The manufacturing and characterization of freeform optical surfaces are influenced by their high sensitivity to misalignments. 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 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. Its computational data processing and precision alignment demonstration accomplished an iterative manufacturing of freeform optical surfaces with a final-form accuracy of about 180 nm.