Large-aperture fused silica phase optical components such as continuous phase plate (CPP) are widely used in large-scale laser devices to achieve beam homogenization and improve beam quality. However, under the action of high-energy lasers, their lower damage threshold seriously restricts their service life and increases cost of using. Compared with other fused silica components, chemical processing technology with hydrofluoric acid solution (HF) is lacking in the processing of phase components because the residual root mean square value (RMS) of phase elements is very high, and it can not guarantee this. Therefore, it is necessary to carry out research on the influence of chemical treatment on phase components. In this paper, we improved the chemical treatment process to achieve the change of residual RMS value not more than 3 nm, and improved the ability of resisting laser damage that the damage threshold of 29J/cm 2 was obtained under the test conditions 351nm@3ns. Finally, we successfully mastered the chemical control process of phase components and applied it to the CPPs as other fused quartz materials engineering production process.

Freeform surfaces play an important role in modern optical systems with compactness and better performance. The fabrication tools tend to impart a structured signature on optical surfaces, called ripple errors, during the freeform surface manufacturing process. The description and extraction of ripple errors for freeform surface fabrication and testing have attracted extensive attention. In this paper, we develop a fast and accurate method to describe ripple errors for the large aperture based on Fourier model coupling. The polynomial expression is transformed into Fourier series form and surface errors are reconstructed by frequency feature extraction combining with the least square method. The high accuracy and efficiency of the proposed method for representing and filtering ripple errors consuming little computer memory are demonstrated using real experimental data. The proposed method offers a robust and powerful tool not only suitable for surface error characterization but also for image filtering and analysis.

Parameters mismatching between the real optical system and phase retrieval model undermines wavefront reconstruction accuracy. The three-dimensional intensity position is corrected in phase retrieval, which is traditionally separated from lateral position correction and axial position correction. In this paper, we propose a three-dimensional intensity position correction method for phase diverse phase retrieval with the cross-iteration nonlinear optimization strategy. The intensity position is optimized via the coarse optimization method at first, then the intensity position is cross-optimized in the iterative wavefront reconstruction process with the exact optimization method. The analytic gradients about the three-dimensional intensity position are derived. The cross-iteration optimization strategy avoids the interference between the incomplete position correction and wavefront reconstruction during the iterative process. The accuracy and robustness of the proposed method are verified both numerically and experimentally. The proposed method achieves robust and accurate intensity position correction and wavefront reconstruction, which is available for wavefront measurement and phase imaging.

Phase retrieval is an attractive optical testing method with a simple experimental arrangement. The sampling grids wave propagation computation based on the FFT operations is usually involved in each iterative process for the classical phase retrieval model. In this paper, a novel non-propagation optimization phase retrieval technique with the FFT-based basis function is proposed to accelerate wavefront measurement. The sampling grids wave diffraction propagation computation is converted to matrix-vector products that have small dimensions to reduce the computational burden. The diffraction basis function based on generalized numerical orthogonal polynomial and two-step Fresnel propagation is deduced, which is suitable for the generally shaped pupil. This paper provides a universal non-propagation framework to accelerate phase retrieval which is applicable to the arbitrarily shaped wavefront measurement.

The specification and characterization of mid-spatial-frequency (MSF) ripples for the large-square-aperture optical elements, typically used in high-power laser systems, have received considerable critical attention. It is necessary to resort to a simple and robust way to characterize error surfaces for facilitating prediction of performance degradation and guiding the fabrication and tolerance settings. In this paper, we characterize residual periodic surface undulations called ripple errors for the large square aperture generated from modern subapertures and deterministic optical fabrication techniques through two methods, taking a step from qualitative judgment to quantitative analysis. The cross artifact reduction technology, instead of traditional windowed preprocessing, is introduced into power spectral density to suppress spectrum leakage while retaining the information about the part. An efficient algorithm to generate Legendre moments for two-dimensional Legendre polynomials is proposed to quantify ripple errors. This work contributes to understanding the optical degradation caused by MSF errors and associating the design and performance index with surface parametric description.

Magnetorheological polishing technology is a new type of ultra-precision processing technology. It has many advantages such as no sub-surface defects, easy realization of numerical precision control, high machining accuracy, and high polishing efficiency; and its small removal function size makes it very suitable for processing optical elements with complex geometric structures. It has been widely used in phase optical processing. In order to realize the processing of phase optical elements with a small space periodic structure, a smaller removal function is required. The traditional magnetorheological fluid circulation system structure is difficult to achieve stable control of the magnetorheological fluid flow under small flow conditions. Therefore, it is difficult to obtain a stable small size removal function. This paper analyzes the characteristics of the peristaltic pump, and aiming at the problem of strong pulse in its output flow; uses a pulsation damper and a variable-diameter back pressure pipeline to eliminate the flow pulse, realizes the stable and smooth output of the peristaltic pump flow. On this basis, this paper proposes a new type of magnetorheological fluid circulation system structure, which realizes the stable control of the flow rate under small flow rate conditions. The magnetorheological fluid flow fluctuation error of the magnetorheological fluid circulation system was from more than 25% reduced to less than 2%, realizing high stability control of magnetorheological fluid flow. Use small size removal function to process Continuous Phase Plates (CPP) with large depth and small periodic structure. The CPP is designed with a PV of 5μm and a minimum space period of 3mm. After processing, the residual error RMS of the CPP from 830nm converges to 24.5nm, realize high-precision processing of phase components with large depth and small structure.

In order to measure the aspherical transmission wavefront of large aperture optics with wedged angle, three compensators were fabricated based on theories of geometrical and diffraction optics, a single null lens and two computer-generated-holograms (CGH) by different frequecy carrier. The results show that both refraction null compensator and diffraction plate can achieve high-precision wavefront measurement of large aperture aspherical optics, the difference of wavefront measured by refraction and diffraction methods is better than 0.01λ(RMS) in the effective aperture area. Because of the measure beam deviation caused by the optic wedge, the results is very sensitive to parts position and gesture. Due to a smaller divergence angle and extra alignment/fiducial area for precision adjustment, the primary aberrations of tilted CGH measurment can get a better control than that of null compensator. Precise control or adjustment of compensator is critical for aspherical wavefront measurement. Null compensator lens can easily induce regulation error while CGH method could cause mid-frequency disturbance.

The non-perfect determined amplitude distribution in the pupil would affect the convergence speed and accuracy of phase retrieval method, which depends on the amplitude of fields to reconstruct the phase. In this paper, we propose two kinds of phase retrieval methods based on hybrid point-polynomial and point-by-point nonlinear optimization algorithms to reconstruct simultaneously the amplitude and phase of the wavefront. Intensity quantized errors are avoided by using modified first derivatives. For simple and general wavefront testing, the accuracy and robustness of proposed algorithms are verified both numerically and experimentally.

Traditional optical processing technology is limited by factors such as the geometric size and stability of the removal function of the processing equipment, and it is very difficult to process optical elements with complex structures with large depths and small periods. In particular, the high-efficiency and high-precision processing of optical elements with complex structures whose depth is micron-level and space period is millimeter-level has always been a technical difficulty. This paper proposes a method for processing optical components with complex structures based on magnetorheological polishing technology, focusing on solving the traditional magnetorheological polishing technology small size removal function generation and stable control problems, and obtaining small size removal with stable removal efficiency and morphology function. The magnetorheological fluid circulation system is a key component of the magnetorheological polishing machine. The structure of traditional magnetorheological fluid circulation system is difficult to match the stable transmission of magnetorheological fluid under small flow conditions. This paper proposes a method of dual peristaltic pump & pulsation damper combined with variable-diameter back pressure pipeline to achieve the stability of magnetorheological fluid control. The flow fluctuation error of magnetorheological fluid is reduced from 10-40ml/min to 1-5ml/min. The diameter of the polishing wheel of the machine is 20mm and the flow rate of the magnetorheological fluid is 200ml/min. A two-dimensional sinusoidal surface processing was performed using magnetorheological machine. Sinusoidal surface design PV=1.0λ (λ=632.8nm), RMS=159.5nm, the space period is 3mm, the element size is 50mm×50mm. The width of removal function is 1.33mm, FWHH (Full Width at Half Height) is 0.98mm, and volume removal rate is 0.004mm 3/min. After the element is completed, the residual RMS is reduced from the original 159.5nm to 15.7nm, and its convergence rate is 90.1%, with high convergence accuracy. The experimental results show that the configuration of the magnetorheological fluid circulation system proposed in this paper realizes the generation and stable control of the small size removal function and finally realize the fabricating of phase components with a minimum space period of 3mm.

As a computational imaging method, phase retrieval has wide applications in image reconstruction, wavefront detection, image encryption, etc. It is an image-based wavefront sensing technique and compared with some other traditional measurement methods such as interferometry, phase retrieval has the advantages of easy operation, high accuracy and strong adaptability to the environment. Conventional phase retrieval algorithms, such as the Gerchberg–Saxton (GS) algorithm, retrieve wavefront by iterative calculation. But limited by finite information of the captured diffractive light filed, the calculation process is easy to fall into local minimum value and stagnation occurs in practical, making it unable to converge to the right wavefront. In this paper, in order to improve this phenomenon, a phase retrieval method combined with the zone plate is proposed in this paper. In this method, zone plates are added into the traditional iterative phase retrieval algorithm to modulate the incident wavefront and combined with the multi-focus property, it can collect more effective information about the wavefront in a single optical intensity distribution image and realize a better wavefront reconstruction result. Simulation results indicate that by taking zone plates into calculation, more effective reconstruction results can be acquired. On the one hand, the recovery residual is smaller compared with conventional lens. On the other, although all of these methods reach to a stagnation, zone-plate-based methods are more efficient to get a better result.

Due to the characteristics of large depth, small period and high steepness, phase optical elements with complex structure need to use a small size removal function in magnetorheological processing, and use very small line spacing and step size values when planning the polishing path，so the dwell time matrix is very large, and the dwell time calculation speed is slow; besides, because of the complicated phase optical profile, it is difficult to achieve high-precision convergence of the dwell time. This paper proposes a fast and high-precision numerical iterative dwell time algorithm for complex structure phase optical elements. this paper proposes the concept of the dwell point matrix, which realizes the methods of the FFT convolution multi-core parallel algorithm to calculate the dwell time in the entire iterative calculation process. Also, to achieve high-precision convergence of the dwell time calculation, this paper proposes a calculation rule based on machine dynamic performance matching, when calculating the dwell time, the speed, acceleration, and speed smoothness of the machine were matched with the performance of the magnetorheological machine, which improves the stability of the machine. A large-diameter Continuous Phase Plate (CPP) is processed on a magnetorheological machine. The shape of the CPP contains a random structure of various periods. The initial RMS = 228.07nm, the CPP data matrix size is 2424 × 2424, and the line spacing is 0.6mm, the dwell time is calculated using the algorithm described in this article, the entire calculation process takes only 4.2 seconds, the calculation speed is about 3 times faster than the traditional iterative methods, the CPP residual error RMS converges to 10.2nm; After the CPP processing is completed, the CPP actual residual error RMS is reduced from the original 228.07nm to 15.6nm, and its convergence rate is 93.1%, which shows that the algorithm has high calculation efficiency and convergence accuracy.

The aliasing effect in the discrete Fourier transform inherent will impose a serious detrimental effect on conventional phase retrieval measurement accuracy with under-sampled intensity. In this Letter, we describe a modal-based nonlinear optimization phase retrieval approach that is capable of retrieving wavefront measurements using under-sampled intensities. The extended Nijboer-Zernike theory is introduced to establish an analytic solution between wavefront phase and intensity image, and then nonlinear optimization is further utilized to solve wavefront aberration coefficients from under-sampled intensity data. The feasibility and accuracy of the algorithm are verified by simulations and experiments. This is a promising method that is especially suitable for full field phase recovery of optical systems with a relatively high numerical aperture.

In the interference test process of a parallel flat optical element, the light beam after multiple reflections on the front and rear surfaces of the element with the wavefront to be measured often cause multi-surface interference, forming spurious fringes on the interferogram, which will introduce large errors to the wavefront measurement. Spurious fringes mainly have a great impact on the parameters such as wavefront gradient root mean square (GRMS) and mid-spatial-frequency power spectral density (PSD). The RMS value of the wavefront containing spurious fringes is generally significantly larger than the true value, which will affect the accurate measurement and evaluation of the wavefront quality of optical components. Existing spurious fringes suppression methods often have the disadvantages of multiple adjustment steps in the test process or high hardware requirements, and it is difficult to match the requirements for rapid and high-efficiency test of high-precision optical flat components. This paper proposes a method for removing spurious fringes in interference test based on characteristic spectrum band-stop filter, which can achieve accurate removal of spurious fringes. First, by using the ZoomFFT algorithm to zoom up the spectrum of the wavefront data points, the effective identification of the spectral characteristics of the spurious fringe is realized; then the band-stop filter in a specific area is used according to the spectral characteristics of the spurious fringes, only the frequency spectrum of the spurious fringes is removed, and the wavefront data of the component to be tested is completely retained without changing its own shape; the Quad-Flip operation and error function filter window are used for spectrum filtering, which effectively reduces Gibb's noise in the frequency domain due to the sudden truncation of the input data edge during FFT transformation. The transmitted wavefront of a fused silica element with a diameter of Φ100mm was tested on the ZYGO static interferometer, and the test results contained a large number of spurious fringes. After processing by this method, the spurious fringes were removed. The mid-spatial-frequency wavefront RMS of the component is reduced from 5.365nm to 3.678nm. The method does not need to add additional hardware and tedious measurement and adjustment operations, the calculation is fast, and the spurious fringes removal is accurate.

为了提高惯性约束聚变(ICF)激光装置中连续相位板(CPP)的焦斑性能,建立了波前畸变下连续相位板焦斑的理论计算和分析模型,并根据CPP使用条件搭建了三倍频大口径CPP远场离线测试系统.对加工330 mm×330 mm口径的CPP和波前畸变元件进行了理论计算和离线测试实验的对比研究.理论计算和实测的焦斑形貌、参数数值均非常一致,验证了计算模型的正确性和实验系统的可靠性.理论和实验结果一致表明,波前畸变对CPP焦斑性能的影响非常严重,当弥散斑为0.5倍CPP焦斑时,畸变量已对CPP焦斑形貌产生了很大影响,能量利用率下降值大于4％,焦斑半径增大超过20μm,陡边阶数下降1.3阶,不均匀性均方根(RMS)值下降6％,旁瓣份额增长超过0.5％.

This paper analyzes characteristics of wavefront and light intensity of large-aperture continuous phase plates(CPPs) fabricated by magnetorheological finishing(MRF). Three groups of CPPs fabricated by different processing parameters such as scanning intervals and scanning offsets are compared, and the influence of mid-frequency error introduced by MRF on CPPs wavefront and light intensity are analyzed as well. Total analysis indicates that the performance of CPP is poor when scanning interval is 2 mm and scanning offsets are 0.1-0.3 mm; The iteration fabrication efficiency is higher when scanning interval is 2 mm and scanning offsets are 0.4-0.5 mm compared with that when scanning interval is 1 mm and scanning offsets are 0.1-0.3 mm, and the mid-frequency error is improved as well. Further analysis indicates that mid-frequency error introduced by MRF has a greater impact on CPPs wavefront gradient, near-field and side lobe.

In order to measure and evaluate the far-field intensity caused by large-aperture continuous phase plates, off-line measurement system with 351 nm laser for the far-field intensity was built according to the physical demand parameters of the laser system in ICF equipment. The experiment for CPP with 330 mm330 mm aperture was carried out. The measurement reproducibility and accuracy were analyzed according to the calculated result with scale diffraction theory. The diameter of dispersion focus is about 2.9 times diffraction-limited diameter and the maximal size that the system can measure is f600 mm or 430 mm430 mm. The reproducibility for measuring encircled energy fraction in defocusing amount 2 mm is better than 0.2%. The shape and distribution from experiment accord with the calculated result, the measured encircled energy percentage is 0.85% less than the calculated result and the measured radius is 13 m larger than the calculated result, the difference is caused by temporal smoothing of the measurement system, so the measurement accuracy could be enhanced through shortening time of exposure of CCD and reducing the optical aberration of the measurement system.

对大口径连续相位板(CPP)在子孔径拼接检测过程中存在的几种影响检测精度的主要因素,包括定位误差、系统误差和拼接模式等进行了归纳并分析了其对检测精度的影响权重.通过对子孔径重叠区域分布的均匀性计算,分析了检测误差对拼接质量的影响.结果表明,定位误差是影响CPP拼接精度的主要原因,而对系统误差进行有效处理可以进一步减小重叠区非均匀性,拼接模式的选择对CPP的拼接结果的影响有限.通过CPP深度特性对重叠区域均匀性的统计分析表明,在像素级别的检测中,重叠区域均方根残差随着CPP深度的增加而线性增加,即拼接精度随CPP深度的增加而降低.

为提高惯性约束聚变系统中聚焦光斑的能量集中度,分析了在应用过程中影响连续相位板性能的主要误差来源,并建立了相应的数学模型.通过分析得出存在误差时远场焦斑的能量集中度和均方根值,且口径误差、对准误差、振幅畸变误差对连续相位板的聚焦性能影响很小,波前畸变影响能量集中度的权重最大.进一步分析可知:当畸变波前相关长度与连续相位板的最小空间周期(10 mm左右)相当时,畸变波前极大地影响激光的聚焦性能,提高惯性约束聚变系统中畸变波前的相关长度是提高聚焦光斑的能量集中度的有效方法.

基于全局最小二乘拼接算法和图像融合算法建立了连续相位板(CPP)子孔径拼接检测算法,并根据全局相关匹配原理提出采用面形残差来评价CPP的加工面形.采用高精度动态干涉仪等设备建立了相应的检测系统,并针对430mm×430mm口径CPP开展了数值模拟和检测实验.理论计算结果表明:系统计算误差为0.005nm.实验结果表明,整个检测系统软硬件RMS误差小于5nm,基本满足CPP面形检测要求.从而验证了CPP检测和评价的正确性和可行性.

连续相位板（CPP）是大型激光装置中用于控制光束形状、能量和波前分布的一种重要衍射光学元件。为改善聚焦光束的质量,建立了基于现有工艺的大口径CPP理论设计模型,优化了传统衍射元件设计算法。采用该算法设计了用于背光照明的Ф330mm CPP,开展了数控化学抛光制作CPP试制,并在大型激光装置上开展了验证实验。结果表明,基于工艺改进算法设计的CPP具有更好的加工特性和焦斑性能,基本实现了整形和匀滑性能,能够较好满足现有工艺约束条件和物理需求。