The two-point resolution of an optical system is the minimum distance between two point sources that can be estimated with a prescribed precision from measurement in the image plane. When the sources are incoherent, then direct measurement of the optical intensity provides resolution limited by Rayleigh’s curse, i.e., the precision diminishes to zero as the separation is reduced to zero. By using quantum Fisher information bounds on the precision, it was shown recently that estimates based on optimal quantum measurements of the optical field can break Rayleigh’s curse and provide estimates with finite precision even at very small separations. We show here that if the point sources are partially coherent with an unknown real degree of coherence, no matter how small it is, then the curse resurges. Since a Lambertian source is not strictly incoherent, having a correlation width of the order of a wavelength, and light gains coherence as it propagates, Rayleigh’s curse endures as a fundamental dictum.

中文翻译：

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在部分连贯的情况下瑞利诅咒的死灰复燃

光学系统的两点分辨率是两点源之间的最小距离，可以根据像平面中的测量以规定的精度估算出这两个点源之间的最小距离。当光源不相干时，直接测量光强度可提供受瑞利诅咒限制的分辨率，即，当间隔减小到零时，精度会降低到零。通过使用精确度上的量子Fisher信息范围，最近表明，基于光学场的最佳量子测量的估计可以打破瑞利的诅咒，即使在很小的间隔下也可以提供有限的精度。我们在这里表明，如果点源与未知的真实连贯程度部分相干，那么不管它有多小，诅咒都会复燃。由于朗伯来源并非严格不相干，