对于一个傍轴标量光场ε=[εx,0,0],考虑其一阶纵向场修正项的影响时,光场的纵向场能量Ez是一个不随光束截面位置z变化的守恒量,其值完全决定于傍轴场(εx)的分布情况。纵向场能量Ez的大小反映了光束的傍轴标量近似程度,定义一个近似因子η用来作为衡量光束的这一特征的量化判据；其值越小,近似程度就越好。以超高斯光束为例,讨论了其一阶纵向场能量及傍轴标量近似等问题。

If only the first order correction to the scalar paraxial field is concerted, then the field can be expressed as =[ε x,0,ε z] and the longitudinal field energy E z is proved to be constantly independent of the position z of the beam cross section. The value of E z stands for the degree of scalar paraxial approximation. An approximation factor η is suggested to characterize this property. The larger η, the worse degree of the approximation. Results are applied to super Gaussian beams.