## 2 Literature Review
### Combining the Geometries
#### 2.3.6 Image Scanning Microscopy
The pixel reassignment strategy was shown to be valid for any value of the pixel reassignment factor, with an optimum being to reassign to the point midway between the illumination and detection points for a system with no Stokes shift. In the presence of a Stokes shift, the reassignment factor should be altered. It was pointed out that although optical methods of reassignment could be used, there was some benefit in recording the complete data in order to retrospectively choose the pinhole size and for subsequent multi-image processing. [PERSON] et al. recognised that only a small number of detector elements in ISM measure a significant signal and proposed using a quadrant avalanche photodiode detector array, i.e., just four pixels [130]. Even with this small number of elements, this is enough to attain a resolution close to an ideal confocal microscope and increases the signal-to-noise ratio by a factor of 1.5. [PERSON] and [PERSON] et al. applied the multifocal ISM approach to two-photon excitation and used multi-image deconvolution [131; 132; 133]. Zeiss introduced the Airyscan microscope, which uses a hexagonally arranged fibre bundle to couple to photomultiplier detectors, simulating a detector array [134]. [PERSON] et al. explored the imaging performance of Airyscan [135]. [PERSON] et al. compared the performance of Airyscan and SIM [136]. They found that SIM gave a better resolution for thin samples, but Airyscan was preferable for thicker samples. [PERSON] et al. investigated the use of the Airyscan for fluctuation correlation spectroscopy [137]. As the PSF in ISM is narrower than in a conventional microscope while almost all the light is detected, [PERSON] et al. investigated the property that the peak of the PSF is higher than physically achievable in an ordinary optical system [138]. They called this effect superconcentration. In fact, this behaviour was also evident in the plots of Ref. [129]. [PERSON] et al. pointed out that for a comparison of OTFs from different optical systems, the absolute strength of the signal is an important factor [139]. Hence, for ISM, the absolute value of the spatial frequency response is much higher than in confocal microscopy with a small pinhole, as most of the light is detected. The unnormalised OTF for confocal microscopy and ISM with different sizes of pinholes/arrays were presented. Although for confocal imaging, the OTF can exhibit negative values for pinholes larger than 0.5 AU, this does not occur for ISM. [PERSON] et al. described a two-photon excitation ISM based on a form of the rescan technique [140]. [PERSON] et al. analysed the imaging properties of ISM in terms of the 4D signal, \(S(\mathbf{x}_{1},\mathbf{x}_{2})\), and proposed reconstruction of the 4D signal in 4D Fourier space [118]. The imaging properties of 2 PF ISM were investigated. The pixel reassignment factor can be chosen to optimise the OTF for a given noise level. The effect of the reassignment factor on image formation in a single photon fluorescence ISM with a Stokes shift was also studied. The effects of using Bessel beam illumination or pupil filters on the OTF for ISM with a large detector array were investigated. [PERSON] et al. developed an ISM system using a novel 25 element (\(5\times 5\)) single-pixel avalanche photodiode array detector (SPAD) and demonstrated its application for FLIM (fluorescence lifetime microscopy) [141]. Pixel reassignment was achieved by an automatic process based on cross-correlation between images from different detector pixels. Multi-image deconvolutions using a Richardson-Lucy algorithm or Wiener filtering were presented. They demonstrated the ability to achieve the same resolution as ideal confocal microscopy at one-tenth of the illumination intensity. [PERSON] et al. reported applying ISM to Raman microscopy [142]. [PERSON] and [PERSON] et al. described ISM in single-photon and 2 PF fluorescence modes using PSF-engineering to obtain a 3D image in a single 2D scan [143; 144]. [PERSON] et al.