In quantitative deflectometry, a test optical component is generally divided into numerous sample regions by the pixels on a camera's CCD detector, and the adjacent intervals of sample regions are unequal in off-axis configurations. In this case, errors will be introduced in the reconstruction result if the traditional Southwell zonal integration method is arbitrarily used. Thus, an improved zonal method is proposed in this paper. Both simulations and experiments are conducted to demonstrate the validity and accuracy of the improved zonal method. In the simulations, compared with the traditional zonal method, the reconstruction accuracy for three different figures of sphere, hyperbolic, and flat surfaces using our proposed method is obviously improved, especially when the aperture of the test optics is not rectangular, but circular. Experimental results also show that when we integrate the slopes measured at unequal-spaced sampling points, the proposed zonal method is superior to the traditional zonal method in accuracy; meanwhile, it has advantages over the modal methods in reconstructing local detail information, such as a slight surface scratch, on the test optical component.
We present a modal wavefront reconstruction from slope measurements for rectangular optical components of high-power laser systems. Wavefront reconstruction with slope data is an important approach used for wavefront control or correction in high-power systems. In this work, we derive a complete set of orthonormal wavefront slope polynomials for rectangular apertures and describe the modal method for obtaining wavefront representation with the aberration balancing property. Error propagation properties for the modal method are evaluated and compared with the Southwell method. The cross-coupling error is also discussed. Numerical experiments are conducted to illustrate that the modal method can achieve a higher accuracy than the Southwell method. In addition, we also investigate the influence of noise on the modal method compared with that of the Southwell method.
Based on the Legendre polynomials expressions and its properties, this article proposes a new approach to reconstruct the distorted wavefront under test of a laser beam over square area from the phase difference data obtained by a RSI system. And the result of simulation and experimental results verifies the reliability of the method proposed in this paper. The formula of the error propagation coefficients is deduced when the phase difference data of overlapping area contain noise randomly. The matrix T which can be used to evaluate the impact of high-orders Legendre polynomial terms on the outcomes of the low-order terms due to mode aliasing is proposed, and the magnitude of impact can be estimated by calculating the F norm of the T. In addition, the relationship between ratio shear, sampling points, terms of polynomials and noise propagation coefficients, and the relationship between ratio shear, sampling points and norms of the T matrix are both analyzed, respectively. Those research results can provide an optimization design way for radial shearing interferometry system with the theoretical reference and instruction.
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