# Three-Dimension Resolution Enhanced Microscopy Based on Parallel Detection
## 3 Experimental Results  
It is known from the principle of 3D-PRFED that the detectors array should be well collimated with the Gaussian center of emission light focus and the 3D negative focus should also be close to the distribution of the theoretical model which will affect the ultimate resolution of 3D-PRFED. Here, 200 nm nanoparticles (ATTO 647N) were imaged to calibrate the system for its' preferable quantum efficiency and appropriate size. In order to guarantee the detector array is aligned with the Gaussian center of emission light focus in the imaging plane, the energy distribution from the center to outer detectors should be diminishing which means that the image intensity captured by the center detector is the highest and the image intensity captured by the second ring detectors is medium and the image intensity captured by the peripheral detectors is the lowest, as shown in Figure 5A. Figure 5B shows the modulation pattern for solid focus, in which the gratings inside and outside the modulation places are different because the different grating patterns can avoid the stray light from environment and the zeroth order unmodulated light into the system. By summing up the photons of each image, the energy distribution for each detector was shown in Figure 5C. By means of Zernike correction [10; 11; 12], the Gaussian energy distribution for the detector array can be promised. By adding vortex pattern and hollow pattern into the solid focus pattern as Figure 5D, the negative confocal image scanned by 3D negative focus can be easily generated, as in Figure 5E. It is needed to illustrate that the solid focus pattern and 3D negative focus pattern are using the same Zernike correction because they are the same excitation light at the common optical path. Figure 5F,G shows the preferable 3D negative focus after Zernike correction while Figure 5H,I are the images before correction. 100 nm nanoparticles (Abberior nanoparticles 4C flour. 100 nm) and nuclear pore complexes (Abberior Cells 3C NPC-START RED) were imaged to further test 3D-PRFED performance. Figure 6 shows the nanoparticles imaging results which were performed with 6\(\upmu\)s acquisition time per scan position and transverse scan step size of 30 nm and axial scan step size of 50 nm. The ultimate images were up to 5 nm pixel size through an interpolation algorithm. Therefore, before processing these images, we would get 19 group images and each group with 50-layer images. The confocal volume image resulted from 19 group images summing up without translation processing. Because the magnification of our system is 800 times, the equivalent pinhole size of the confocal volume image is 1.4 AU. The PRISM volume images were performed with pixel reassignment algorithm and the equivalent pinhole size is 0.25 AU. The 3D-PRFED volume image was performed with the subtraction coefficient of 0.7 and the negative value was set to zero. As shown in Figure 6, 3D-PRFED can obviously reduce the noise of CLSM and PRISM and improve transverse and axial resolution. The transverse and axial resolution of 3D-PRFED can be up to 116 nm and 406 nm. In order to reduce measurement error, 18 nanoparticles were selected to measure their transverse profile data and axial resolution. The results indicate that the mean transverse resolution of CLSM, PRISM, and 3D-PRFED are 264 nm, 191 nm, and 143 nm and meanwhile the mean axial resolution of CLSM, PRISM, and 3D-PRFED are 769 nm, 645 nm, and 518 nm respectively. The nanoparticles imaging experiment indicates that the transverse resolution of 3D-PRFED can be improved 1.85 times better than CLSM and 1.33 times better than PRISM, and the axial resolution of 3D-PRFED can be improved 1.48 times better than CLSM and 1.24 times better than PRISM. Figure 5: The calibration process of the system by imaging 200 nm nanoparticles. **(A)** The images from each detector for a single nanoparticle at the focal plane. **(B)** The solid focus pattern. **(C)** The normalization energy distribution of detector array.