## 2 Literature Review
### Combining the Geometries
#### 2.3.6 Image Scanning Microscopy
proposed using annular illumination to improve the transverse resolution [145]. [PERSON] et al. described 2 PF ISM with a SPAD detector and blind deconvolution [146]. The group of [PERSON] and [PERSON] has published many relevant papers [147; 148; 149; 150; 151]. They proposed a subtractive imaging method with pixel reassigned and non-reassigned images [150], also using doughnut illumination [147]. They explored ISM with maximum-likelihood estimation [148]. They investigated reassignment based on image cross-correlation [149]. They investigated 2 PF ISM [151]. [PERSON] and [PERSON] investigated pixel reassignment in a reflection microscope [152]. [PERSON] et al. used pixel reassignment in an ophthalmoscope [153]. [PERSON] et al. reported a spectral ISM [154]. [PERSON] et al. used pixel reassignment in an optofluidic microscope [155]. [PERSON] et al. used pixel reassignment in a SHG microscope [156]. [PERSON] et al. used pixel reassignment to reconstruct SIM images [157]. [PERSON] et al. investigated different post-processing strategies in ISM [158]. [PERSON] et al. investigated the effect of altering the pixel reassignment factor as a function of the detector pixel offset and proposed reassigning it to the peak of the PSF for a particular detector element [159]. They included array sizes up to 2 AU, for which the peak of the PSF is 1.9 times that of a conventional microscope. They found that although the PSF from a single offset detector pixel can become distorted, after its integration around a ring of elements, the PSF is compact and well-behaved. The axial resolution was found to be higher than that for a confocal microscope with a pinhole of the same size as the array. It was found that the detectability for ISM is optimised for an array of 1.1 AU. The effect of weighting the array signals was also considered. This study was extended to the cases of Bessel beam illumination and to 2 PF and 3 PF [160]. Although Bessel beam illumination gives poor imaging in ISM with a large array, the PSF is well-behaved for a small array. A pixel offset of 0.836 AU corresponds to the case when the PSF for that pixel exhibits two peaks of equal height. The PSF from a detector pixel can be interpreted as showing the probability density function of the signal, the peak giving the most likely origin in the object of a detected photon. It has been pointed out that reassigning the maximum of the PSF for each detector pixel is similar to a maximum likelihood restoration [161]. Pixel reassignment was applied to the case of a vortex doughnut beam. The transverse width of the PSF was found to be smaller than in a conventional imaging system for any size of detector array and smaller than a true confocal microscope (point detector) for arrays larger than about 1.3 AU. The axial resolution was greater than in a conventional imaging system for any size of array and greater than in a confocal microscope for arrays larger than about 0.9 AU. The optical sectioning was stronger, even than for ISM with Airy disk illumination, for array sizes larger than 1.1 AU. [PERSON] et al. proposed that in the image in the detector plane, sparsity is imposed by the illumination spot, which greatly improves the deconvolution of this data [162]. Theyclaimed resolving 70 nm resolution test objects. Subsequently, they used \(l_{1}\) regularisation and claimed a resolution of 60 nm [163]. Fluorescence is basically an incoherent effect, as there is no phase correlation between fluorescent molecules. Weak fluorescence displays quantum effects, such as antibunching. Fluorescence also exhibits blinking, which has been exploited in super-resolution optical fluctuation imaging (SOFI), where low order or higher order time correlations are used to extend the spatial frequency cut-off [164; 165]. The group of [PERSON] has exploited both antibunching (Q-ISM: Quantum ISM) and time correlations (SOFISM: SOFI-ISM) in ISM [166; 167].