A Bilinear Interpolation Approach for Wavefront Reconstruction in Rotational Shearing Interferometry

A wavefront reconstruction method based on bilinear interpolation (BLI) is proposed for the rotational shearing interferometer (RSI). The proposed algorithms does not rely on predefined global basis functions. Instead, it directly reconstructs the wavefront from the interferogram wavefront through a pixel-wise interpolation framework, making it particularly suitable for practical implementations based on digital camera sensors. The reconstruction approach is formulated as a linear system describing the relationship between the original wavefront and its rotationally sheared one, thereby enabling numerical recovery of the original wavefront. This study identifies the primary source of reconstruction error in BLI as the neighbor-deficient error occurring near the boundary of a circular ROI, where insufficient neighboring points lead to localized reconstruction artifacts. To overcome this limitation, a padding strategy combined with extrapolation is introduced to recover the neighbor-deficient points before reconstruction. Simulation results demonstrate that the proposed approach effectively eliminates the neighbor-deficient error and significantly improves reconstruction accuracy, reducing the peak-to-valley (PV) error from 0.476λ to 0.003λ with a 9% padding ratio. Over rotational shearing angles ranging from 1° to 179°, the reconstruction errors remain on the order of 10-3λ in PV and 10-6λ in root-mean-square (RMS). The robustness of the proposed method under noisy conditions was also investigated using interferograms corrupted with additive noise corresponding to an SNR of 15, which is representative of practical measurements. Despite the increased reconstruction error under this noise condition, the dominant wavefront characteristics were successfully preserved, as confirmed by the strong agreement between the Zernike coefficients of the original and reconstructed wavefronts.