# A Review of Super-Resolution Imaging through Optical High-Order Interference [Invited]
## 4 Super-Resolution via Bunching Effect  
The Rayleigh resolution limit can be surpassed by considering the bunching effect of chaotic light [49; 50]. The initial work in this direction was done by [PERSON] et al., termed as super-resolution optical fluctuation imaging (SOFI) [33]. SOFI is a fluorescent imaging scheme for object consisting of many fluorescent point emitters as illustrated in Figure 3A. In this case, the cross talk between different positions of the object is inevitable, and the nth-order cumulant function needs to be extracted out from the measured nth-order correlation function. Interestingly, by considering the emission fluctuation of single fluorescent emitter (Figure 3C) [51], the bunching effect of the fluorescent light provides the possibility to separate the nth-order cumulant function through computation with the measured lower order autocorrelation function (Figure 3D). Consequently, super-resolution is achieved in SOFI with the resolution reaching the SQL (Figure 3E). In this scenario, the obtained SQL image is an incoherent one as described in Equation (4). The experiment was done in an inverted wide-field microscope, and the sample was excited by a 470 nm LED array. The fluorescence light was recorded by an electron multiplying CCD (EMCCD) camera at a relatively low acquisition rate (10 Hz) that is limited mainly by the blinking behavior of the quantum dots used in the experiment. The results show that the imaging resolution increases with the increase of the order of autocorrelation measurement, demonstrating the \(\sqrt{n}\)-scaling of SQL super-resolution imaging as shown Figure 3F-H.  
For non-fluorescent imaging, the SQL super-resolution imaging can be achieved by employing thermal/pseudothermal light for illumination. In fact, the working principle is similar to SOFI, since the thermal/pseudothermal source is constituted by many independent fluctuating point sources [52; 53]. In the work reported by [PERSON] et al. [34], the pseudothermal light is generated by focusing a 783 nm laser beam onto a rotating ground glass disk as shown in Figure 4a. A CCD camera was used to measure the second-order correlation function on the image plane. By calculating the second-order cumulant function, sub-Rayleigh imaging has been demonstrated with the resolution improved by a factor of \(\sim\)1.4. Notably, the resolution enhancement is limited by the spatial correlation length of the pseudothermal source [54], i.e., the size of single speckle of the light field employed for illuminating the object as shown in Figure 4b,\(c\). The smaller the correlation length, the finer the imaging resolution, as shown in Figure 4e,f. In addition, other types of artificial fluctuating light source are also applicable for realizing the SQL super-resolution imaging [35]. Figure 4: Super-resolution imaging with pseudothermal light illumination. (**a**) represents the schematic of experimental setup with the pseudothermal light generated by launching a focused laser beam onto a rotating ground glass disk (RD). The spatial correlation length of the illumination pseudothermal source is controlled by varying the distance (\(d_{s}\)) between the lens \(L_{1}\) and the RD, which is revealed by the instantaneous intensity image of the illumination speckle field on the object plane (**b**,**c**). Compared to the conventional intensity image (**d**), second-order correlation measurement leads to super-resolution image of the object, such as that shown in (**e**) with speckle illumination (**b**), and (**f**) with speckle illumination (**c**). The figure is reproduced with permissions from Ref. [34] of OSA. Figure 3: Super-resolution fluorescence imaging through optical fluctuation. The object to be imaged consists of many independent fluorescent emitters (**A**); and the fluorescent intensity of the image spot fluctuates independently for different emitters (**B**,**C**). By taking advantage of the bunching effect of the optical fluctuation (**D**); super-resolution image can be realized (**E**).