In this publication, the Luneberg integrals are revisited and the conditions of the using of such integrals have been recalled. Additivity law of Luneberg’s integrals and the link with the Frenel kernel for the propagation are discussed. By means of the definition of the Luneberg’s integrals, the propagation of a vectorial electromagnetic field (Hertz potentials) is developed and a new approach of the computation have been proposed based on Zernike polynomials. With this new approach simulations of holograms is illustrated in the case of the digital in-line holography with an opaque disk.

中文翻译：

---

Luneberg 积分的评估及其在数字在线全息术中的应用

在本出版物中，重新审视了 Luneberg 积分，并回顾了使用此类积分的条件。讨论了 Luneberg 积分的可加性定律和与 Frenel 核传播的联系。通过定义 Luneberg 积分，开发了矢量电磁场（赫兹势）的传播，并提出了一种基于 Zernike 多项式的新计算方法。使用这种新方法，在具有不透明盘的数字在线全息术的情况下说明了全息图的模拟。