Can uncorrelated surrounding sound sources be used to generate extended diffuse sound fields? By definition, targets are a constant sound pressure level, a vanishing average sound intensity, uncorrelated sound waves arriving isotropically from all directions. Does this require specific sources and geometries for surrounding 2D and 3D source layouts? As methods, we employ numeric simulations and undertake a series of calculations with uncorrelated circular/spherical source layouts, or such with infinite excess dimensions, and we point out relations to potential theory. Using a radial decay 1/r^b modified by the exponent b, the representation of the resulting fields with hypergeometric functions, Gegenbauer polynomials, and circular as well as spherical harmonics yields fruitful insights. In circular layouts, waves decaying by the exponent b=1/2 synthesize ideally extended, diffuse sound fields; spherical layouts do so with b=1. None of the layouts synthesizes a perfectly constant expected sound pressure level but its flatness is acceptable. Spherical t-designs describe optimal source layouts with well-described area of high diffuseness, and non-spherical, convex layouts can be improved by restoring isotropy or by mode matching for a maximally diffuse synthesis. Theory and simulation offer a basis for loudspeaker-based synthesis of diffuse sound fields and contribute physical reasons to recent psychoacoustic findings in spatial audio.

翻译：能否利用不相关的环绕声源生成扩展的漫射声场？其目标定义为恒定的声压级、消失的平均声强，以及从所有方向各向同性入射的不相关声波。这是否要求二维和三维环绕声源布局采用特定声源与几何结构？作为方法，我们采用数值模拟，对不相关的圆形/球形声源布局或具有无限超额维度的布局进行一系列计算，并指出其与位势理论的关系。利用指数b修正的径向衰减1/r^b，通过超几何函数、盖根鲍尔多项式以及圆形与球谐函数对所得场进行表征，获得了富有成效的洞见。在圆形布局中，以指数b=1/2衰减的波可合成理想的扩展漫射声场；球形布局则对应b=1。所有布局均无法合成完全恒定的预期声压级，但其平坦度在可接受范围内。球形t-设计描述了具有良好界定高漫射区域的最优声源布局，而非球形凸布局可通过恢复各向同性或模式匹配实现最大漫射合成来改进。理论与仿真为基于扬声器的漫射声场合成提供了基础，并为空间音频领域近期心理声学发现贡献了物理解释。