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.
The ripple errors of the lens lead to optical damage in high energy laser system. The analysis of sidelobe on the focal plane, caused by ripple error, provides a reference to evaluate the error and the imaging quality. In this paper, we analyze the diffraction characteristics of sidelobe of optical elements with ripple errors. First, we analyze the characteristics of ripple error and build relationship between ripple error and sidelobe. The sidelobe results from the diffraction of ripple errors. The ripple error tends to be periodic due to fabrication method on the optical surface. The simulated experiments are carried out based on angular spectrum method by characterizing ripple error as rotationally symmetric periodic structures. The influence of two major parameter of ripple including spatial frequency and peak-to-valley value to sidelobe is discussed. The results indicate that spatial frequency and peak-to-valley value both impact sidelobe at the image plane. The peak-tovalley value is the major factor to affect the energy proportion of the sidelobe. The spatial frequency is the major factor to affect the distribution of the sidelobe at the image plane.