Improving the resolution of fluorescence microscopy beyond the diffraction limit can be achievedby acquiring and processing multiple images of the sample under different illumination conditions.One of the simplest techniques, Random Illumination Microscopy (RIM), forms the super-resolvedimage from the variance of images obtained with random speckled illuminations. However, thevalidity of this process has not been fully theorized. In this work, we characterize mathematicallythe sample information contained in the variance of diffraction-limited speckled images as a functionof the statistical properties of the illuminations. We show that an unambiguous two-fold resolutiongain is obtained when the speckle correlation length coincides with the width of the observationpoint spread function. Last, we analyze the difference between the variance-based techniques usingrandom speckled illuminations (as in RIM) and those obtained using random fluorophore activation(as in Super-resolution Optical Fluctuation Imaging, SOFI).

翻译：提高荧光显微术分辨率超越衍射极限，可以通过在不同照明条件下采集并处理样品的多幅图像来实现。其中一种最简单的技术是随机照明显微术（RIM），它通过随机散斑照明下获得的图像方差来形成超分辨图像。然而，这一过程的有效性尚未得到充分的理论化。在本工作中，我们从数学上表征了衍射受限的散斑图像方差中包含的样品信息，并将其表达为照明统计特性的函数。我们表明，当散斑相关长度与观测点扩散函数的宽度一致时，可以获得明确的两倍分辨率提升。最后，我们分析了基于方差的两种技术之间的差异：一种使用随机散斑照明（如RIM），另一种使用随机荧光团激活（如超分辨率光学涨落成像，SOFI）。