Since the invention of stimulated emission depletion (STED) microscopy by Stefan Hell at the beginning of the 1990s [1,2], the eld of super-resolution uorescence microscopy (microscopy beyond Abbe’s classical resolution limit) has seen a dramatic development with the invention and renement of a plethora of powerful techniques and methods, see for example, . From a physics point of view, these methods can be roughly divided into three categories: the rst category comprises methods such as STED, ground-state depletion or GSD microscopy [4,5], or nonlinear structured-illumination microscopy (nlSIM) , which use the photoswitching or nonlinear response between excitation and uorescence emission of a large number of molecules within a focal region or structured excitation pattern. e second category comprises methods which are based on the identication and localization of individual molecules within a uorescence image. e two most prominent examples here are photoactivated localization microscopy (PALM)  and stochastic optical reconstruction microscopy (STORM) , with its most widely used variant direct STORM (dSTORM) [9-11]. e third and most recent category comprises methods which directly convert the temporal information of a uorescence signal into an enhanced spatial resolution of imaging. e rst method promoting this idea was named dynamic saturation optical
9.1 Introduction 9.2 Theoretical Basis 9.3 SOFI Computation
Algorithm 9.4 Detector Pixel
Size and Fourier Interpolation
9.5 Fourier Reweighing 9.6 Fluctuation-Based
PSF Estimation 9.7 Conclusion and
Outlook Acknowledgments References
microscopy or DSOM [12,13], which proposed to use the temporal dynamics of a uorescence signal upon triplet state shelving (or similar photophysical shelving into a dark state) for achieving enhanced spatial resolution with a laser scanning confocal microscope. However, similar to nlSIM, DSOM suers from excessive photobleaching, which limits its practicability. Nonetheless, this general idea of converting temporal dynamics information into an enhanced spatial resolution has been successfully and ingenuously implemented into a uorescence lifetimeimaging STED microscope to enhance spatial resolution and contrast . A more successful, as compared to DSOM, realization of this idea was the invention of stochastic optical uctuation imaging or SOFI . In this method, one employs the stochastic temporal intensity uctuations of emitters for enhancing the spatial resolution of an image. SOFI uses a conventional wideeld microscope and does not require any change in hardware or setting. e only requirement is that the microscope has to be able to rapidly record images with high sensitivity. Only aer a stack of images is recorded, SOFI evaluates the temporal uctuations in each pixel of the images and computes a super-resolved nal image. SOFI will work with any labeling where the labels exhibit stochastic, statistically independent intensity uctuations. Typically, this is intrinsically the case for labels such as uorescence quantum dots (QDs). However, it has been shown that all conventional uorescence dyes which are suitable for dSTORM can be used for SOFI, aer intensity uctuations are induced by suitable buers . Finally, also photoswitchable uorescent proteins have been successfully used for obtaining highquality SOFI images in biological samples . Besides enhancing the spatial resolution of imaging, SOFI also provides a very ecient suppression of scattering background and autouorescence , and it endows a wideeld microscope with optical sectioning capability, thus allowing to use a wideeld microscope for obtaining true three-dimensional images of a sample [18,19]. is chapter gives a comprehensive description of how SOFI works, and provides all the algorithmic details. Moreover, it summarizes recent progress in improving the eciency and applicability of SOFI.