Investigation of far-field super-resolution imaging by microsphere-based optical microscopy
Introduction
The spatial resolution of a conventional optical microscopy is restricted by the diffraction limit, which prevents the imaging of sub-wavelength objects with dimensions of less than half of the wavelength of the illuminating light λ, as only the propagating wave components emanating from the illuminated object can be captured [1]. The evanescent waves that carry sub-wavelength information about a sample decay exponentially in a medium with positive permittivity and permeability, and are lost before they reach the image plane. Super-resolution imaging can be achieved by capturing these near-field evanescent waves from the objects. Numerous methods have been proposed for overcoming the diffraction limit, such as solid immersion lenses, near-field probes, fluorescent microscopy techniques and a negative index material superlens [2], [3], [4], [5]. However, these techniques each have certain limits, such as the need for sophisticated engineering designs or operation in the near field. A nanoscope based on microspheres has emerged as a simple and effective way of achieving optical super-resolution imaging [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. By depositing a transparent microsphere onto the surface of the object, we can achieve near-field focusing in which features are resolved beyond the diffraction limit. This system can provide a direct, non-invasive, and far-field method of observing both metallic and non-metallic objects. Wang et al. first proposed the use of SiO2 microspheres located above a sample to overcome the white light diffraction limit in experiments, and obtained sub-wavelength information from the imaging of a nano-structure [6], [7], [8], [9], [10], [11]. Hao et al. used a SiO2 microsphere that was semi-immersed in a liquid droplet to discern the details of an object with a size below the Abbe diffraction limit [12]. Darafsheh et al. used a barium titanate (BaTiO3) glass microsphere with high refractive index that was immersed in liquids and elastomers to achieve super-resolution imaging of nano-structures and biological structures [13], [14], [15], [16]. In these studies, it was demonstrated experimentally that microspheres can be used to collect near-field evanescent waves and to transform them into far-field propagating waves. In microsphere-based optical microscopy, a phenomena known as a ‘photonic nanojet’ occurs, in which the focus is located very close to the surface of the microsphere and evanescent wave components may be involved [20]. Wang et al. used a pupil mask and a centrally covered engineered microsphere to reduce the spot size in order to improve the resolution [21,22]. Although it was suggested that the development of a photonic nanojet was essential for the super-resolution imaging capability of a microsphere, the exact link remains unclear.
In this paper, we study the role of the photonic nanojet in super-resolution imaging. We first analyse the mechanism involved in the far-field super-resolution imaging of the microsphere-based optical microscopy. Next, we carry out a numerical study of light propagation through microspheres using the finite element method, which allows us to characterise the photonic nanojet at the rear surface of the microsphere and the light focusing capability of the photonic nanojet. Following this, we perform an experimental study in which we show that the resolution of the optical system is directly correlated with the properties of the photonic nanojet for a microsphere. Our theoretical analysis of super-resolution imaging is then verified based on numerical and experimental results.
Section snippets
Theoretical analysis
In [7], the authors show that a photonic nanojet is generated below the microsphere in both the transmission and the reflection modes, and that it arrives at the sample surface and illuminates the area below the microsphere. In order to illustrate this effect, a two-microsphere model is developed in the reflection mode (as shown in Fig. 1), based on a conventional optical microscopy with a 100×, NA = 0.9 objective lens. When an EM plane wave passes through the microsphere (Fig. 1), the light is
Super-resolution focusing using a microsphere
A full-wave simulation using COMSOL Multiphysics software was used to study the focusing properties of the microsphere [19]. COMSOL Multiphysics is based on the finite element method. In our simulation, SiO2 microspheres with a refractive index of 1.46 and a BaTiO3 microsphere with a refractive index of two were used. These were illuminated by a plane wave with a wavelength of 400 nm, and sub-diffraction photonic nanojets were generated on the shadow sides of the microspheres, as shown in Fig. 5
Image of the grating
Fig. 7 shows a schematic diagram of a microsphere-based optical microscopy experiment. The microsphere (supplied by Bangs Laboratories) was placed on the top of the sample surface. A standard optical microscope with a 100× NA = 0.9 objective lens was used, and a halogen lamp provided the white-light illumination source. The resolution limit of the optical microscope with the microscope objective (100×, NA = 0.9) can be calculated using d = 0.61 × λ/NA. Without the microsphere, the objective
Conclusion
A mechanism of far-field super-resolution imaging using microsphere-based optical microscopy was developed based on the conversion of evanescent waves containing high-frequency spatial information on the sample into propagating waves by the microsphere, within the optical resolution limit of a conventional optical microscope. The formation of a photonic nanojet through focusing of light by the microsphere plays an important role. The size of this nanojet is associated with the radius and
CRediT authorship contribution statement
Qiaowen Lin: Conceptualization, Methodology, Formal analysis, Software, Writing – review & editing, Writing – original draft, Funding acquisition. Hongmei Liu: Funding acquisition, Project administration, Supervision. Yongqiang Kang: Investigation, Validation, Data curation, Software, Funding acquisition.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the Applied Basic Research Project of Shanxi Province (Nos. 201801D121071, 201901D211431), Natural Science Fund of Datong City (Grant No. 2017131). Key Research and Development Project of Datong city (No. 2020019).
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