# Selecting a Proper Microsphere to Combine Optical Trapping with microsphere-Assisted Microscopy
## 1 Introduction  
Optical microscopes have been widely used in medical sciences, biological observations and semiconductor detections. The resolution of conventional optical microscopes is restricted to around half of the illumination wavelength, due to the classical diffraction limit, which has greatly limited its applications in a variety of fields. Several super-resolution imaging techniques were developed, including near-field scanning optical microscope [1], superoscillatory lens [2], solid immersion lens [3], fluorescence microscopy [4], and nanohole-structured mesoscale particles [5]. Besides these techniques, in 2011, an optical microscope aided by fused silica (SiO\({}_{2}\)) microspheres with low index (\(n\sim 1.46\)) in air was used to achieve 100-nm-resolution imaging under white light illumination [6], and the observation power of microscopes was enhanced greatly. The microscopy assisted by index-different microspheres, typically the SiO\({}_{2}\), polystyrene (PS), melamine formaldehyde (MF), barium titanate glass (BTG) microsphere, demonstrates the feasibility to realize super-resolution imaging of nanostructures and biological samples in different conditions [7; 8; 9; 10; 11; 12]. Many other non-spherical and non-symmetrical particle-lens have also been investigated [13; 14], and the main advantage of a sphere is that it can achieve ultra-sharp focusing of the incoming wave to generate extreme spatial field localization. The mechanism of the microsphere-assisted microscopy is still a heated topic [15; 16; 17]. Normally, microspheres are directlyput onto the sample surface, which means the spheres are difficult to be controlled for imaging at a specific region. The lack of manipulation of microspheres restricts the applications greatly. To solve this problem, the position of microspheres is guided by fine glass micropipettes [18], scanning superlens microscopy [19], transparent solidified films [20], and remote-mode microsphere nano-imaging platform [21]. These techniques require direct contact with microspheres, and a non-contact optical manipulation technique of microspheres for imaging tends to be more attractive. As the most typical non-contact optical manipulation technique of microparticles, optical trapping [22; 23; 24], also known as optical tweezers, has been widely used for the manipulation of microspheres for nano-fabrication and imaging applications. [PERSON] at al. used Bessel beam laser trapping of 0.76 um PS microspheres to achieve near-field direct-write subwavelength nanopatterning, with minimum sizes of \(\sim\)100 nm [25]. For imaging applications, the magnification property of the PS microsphere in liquid was investigated using optical tweezers [26]. An optically trapped SiO\({}_{2}\) microsphere was utilized for surface imaging in air condition [27]. More recently, a localized plasmonic structural illumination microscopy, together with an optically trapped PS and TiO\({}_{2}\) bead, in which fluorescent objects were used, was developed as a new microscopy technique with 7-11 times improvements of full width at half maximum (FWHM) compared with the result using only the objective [28]. In these research studies, especially for imaging applications, with optical tweezers, researchers investigated the imaging magnifying property of microsphere at visible frequencies or the combination of microsphere with other imaging techniques, and few super-resolution imaging results by a single-beam optically trapped microsphere are demonstrated under white light illumination. Meanwhile, less attention has been focused on the selection of microsphere types which affect both the optical trapping and the imaging performance. The refractive index of the trapped particle in optical trapping is required to be larger than the index of immersion medium (normally the deionized water), which is compatible with the microsphere-assisted microscopy. However, microspheres of different types in the same immersion medium result in different optical trapping performances and varied imaging properties.