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.
Star tracker is a high-accuracy attitude determination device widely used in spacecraft. A traditional star tracker obtain the attitude angle by calculating the centroids of star spots on photo detector. However, the directional accuracy is limited to arc-second level. In this paper, we introduce an interferometric star tracker. The interferometric star tracker improve the attitude accuracy by using interferometric components, the interference components consist of two identical gratings and several wedge plates. Tiny change of incident angle can be sensed by detecting the relative intensity of spots divided by the wedge plates. Optical design and accuracy analysis of interferometric star tracker were illustrated in this paper. The theoretical analysis indicates that accuracy of interferometric star tracker depend on the grating distance, grating period and gray level. In the laboratory experiment, the results show that that the relationship between the light intensity of each spot and incident angle can be expressed as a sinusoidal function, and the gray level difference of each spot can reach 1500, which means the accuracy can reach '' 0.2 or even higher.
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.
A traditional tracking device obtain the attitude angle by analyzing the spots position on photodetector. However, the attainable angular measurement accuracy depends on the field of view (FOV), number of pixels of the photodetector and the centroiding algorithm. In this paper, we present a high-precision attitude angle measuring system based on Talbot interferometry using cross-gratings and four wedge plates, which can acquire the real-time change of incident angle along two axis. The specific structure of the system is introduced, and the formula for calculating the relative angle is derived. The tracking accuracy is analyzed to be better than 0.2 arcsecond, which is dependent on the grating period, the distance between the two gratings and the gray scale of image. The Simulation results show that the RMS error of relative angle is better than 0.1 arcsecond both in x and y direction.
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.