# Selecting a Proper Microsphere to Combine Optical Trapping with microsphere-Assisted Microscopy
## 3 Experiments and Analysis
### Results and Analysis  
Figure 4a shows the scanning electron microscopy (SEM) image of the SNG with 139-nm steps separated by a 139-nm gap, which cannot be discerned by the objective (100\(\times\), NA = 0.9) under white light illumination, as seen in Figure 4b. Figure 3: Schematic of the constructed optical system. The red path represents the optical trapping system and the tangerine path serves as the imaging part. The same objective lens is used for both the trapping process and the observation. Figure 5a-c illustrate super-resolution images of the grating, through the optically trapped PS/MF microsphere. Figure 5a illustrates the super-resolution image by the trapped PS sphere without a filter, in which a highly focused laser spot is in the center of the sphere. The laser spot is harmful to the imaging processing and this negative effect can be eliminated by a short-pass filter, as seen in Figure 5b. The position of the SNG sample changes with the 3-axis stage; we can observe the area of interest. When moving the sample into different positions, only the trapped microsphere is nearly motionless, while the positions of other spheres are unpredictable, because of the movement of the sample and the Brownian motion, like in Figure 5b. Figure 5c shows the SNG structure image by the trapped MF sphere. Figure 5d-f show the enlarged view of section of Figure 5a-c, from which we can see the enlarged image of the grating, and the conventional optical microscope can capture the enlarged virtual image. The capability of microspheres to break the diffraction limit and magnify the nanostructure is related to the refractive index contrast (RIC, \(n/n_{m}\)) between the microspheres (\(n\)) and the immersion medium (\(n_{m}\)) [37]. The RIC of the MF sphere in water is 1.26, which is larger than 1.20 of the PS sphere, and a better image quality by the MF sphere is obtained compared to that by the PS sphere, as illustrated in Figure 5e,f. A 2\(\times\) lateral magnification is offered by the 10-um PS sphere, while a 2.2\(\times\) magnification for the 10-um MF sphere. The magnification factor is affected by the RIC, and normally a higher RIC leads to a larger magnification factor. The difference of image quality by these two spheres can be partially explained by the photonic nanojet (PNJ) [12; 29; 30; 31], which is formed on the vicinity of the rear-surface of a microsphere with a narrow FWHM waist and extraordinarily high optical intensity. To study the PNJ properties of these two index-different microspheres in water, we perform the finite-difference time-domain (FDTD) numerical simulations using CST MWS software package (computer simulation technology). The simulation domain includes the 10-um-diamater sphere at the center and the immersion medium. The computational grid unit is a hexahedron of 5 nm size. Perfect matched layer (PML) is used for terminating the computation domain. For the incident wave, a linearly polarized wave with a free space wavelength 600 nm is propagating along the \(z\)-axis. The PS sphere (RIC = 1.20) and the MF sphere (RIC = 1.26) with the same diameter (10 um) is covered by water medium. Figure 6a,b show the electric field distributions of PNJs generated on the shadow sides of two spheres. Note that different RICs will produce different PNJs. We can see that that the MF sphere has a higher intensity of the PNJ due to the larger RIC, and it also has a narrower FWHM (400 nm) compared to that of PS sphere (454 nm), as illustrated in Figure 6c. A higher intensity and a narrower FWHM of PNJ may contribute to a better image quality, as demonstrated in [12; 38]. We can expect that the use of higher-refractive-index microspheres is beneficial to a better experimental result under the condition of a stable optical trapping. We want to point out that there is a qualitative relation instead of quantitative relation between the simulation results and the experiments, and more advanced simulations need to be performed to reveal the imaging mechanism, which is beyond the scope of our focus in this research.