A study by the Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, titled "Error separation method in null interferometric testing of freeform mirrors," published in the journal Optics and Lasers in Engineering, reports a comprehensive error separation methodology and achieves highly precise calibration for advanced optical surface measurements.

Freeform mirrors represent a revolutionary leap forward in modern optical designs. Unlike conventional spherical or symmetric aspherical lenses, these mirrors possess non-symmetric, complex shapes that offer unprecedented design freedom. This unique geometry allows engineers to create extremely compact, lightweight, and high-performance optical systems, which are essential for space exploration telescopes, virtual reality headsets, and advanced semiconductor lithography equipment. However, manufacturing these sophisticated surfaces requires testing them with nanometer-level accuracy. Scientists typically use laser interferometers combined with customized computer-generated holograms to measure the shape of the mirror. Despite the high precision of these instruments, the physical setup inevitably introduces alignment errors, while the holograms themselves contain subtle fabrication flaws. These blended errors distort the test results, creating a major metrology bottleneck where engineers struggle to distinguish the true surface figure of the manufactured mirror from the imperfections of the measuring system itself.

To resolve this critical measurement ambiguity, the research team develops an integrated mathematical framework that systematically isolates and removes these coupled errors. First, the researchers establish a sensitivity matrix model to analyze how tiny misalignments in the optical test setup affect the final measurement results. By employing a damped least-squares mathematical algorithm, the system calculates the exact alignment parameters. This calculation allows the model to mathematically separate the low-order aberrations, such as astigmatism and coma, induced by setup errors.

Second, to address the errors originating from the computer-generated hologram itself, the team introduces a two-angle measurement technique. By rotating the freeform mirror to specific angles, the system captures multiple interferometric data sets. Since the fabrication errors of the hologram remain stationary while the optical projection of the rotated mirror changes, the algorithm successfully extracts and isolates the subtle substrate and manufacturing errors of the hologram from the actual surface profile of the mirror. This systematic approach effectively cleans the measurement data of external instrument errors, leaving only the genuine surface map of the tested optical element.

The experimental implementations show that this combined error separation method significantly enhances the reliability of freeform mirror testing. By accurately neutralizing alignment deviations and hologram fabrication errors, the framework reveals the true surface shape of the optical components with extreme precision. This breakthrough effectively removes the reliance on perfect calibration components, lowering the manufacturing cost of high-precision optics while expanding their design limits. Ultimately, this robust diagnostic methodology offers a practical design reference for optical metrology, paving the way for the development of next-generation space observation instruments and ultra-precision industrial manufacturing systems.