渐进多焦点自由曲面镜片的后表面由多个曲面拟合而成，其衔接处曲率变化较大且不连续，初始的自由曲面镜片往往需要通过局部或者全局优化来改善其光学性能以及表面光顺性。提出基于NURBS曲线和最小二乘曲线的全局拟合方法来对渐进多焦点自由曲面镜片后表面进行优化重构。介绍了最小二乘曲线拟合的算法原理，在相同参数下对两组光焦度不同的镜片后表面进行重构，并进行仿真分析和测量分析，对其光学性能进行评价。实验结果表明：两组镜片最大像散分别减小了0.61 D和0.45 D，远用区像散分别减小了0.15 D和0.16 D，中间通道（Y=0 mm处）宽度增加超过1.8 mm。重构后的曲面能够在保持光焦度基本不变的情况下，提高了后表面的光滑性，有效减小了渐进片的最大像散，同时渐变通道的宽度也有一定程度的改善。

The rear surface of a freeform progressive addition lens （PAL） is often fitted using multiple surfaces， and curvature changes at the joints are usually large and discontinuous. Initial freeform PALs frequently required local or global optimization to improve their optical properties and surface smoothness. A global fitting method based on the non-uniform rational B-spline curve and least squares curve is proposed to optimize reconstruction of the rear surface of a lens. The algorithm principle of least squares curve fitting is introduced， and the rear surfaces of two sets of lenses with different powers are reconstructed under the same parameters； moreover， their optical properties are simulated， quantified， and evaluated. Experimental results demonstrate that the maximum astigmatism of both lens groups reduces by 0.61 D and 0.45 D， respectively. The astigmatism in the distance area decreases by 0.15 D and 0.16 D， respectively， and the middle channel width （Y = 0 mm） increases by over 1.8 mm. The proposed reconstructed surface improves the rear surface smoothness， gradient channel width， and effectively reduces PAL maximum astigmatism.