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An efficient way of estimating orthonormal aberration coefficients on variable noncircular pupils is proposed. The method is based on the fact that all necessary pieces of information for constructing orthonormal polynomials (via the Gram-Schmidt process) can be numerically obtained during a routine least-squares fit of Zernike polynomials to wavefront data. This allows the method to use the usual Zernike polynomial fitting with an additional procedure that swiftly estimates the desireddoi:10.1364/ol.35.002173 pmid:20596184 fatcat:i4sv52btsbhrzeebogehm443ju