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扩散声场？根据定义，目标需满足恒定声压级、平均声强为零、各向同性入射的不相关声波。这是否需要针对二维和三维声源布局采用特定声源与几何结构？作为研究方法，我们采用数值模拟及一系列计算，涉及非相关圆形/球形声源布局，或具有无限超维度的布局，并指出其与位势理论的关联。通过指数b修正的径向衰减1/r^b，利用超几何函数、盖根鲍尔多项式以及圆谐和球谐函数表示所得声场，获得了富有成效的见解。在圆形布局中，指数b=1/2的衰减波可合成理想的扩展扩散声场；球形布局则需b=1。所有布局均无法合成完全恒定的期望声压级，但其平坦度可接受。球面t-设计描述了具有明确高扩散区域的最优声源布局，而非球面凸布局可通过恢复各向同性或模式匹配实现最大扩散合成。理论与模拟为基于扬声器的扩散声场合成提供了基础，并为空间音频中近期心理声学发现提供了物理原理解释。