Researchers from the Changchun Institute of Optics, Fine Mechanics and Physics have developed an in-situ absolute measurement method for optical flats, offering a more reliable way to characterize ultra-precision optical surfaces under real working conditions. The study introduces an improved four-flat interferometric approach that can separate multiple sources of measurement error at the same time, helping push optical surface metrology toward sub-nanometer accuracy. The research was published inOptics & Laser Technology.

Optical flats are fundamental components in precision optical systems, where surface quality directly affects imaging, beam control, and system stability. In large telescopes, high-power laser facilities, semiconductor equipment, and other advanced instruments, even extremely small surface deviations can degrade performance. Measuring such surfaces, however, is not straightforward. Conventional interferometric methods compare an unknown surface with a reference flat, which means the final result is often limited by the quality of that reference. In practice, this creates a difficult problem: the more precise the surface being tested, the harder it becomes to find a reference accurate enough to measure it.

To overcome this limitation, the research team turned to the classic four-flat method, an absolute measurement strategy designed to recover the real surface shape without relying entirely on a superior reference. But the traditional version of this method still faces an important obstacle in horizontal measurement setups. In such systems, the auxiliary transmission flat can deform under its own weight or due to clamping stress from the mounting structure. These effects become mixed into the interferometric signal, making it difficult to tell whether an observed error comes from the test surface itself or from the measurement setup.

The new work addressed this problem by redesigning both the measurement sequence and the data-processing model. The researchers built a four-step interferometric procedure involving a reference flat, an auxiliary transmission flat, and a test flat. During the measurement, only the auxiliary flat was rotated and flipped, while the reference and test optics remained fixed in place. This arrangement preserved the in-situ configuration of the system and avoided repeated disassembly or realignment. More importantly, the team introduced a Moore–Penrose pseudoinverse-based reconstruction algorithm to separate different error sources mathematically, including gravity-induced deformation and clamping-induced distortion of the auxiliary optic.

A notable advantage of the method is that it improves the recovery of surface features that are traditionally difficult to reconstruct, especially low-order terms such as power. In conventional absolute tests, these components can be masked by mechanical deformation or become entangled with reference errors. In the new framework, however, the measurement data were processed in a way that distinguished distortions that stay fixed in the laboratory frame from those that rotate with the auxiliary flat. This made it possible to isolate the actual surface figure more faithfully and to recover the absolute topography of the optical flat with higher confidence.

The team first verified the method through numerical simulation, showing that the reconstruction model remained stable under realistic levels of noise, rotation error, and pixel misalignment. They then carried out proof-of-concept experiments using 4-inch optical flats and intentionally introduced clamping stress to simulate the kinds of deformation encountered in large-aperture systems. The experimental results showed that the proposed method achieved an absolute measurement accuracy of about 0.9 nm RMS, with a repeatability of about 0.5 nm RMS. Cross-validation tests using different reference and auxiliary flats further confirmed the robustness of the approach.

Beyond the reported accuracy, the broader significance of the study lies in its practical measurement philosophy. Rather than trying to eliminate every mechanical disturbance in advance, the method was designed to identify and decouple those disturbances from the measurement itself. This makes it especially attractive for in-situ testing of large optical components, where gravity, mounting conditions, and environmental effects are difficult to avoid completely.

The researchers believe the method could provide a cost-effective and scalable route for high-precision optical calibration in next-generation astronomical telescopes, high-energy laser facilities, and other advanced optical systems that demand both large apertures and extremely stable surface figures.