利用原子力显微镜( AFM) 获取纸张表面微观形貌数据，使用海伦公式对分形维数的算法进行优化，研究了纸张表面的分形特性及用分形维数表征纸张表面微观形貌的可行性． 以不同范围和不同计算角度下的均方根粗糙度的标准差的平均值为研究纸张表面高度分布均匀性的参数，探讨了光泽涂布和真空镀铝对纸张表面微观形貌的影响．结果表明: 采用未优化的算法所计算的纸张表面分形维数超出了理论值，而用优化后的算法所得的分形维数在理论值范围内; 纸张表面具有分形特性，经算法优化后得出的分形维数可作为评价纸张表面微观形貌的参数，其值越大表示微观形貌越复杂; 纸张表面高度分布均匀性参数越小，表示高度分布越均匀; 当涂布量为3 g /m2 时，光泽涂布对纸张表面分形维数无影响，而表面高度分布均匀性参数从4.05 nm 降低至2.11 nm; 真空镀铝后，纸张表面分形维数从2.58 减小至2.21，且表面高度分布均匀性参数从2.54 nm 降低至0.78 nm．

In this paper,the fractal characteristics of paper surface and the feasibility to use fractal dimension tocharacterize the micro-topography of paper surface are investigated through AFM to acquire the micro-topographydata and through Heron formula to optimize the algorithm on the fractal dimension.Then,the distribution homogeneityof surface height is evaluated with the average value of standard deviations of ＲMS roughness in differentscales and at different angles as parameter,and the effects of the gloss coating and the vacuum aluminizing onmicro-topography are discussed.The results show that ( 1) the fractal dimension based on the original algorithmexceeds the theoretical value while that based on the optimized algorithm is within the range of theoretical value;( 2) paper surface displays fractal characteristics and optimized fractal dimension can be used to characterize thesurface of micro-topography; ( 3) the higher fractal dimension is,the more complicated surface of micro-topographywill be; and ( 4) when a coating weight is 3 g /m2,the gloss coating do not affect the fractal dimension but causesthe homogeneity parameter of superficial height distribution to decrease from 4.05 nm to 2.11 nm,and the vacuumaluminizing causes the fractal dimension to decrease from 2.58 to 2.21.In addition,the homogeneity parameter ofsuperficial height distribution reduces from 2.54 nm to 0.78 nm．