the study of arbitrary input wave fronts and subdomain sizes. While wave-front measurements on a restricted subdomain are insufficient for predicting the wave front of the full-pupil domain, studying the relationship between known full-pupil wave fronts and subdomain wave fronts allows us to set subdomain size limits for arbitrary measurement fidelity.