In inertial confinement fusion high energy system, the mid-spatial frequency (MSF) errors of optical elements induced by computer numerical control tools lead to damage to the optical system. Based on the characteristics of the mid-spatial frequency errors, it is measured by using phase retrieval technology. Compared with conventional measurement methods such as interferometry, MSF errors can be measured by phase retrieval without complex measurement systems and large aperture optical elements with MSF errors can be measured via phase retrieval in theory. In this paper, we compare multiple phase retrieval algorithms that are used to measure optical element with MSF errors and explore approaches to improve the quality of results. First, we briefly introduce the feature of MSF errors and the relation between the wavefront of optical element with MSF errors and its diffraction pattern. Second, multiple phase retrieval algorithms including error-reduction (ER) algorithm, hybrid input-output (HIO) algorithm and oversampling smoothness (OSS) algorithm are adapted for the measurement of MSF errors. According to the bandwidth and structure characteristics of MSF errors, the convergence speed and the accuracy of above algorithms are discussed and compared. Then, according to the characteristics of different algorithms, different retrieved wavefront phase via using these algorithms are integrated to improve the accuracy of results. Last, based on the feature of MSF errors, the priori knowledge of algorithms is also discussed to further gear up the convergence speed and the accuracy of algorithms.
Large-aperture and long focal-length lens is widely used in high energy laser system. The method based on Talbot interferometry is a reliable method to measure the focal length of such elements. By employing divergent beam and two gratings of different periods, this method could realize full-aperture measurement, higher accuracy and better repeatability. However, it does not take into account the spherical aberration of the measured lens resulting in the moiré fringes bending, which will introduce measurement error. Furthermore, in long-focal measurement with divergent beam, this error is an important factor affecting the measurement accuracy. In this paper, we propose a new spherical aberration compensation method, which could significantly reduce the measurement error. Characterized by central-symmetric scanning window, the proposed method is based on the relationship between spherical aberration and the lens aperture. Angle data of moiré fringes in each scanning window is retrieved by Fourier analysis and statistically fitted to estimate a globally optimum value for spherical-aberration-free focal length calculation. Simulation and experiment have been carried out. Compared to the previous work, the proposed method is able to reduce the relative measurement error by 50%. The effect of scanning window size and shift step length on the results is also discussed.