The generation of speckle patterns via random matrices, statistical definitions, or apertures may not always result in optimal outcomes. Issues such as correlation fluctuations in low ensemble numbers and diffraction in long-distance propagation can arise. Instead of improving results of specific applications, our solution is catching deep correlations of patterns with the framework, Speckle-Net, which is fundamental and universally applicable to various systems. We demonstrate this in computational ghost imaging (CGI) and structured illumination microscopy (SIM). In CGI with extremely low ensemble number, it customizes correlation width and minimizes correlation fluctuations in illuminating patterns to achieve higher-quality images. It also creates non-Rayleigh nondiffracting speckle patterns only through a phase mask modulation, which overcomes the power loss in the traditional ring-aperture method. Our approach provides new insights into the nontrivial speckle patterns and has great potential for a variety of applications including dynamic SIM, X-ray and photo-acoustic imaging, and disorder physics.

中文翻译：

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深相关散斑：抑制相关波动和光学衍射

通过随机矩阵、统计定义或孔径生成散斑图案可能并不总是能产生最佳结果。可能会出现低系综数中的相关波动和长距离传播中的衍射等问题。我们的解决方案不是改进特定应用程序的结果，而是通过框架 Speckle-Net 捕获模式的深层相关性，该框架是基本且普遍适用于各种系统的。我们在计算重影成像（CGI）和结构照明显微镜（SIM）中证明了这一点。在集成数极低的CGI中，它可以定制相关宽度并最大限度地减少照明图案中的相关波动，以获得更高质量的图像。它还仅通过相位掩模调制即可创建非瑞利非衍射散斑图案，从而克服了传统环孔径方法中的功率损耗。我们的方法为非平凡的散斑图案提供了新的见解，并且在动态 SIM、X 射线和光声成像以及无序物理学等各种应用中具有巨大的潜力。