# Three-Dimension Resolution Enhanced Microscopy Based on Parallel Detection
## 1 Introduction  
Over the past several decades, confocal laser scanning microscopy (CLSM) has become a basic tool for most fluorescence microscopy applications, such as observing morphologies and dynamics in living cells, which has contributed to its ability to produce high-contrast, optical sectioned images while providing enough versatility to satisfy plentiful samples and application demands [1]. It is significantly noted that the resolution of CLSM, including lateral resolution and axial resolution, can even be improved by a factor of \(\sqrt{2}\) with infinitely small pinhole compared to wide-field fluorescence microscopy, which cannot be achieved in practice for the awful signal-to-noise (SNR) and the inexistence of infinitely small pinhole [2, 3]. Actually, compared with wide-field fluorescence microscopy, CLSM can supply little lateral resolution improvement but superior sectioned imaging with a finite-size pinhole [4]. It is well known that the resolution of classical fluorescence microscopy is limited by the wavelength of light according to [PERSON]'s diffraction limit theory, restricting lateral resolution to ca. 200 nm and axial resolution to ca. 500 nm at a typical excitation and emission wavelength of around 500 nm [5]. To further dig out the potential of CLSM, for the past thirty years, lots of super-resolution microscopy methods based on CLSM have been proposed, such as stimulated emission depletion microscopy (STED) [6], fluorescence emission difference microscopy (FED) [7], and image scanning microscopy (ISM) [8]. Fluorescence emission difference microscopy (FED), breaking the resolution limit by nonlinearly decreasing the peripheral fluorescence signal of the focus through digitalsubtraction between positive confocal image and negative confocal image, is versatile to all kinds of fluorophores as same as CLSM [7]. Over the past several years, several three-dimension fluorescence emission difference microscopy (3D FED) methods have been proposed which utilize three-dimension negative focus modulated by spatial light modulator (SLM) to realize 3D resolution improvement [9; 10]. There are numerous advantages using an SLM to generate a doughnut focus, such as flexibly modulating excitation light and applying adaptive optics and wavefront optimization to correct system aberrations [11; 12]. Using SLM, a compact system can be designed to generate a three-dimension doughnut focus [10]. ISM, which has succeeded all advantages of CLSM, is a useful and much more approachable technique to achieve super-resolution in CLSM by replacing a single point detector with a detector array or fast wide-field CCD (charge-coupled device) detection [1; 8; 13]. This method can double the lateral resolution of classical CLSM, which is similar to structure illumination microscopy (SIM) in principle [8; 14]. In 2013, [PERSON]. [PERSON] further clarified the principle of ISM using a detector array by pixel reassignment and discuss much more details about the effect of detector array size on resolution and signal collection efficiency, which can be called pixel reassignment image scanning microscopy (PRISM) [13]. Recently, PRISM has been combined with many other methods to further improve the resolution, such as FED, which just improves lateral resolution for it only makes use of the transverse vortex modulated light [15]. In recent years, as research for activities of the subcellular structure continues, an increasing number of researches require insights into intrinsic three-dimension organization of subcellular structures, all-directional resolution of microscopy including lateral and axial resolution should be much more improved than ever before. To follow this trend, here, a novel three-dimension resolution-enhanced microscopy is proposed by merging the 3D FED technique and PRISM technique, named with three-dimension pixel reassignment fluorescent emission different microscopy (3D-PRFED), which can further improve both lateral and axial resolution.