Interpolation (mapping) of data from a given antenna array onto the output of a virtual array of more suitable configuration is well known in array signal processing. This operation allows arrays of any geometry to be used with fast direction-of-arrival (DOA) estimators designed for linear arrays. Conditions for preserving DOA error variance under such mappings have been derived by several authors. However, in many cases, such as omnidirectional signal surveillance over multiple octaves, systematic mapping errors will dominate over noise effects and cause significant bias in the DOA estimates. To prevent mapping errors from unduly affecting the DOA estimates, this paper uses a geometrical interpretation of a Taylor series expansion of the DOA estimator criterion function to derive an alternative design of the mapping matrix. Verifying simulations show significant bias reduction in the DOA estimates compared with previous designs. The key feature of the proposed design is that it takes into account the orthogonality between the manifold mapping errors and certain gradients of the estimator criterion function. With the new design, mapping of narrowband signals between dissimilar array geometries over wide sectors and large frequency ranges becomes feasible.