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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
For a paraxial scalar light field ε = [εx, 0,0], considering the influence of the first-order longitudinal field correction term, the longitudinal field energy Ez of the light field is a conserved quantity that does not vary with the beam position z, and its value Completely depends on the paraxial field (εx) distribution. The magnitude of the longitudinal field energy Ez reflects the paraxial scalar approximation of the light beam and an approximation factor η is defined as a quantitative criterion for this characteristic of the beam; the smaller the value, the better the approximation. Taking the super-Gaussian beam as an example, the problems of first-order longitudinal field energy and paraxial scalar approximation