We revisit the spectral coherence properties of far-field radiation emanating from an aperture in a blackbody cavity on the basis of Kirchhoff’s boundary conditions. We point out that the far zone cross-spectral density matrix derived earlier in the literature by separately propagating all three aperture-field components does not show transversality of the field at nonparaxial directions. This is not the case when Luneburg’s diffraction integrals are applied on the transverse source field components to determine the entire far field. We compare the electromagnetic degrees of coherence for the two methods and show that over important angular separations their values coincide with high accuracy. The results of this work and of others concerning the far-field intensity, polarization, and paraxial angular coherence are in full agreement.

中文翻译：

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黑体远场连贯性。

我们根据基尔霍夫的边界条件，重新研究了从黑体腔中的一个孔发出的远场辐射的光谱相干特性。我们指出，文献中较早时通过分别传播所有三个孔径场分量而得出的远区交叉光谱密度矩阵在非傍轴方向上并未显示出场的横向性。当Luneburg的衍射积分应用于横向源场分量以确定整个远场时，情况并非如此。我们比较了这两种方法的电磁相干度，并表明在重要的角度间隔上，它们的值具有很高的精度。这项工作以及其他有关远场强度，极化和近轴角相干性的结果是完全一致的。