Model reference adaptive control-based differential confocal global subaperture concentric-spherical automatic stitching measurement method

To address the demand for high-precision surface profiling of non-full spherical surfaces and the issues of low accuracy, inefficiency, and poor stability associated with current manual subaperture stitching measurement methods, this paper proposes a model reference adaptive control (MRAC)-based automatic stitching method for differential confocal global subaperture measurements using a common sphere centre. Utilising MRAC as the decision centre for global pose control of the tested mirror, it generates desired trajectories via reference models and adapts control parameters online through adaptive laws, thereby resolving the issues of insufficient robustness and ineffective suppression of non-linear disturbances caused by fixed parameters in traditional PID control. High-resolution axial focusing achieved through laser differential confocal zero-crossing fitting provides nanometre-level co-centredness reference input to MRAC, establishing a unified global co-centredness origin for stitching. In-situ multi-aperture phase-shifting interference stitching enables MRAC to implement high-precision closed-loop feedback, accomplishing high-fidelity surface data acquisition and phase reconstruction. This approach achieves high-precision, high-stability, and high-efficiency automated stitching measurement of non-full spherical surface using a global subaperture co-centred approach. Based on the proposed method, an MRAC-based differential confocal global subaperture concentric-spherical automatic stitching measurement instrument was constructed. Experimental results demonstrate that the axial focusing accuracy of the proposed method is better than 40 nm, the adaptive pose-control accuracy of the measured mirror reaches 0.74 μm (0.012%), the RMS repeatability of the full-area automatic stitching measurement is better than 0.00042λ (λ = 632.8 nm) and a single stitching measurement cycle is completed within 4.4 min, which transcends the performance limitations of fixed-gain control, offering an effective technical approach for high-precision, high-efficiency, and highly robust automatic stitching measurement of non-full spherical surfaces.