Analysis of multi-wavelength co-phasing detection method for segmented mirrors using enumeration

We present a multi-wavelength piston error enumeration detection (MPEED) method and a corresponding wavelength combination selection framework to address the typical limitations of multi-wavelength techniques in segmented mirror co-phasing stage. We analyze four key performance metrics and two influencing factors, and reveal how single-wavelength detection errors and wavelength selection can reduce the theoretical piston capture range to a smaller practical range, leading to the “edge jump” phenomenon and degraded accuracy and precision. Unlike most existing multi-wavelength approaches, our framework explicitly incorporates these constraints and maps the two influencing factors to practical engineering disturbances, thereby enhancing robustness and providing a theoretical foundation for wavelength selection in practical applications. Applied to the visible spectrum, the framework identifies 13 candidate quaternary wavelength combinations that enable ±100μm piston error measurements with tolerance to ±0.03λ single-wavelength detection errors and ±0.1nm central wavelength shifts. Large-scale simulations confirm its robustness and effectiveness.