The discharged capillary plasma channel has been extensively studied as a high-gradient particle acceleration and transmission medium. A novel measurement method of plasma channel density profiles has been employed, where the role of plasma channels guiding the advantages of lasers has shown strong appeal. Here, we have studied the high-order transverse plasma density profile distribution using a channel-guided laser, and made detailed measurements of its evolution under various parameters. The paraxial wave equation in a plasma channel with high-order density profile components is analyzed, and the approximate propagation process based on the Gaussian profile laser is obtained on this basis, which agrees well with the simulation under phase conditions. In the experiments, by measuring the integrated transverse laser intensities at the outlet of the channels, the radial quartic density profiles of the plasma channels have been obtained. By precisely synchronizing the detection laser pulses and the plasma channels at various moments, the reconstructed density profile shows an evolution from the radial quartic profile to the quasi-parabolic profile, and the high-order component is indicated as an exponential decline tendency over time. Factors affecting the evolution rate were investigated by varying the incentive source and capillary parameters. It can be found that the discharge voltages and currents are positive factors quickening the evolution, while the electron-ion heating, capillary radii and pressures are negative ones. One plausible explanation is that quartic profile contributions may be linked to plasma heating. This work helps one to understand the mechanisms of the formation, the evolutions of the guiding channel electron-density profiles and their dependences on the external controllable parameters. It provides support and reflection for physical research on discharged capillary plasma and optimizing plasma channels in various applications.

自由曲面为光学系统设计带来了新的设计自由度，可以实现性能与参数更高、结构更紧凑的系统，但自由曲面的加工与检测难度较大，应在设计过程中对工艺性进行实时表征与控制。使用正交多项式面型可以较为容易地实现自由曲面同基底曲面矢高差的控制，但目前常用的大多是在圆域内正交的多项式，对于自由曲面离轴非对称系统中曲面常用的矩形孔径或者方形孔径局限性较大。针对以上问题，提出了采用方域内具有正交特性的二维Chebyshev多项式以及二维Legendre多项式进行自由曲面成像系统设计的方法。提出采用正交多项式孔径边缘积分的约束方法，以及采用控制方域正交多项式系数平方和的方法，配合正交多项式系数的其他线性约束，在不明显降低系统成像质量的情况下，实现高效的自由曲面系统设计以及曲面检测难度的实时表征与控制。通过多个不同结构的自由曲面成像系统设计实例，说明了所提出的设计方法的可行性与效果。所提出的方法为常用的有矩形曲面孔径的自由曲面系统设计提供了新思路，可以有效提升整个自由曲面系统研制过程的效率。

Using freeform optical surfaces in lens design can lead to much higher system specifications and performance while significantly reducing volume and weight. However, because of the complexity of freeform surfaces, freeform optical design using traditional methods requires extensive human effort and sufficient design experience, while other design methods have limitations in design efficiency, simplicity, and versatility. Deep learning can solve these issues by summarizing design knowledge and applying it to design tasks with different system and structure parameters. We propose a deep-learning framework for designing freeform imaging systems. We generate the data set automatically using a combined sequential and random system evolution method. We combine supervised learning and unsupervised learning to train the network so that it has good generalization ability for a wide range of system and structure parameter values. The generated network FreeformNet enables fast generation (less than 0.003 s per system) of multiple-solution systems after we input the design requirements, including the system and structure parameters. We can filter and sort solutions based on a given criterion and use them as good starting points for quick final optimization (several seconds for systems with small or moderate field-of-view in general). The proposed framework presents a revolutionary approach to the lens design of freeform or generalized imaging systems, thus significantly reducing the time and effort expended on optical design.

机器视觉检测技术具有非接触、高精度的优点，正在逐渐取代人工检测，成为工业生产检测的重要一环，作为前端的光学系统是机器视觉检测技术的核心部分。文中针对半径10 mm以内的光滑球体表面检测设计了一款双远心光学成像系统。系统由7片镜片和1片滤光片组成，采用了2个非球面校正像差，调制传递函数曲线在40 lp·mm^?1处大于0.3，具有良好的成像性能。由于该系统光圈较小且待测物为类镜面反射材料，设计完成后进行了照明模拟，选择采用多个面光源对待测物进行照明。模拟结果表明，文中设计的双远心光学系统实现了对较大曲率表面成像，并给出了一种配套的照明方式。