A method utilizing matrix analysis has been presented for a full-area three-flat test. With the aid of the Moore–Penrose pseudoinverse of a circulant matrix, a set of closed mathematical formulas has been derived to obtain the absolute profiles of samples. According to the simulation results, the matrix analysis method shows better performances for determining the absolute profiles and suppressing the decorrelation residuals of the reconstructed wavefronts, compared to the iterative method. Three optical flats with 135-mm apertures are measured. The results obtained with the new method agree well with those obtained with the iterative algorithm and the classical three-flat test. Furthermore, the relationship between the decorrelation residual and the wavefront error introduced in the rotation measurement has been studied. Theoretical and experimental results show that the odd-symmetric component contributes significantly to the decorrelation residual.
In a high-power laser system, thermally induced aberrations, which can influence the laser beam quality, are caused by thermal deformations of the optical elements when they are irradiated by the laser. We evaluate the mechanism responsible for the influence of thermally induced aberrations on the laser beam quality factor (M2) using the finite element method and angular spectrum theory. The thermally induced aberrations are decomposed into their constituent Zernike terms, showing that the influence of the thermally induced aberrations on M2 comprises a mixed contribution of different aberrations. The M2 of a fiber laser is simulated and measured when the laser transmits through organic glass. The simulation results have a good consistency with the experimental results, indicating that the method used in this study is effective when analyzing the influence of thermally induced aberrations on M2.