Unified variational framework for simultaneous correction of non-uniform sampling and diffraction-induced slope errors in coherence scanning interferometry.

Coherence scanning interferometry (CSI) enables non-contact surface measurement with high axial resolution, but its accuracy is degraded in practical complex-surface metrology by two coupled effects: vibration-induced non-uniform axial sampling and diffraction-induced slope/edge errors. Axial-position sensing can provide frame-wise scanning positions, but it does not correct the optical-transfer-function degradation caused by finite-aperture imaging. Conversely, conventional inverse filtering compensates for diffraction-related attenuation but usually assumes uniform axial sampling. This paper proposes a unified variational reconstruction framework that incorporates measured non-uniform axial positions into an NUFFT-based CSI forward model with sparse regularization. The proposed method jointly models non-uniform sampling and optical-transfer-function degradation, and is evaluated against uniform-sampling inverse filtering, non-uniform least-squares phase recovery, and a two-step adjoint-NUFFT/IF baseline. Numerical simulations demonstrate improved robustness under strong sampling non-uniformity, residual axial-position errors, detector noise, and varying spectral widths. For the tested step sample, the proposed method achieves a step-height error of 0.052 nm and suppresses directional batwing artifacts to approximately the nanometer level. GPU implementation on an NVIDIA RTX 5070 Ti processes a representative 400×400×500 volume in 8.929 s, with only about 12.5% overhead relative to the two-step adjoint-NUFFT/IF baseline. These results indicate that the proposed framework is promising for calibrated CSI systems with available frame-wise axial positions.