The manufacturing and characterization of freeform optical surfaces are influenced by their high sensitivity to misalignments. In this work, the computational sampling moiré technique combined with phase extraction is developed for the precise alignment of freeform optics during fabrication and in metrology applications. This novel, to the best of our knowledge, technique achieves near-interferometry-level precision in a simple and compact configuration. This robust technology can be applied to industrial manufacturing platforms (such as diamond turning machines, lithography, and other micro-nano-machining techniques) as well as their metrology equipment. In a demonstration of computational data processing and precision alignment using this method, iterative manufacturing of freeform optical surfaces with a final-form accuracy of about 180 nm was accomplished.