The power-in-the bucket and the intensity distribution generated by the coherent combination of a definite number of similar laser beams with Gaussian profiles are numerically studied at different observation planes in the far-field. A precise method is introduced for optimal engineering of the array aperture size and the observation plane location in the far-field. A relation between the array aperture size and the observation plane distance is proposed using the Fresnel zone concept for coherent beam combining to achieve the maximum power-in-the bucket (PIB). The results reveal that the maximum PIB in a small bucket radius of 5 or 10 cm in the observation plane (radii in directed-energy applications) can be obtained either when the observation plane is located at the primary region of the far-field for a specified array aperture size or when the array aperture size is equal to or less than the size of the first Fresnel zone . Also, the proposed approach is independent of array geometry so that it will be practical for different array geometries, namely square, circular, and hexagonal. Furthermore, it is also independent of other parameters such as numbers and divergence of beams. The maximum amount of PIB in a specified observation plane location can be obtained for array aperture sizes lower than the first Fresnel zone, regardless of the number of beams or their waist radius.

中文翻译：

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一种确定观察平面最佳位置或阵列孔径最佳尺寸的精确方法，以在相干光束组合中实现最大桶内功率

在远场的不同观察平面上数值研究了桶内功率和由一定数量的具有高斯分布的相似激光束相干组合产生的强度分布。引入了一种精确的方法来优化设计阵列孔径大小和远场中的观测平面位置。使用菲涅耳区概念提出了阵列孔径大小与观察平面距离之间的关系，用于相干光束组合以实现最大桶中功率 (PIB)。结果表明，当观察平面位于远场的主要区域时，可以在观察平面中 5 或 10 cm 的小桶半径（定向能应用中的半径）中获得最大 PIB。指定阵列孔径大小或当阵列孔径大小等于或小于第一个菲涅耳区域的大小时。此外，所提出的方法与阵列几何形状无关，因此它适用于不同的阵列几何形状，即方形、圆形和六边形。此外，它还独立于其他参数，例如光束的数量和发散度。对于小于第一菲涅耳区的阵列孔径尺寸，无论光束数量或其腰部半径如何，都可以获得指定观察平面位置中的最大 PIB 量。