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Abstract
Microspheres as special optical lenses have extensive applications due to their super-focusing ability and outstanding resolving power on imaging. The interface reflection between the microsphere and sample surface significantly affects nano-imaging as exhibited in the form of the Newton’s rings pattern in virtual images. In this work, a new scheme of decorating the microsphere with a dielectric bilayer thin film is proposed to suppress the interface reflection and thus enhance the imaging performance. The particle swarm optimization algorithm is performed with a full-wave simulation to refine the bilayer thin film decorated microsphere design, which is successfully realized via a novel fabrication strategy. Experimental imaging results demonstrate that the Newton’s rings pattern in virtual images is substantially diminished. Both the imaging contrast and effective field-of-view of the microsphere nano-imaging are improved via this effective light manipulation scheme, which is also applicable to promoting the performance of the microsphere in other optical applications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Microspheres as special optical lenses have applications in many areas, including optical nano-imaging [1,2], visualized nano-manipulation [3], spectroscopy [4] and ultrafast laser processing [5]. It mainly accounts for two powerful capacities of the microsphere, i.e. diffraction-limited focusing and super-resolution. Since the microsphere nanoscope was first proposed, it has attracted the broad interest of researchers due to its real-time imaging ability with high resolving power, label-free nature, and low cost [6,7]. To date, many advances have been achieved in promoting the performances of the microsphere nanoscope and extending its applications. Microsphere arrays are proposed to raise imaging speed for large-area samples [8]. To realize remote and non-invasive imaging, diverse holders for microspheres are designed and employed [9–11]. Embedding high-index microspheres in the PDMS slabs is a good approach to control the position of microspheres and improve the resolution [12,13]. Microsphere compound lens has been demonstrated to be an effective configuration to increase magnification and field-of-view (FOV) [14–16]. Moreover, it has also been a trend to combine the microspheres with other microscopy techniques, such as dark-field microscope and interference microscope [17,18], to incorporate the advantages of different technologies.
Imaging contrast is a key factor to evaluate the performance of an imaging system [19]. To achieve a better imaging contrast in microsphere nano-imaging, many modification schemes have been developed. Immersing the microsphere in a solid or liquid dielectric is a simple but effective approach to suppress environmental noise and thus improve the imaging contrast [20,21]. Another route is to optimize the illumination conditions, including but not limited to the bandwidth of the light source, condenser diaphragm and field diaphragms [22]. However, all the measures mentioned above are focused on promoting the imaging contrast by reducing the environmental noise at a system level. Yet to be studied is the drawback of microsphere that degrades the imaging contrast, i.e. the interface reflection of microsphere which induces Newton’s rings in virtual images. As reported in many works, virtual images captured by microsphere are mixed with alternating bright and dark ring patterns [23–25]. Such patterns are generated by interference between reflected light from microspheres and sample surfaces. The alternating intensity changes in the background of image affect the overall image quality and decrease imaging contrast in some regions. Besides, when the Newton’s rings effect is severe, some sample features within the FOV of microsphere is covered by the interference pattern and cannot be visualized. As such, the actual visible area in microsphere nano-imaging is reduced. Therefore, it is of critical importance to suppress the interface reflection of microspheres in nano-imaging.
In this work, we propose a new scheme of engineered microsphere made of a transparent microsphere decorated with a dielectric bilayer thin film. Utilizing the light manipulation of the thin films, successful suppression of interface reflection is realized and demonstrated by diminishing Newton’s rings in microsphere nano-imaging. A physical model is proposed to study the formation and characteristics of the Newton’s rings. To optimize the bilayer thin films, the particle swarm optimization algorithm is combined with finite-difference time-domain (FDTD) simulation. The efficacy of the optimized bilayer dielectric thin films is verified by evaluating the visibility of Newton’s rings in the full-wave imaging simulation during the design steps. Moreover, the bilayer thin film decorated microspheres are realized through a new experimental scheme, and imaging results demonstrate that the Newton’s rings are significantly diminished within the FOV of the engineered microsphere. The virtual images without the Newton’s rings exhibit better contrast and a larger effective FOV. This suppression of interface reflection can also enhance performances in other microsphere applications.
2. Analysis and model
In general, the interface reflection of light between two surfaces, i.e. a spherical surface and an adjacent flat surface, can create an annular interference fringes pattern called “Newton’s rings”. An in-depth analysis of the formation of Newton’s rings in microsphere virtual imaging due to interface reflections is carried out to effectively design the bilayer-film-decorated microsphere. To determine whether a full-surface modification is required, we divide the surface of a microsphere into two parts, i.e. the upper and bottom hemispherical surfaces, and analyze them separately.
In microsphere nano-imaging, as the gap between the bottom of the microsphere and the sample surface is typically small, light interference between them is inevitable. Unlike conventional micro-lenses, the surface of a microsphere possesses exceptionally high curvature. This special configuration leads to a unique two-step formation of the Newton’s rings pattern, as shown in Fig. 1(a). Firstly, the components of light reflected from both the underside of the microsphere and the sample surface interfere to form a three-dimensional interference pattern local to the object. Secondly, the sample pattern with the interference light field is relayed and magnified by the upper surface of the microsphere and is visualized in image space. The magnification process is negligible for low-curvature microlenses, but it is significant in microspheres.
Fig. 1. (a) Schematic of Newton’s rings formation in the virtual image produced by a microsphere. (b) Optical field distribution in $xz$ plane when a microsphere is placed on a glass slide. The color bar shows the normalized light intensity. (c) and (d) are images taken from xy planes with z positions indicated by ${z_4}$ and ${z_3}$, respectively.
Interference including reflected light from the upper spherical surface also occurs in the space above the microsphere, but it does not experience a virtual imaging process. Moreover, considering the short coherent length of the illumination light (See more details in Supplement 1, sec. 5), the interference is weak and almost invisible. Therefore, the reflection of the upper hemispherical surface has negligible influence on microsphere nano-imaging. In an experiment to prove this, a 50 µm borosilicate glass microsphere (n = 1.5217) is put on a glass slide under epi-illumination (light wavelength 420 nm). The three-dimensional optical field distribution above and below the sample surface is acquired by z scanning using an optical microscope. The optical field distribution in xz plane is extracted and displayed in Fig. 1(b). ${z_1}$ and ${z_2}$ mark the bottom and top boundaries of the microsphere, respectively. The Newton’s rings exist across almost the entire virtual image formation space, which is under the bottom boundary of the microsphere (z < z1). However, no significant interference pattern is observed in the space above ${z_2}$. Figures 1(c) & (d) display xy plane light field distributions at ${z_4}$ and ${z_3}$, respectively. Since reflection from the upper hemispherical surface has negligible influences on microsphere nano-imaging, only the bottom hemispherical surface requires modification.
Furthermore, a model for the Newton’s rings in virtual images is established to quantitatively verify the proposed formation processes. It provides necessary information for optimizing the thin films design, such as the minimum microsphere surface area required to be coated. According to the light wave interference theory and considering the magnification step as mentioned earlier, when a microsphere is placed on the sample surface, the optical field profile of the Newton’s rings pattern along x direction in image space is calculated as:
The validity of the model is checked by comparing the intensity profiles of Newton’s rings along x-axis from experimental and calculated results, as presented in Figs. 2(a) and (b), respectively. In the calculation, the values of ${E_m}$ and ${E_s}$ are set as 0.5. The illumination wavelength $\lambda $ = 420 nm refers to the optical source used in the experiment and is applied throughout this paper. Notably, due to distortion induced by the upper spherical surface, the actual magnification varies with the radial distance from the optical axis, which is estimated using ZEMAX simulation (See more details in Supplement 1, sec. 1) [26]. It is found that the diameters of the first three calculated bright rings are close to the experimental results. As such, the proposed two-step formation model for the Newton’s rings is demonstrated to be effective. According to this model, the required minimum modified surface area is roughly estimated as the area enclosed by the outmost bright ring in the interference pattern near the undersurface of the microsphere.
Fig. 2. Normalized intensity profiles of Newton’s rings in the virtual image along x direction obtained by (a) experiment and (b) theoretical calculation.
3. Methods and results
Multilayer thin films are widely used to suppress the interface reflection in optical devices [27,28]. However, there is no conventionally available scheme for designing multilayer thin films and demonstrating their performance in microsphere nano-imaging. Also, high precision rotations and three-dimensional translational movements of the microsphere are to be performed throughout the entire experimental procedures, from thin film deposition to optical nano-imaging experiments. Unlike macroscopical optical devices, performing multi-dimensional movements of the microsphere is complicated. Thus, a set of new simulation and experimental schemes is needed.
The particle swarm optimization algorithm is applied in the FDTD software to optimize the thin films for the microsphere (see simulation settings in Supplement 1, sec. 2). This is a numerical optimization method and is applicable to most commonly used microspheres (diameters 4 µm∼100 µm and refractive indices 1.4∼2.2) working in the visible spectrum (wavelength 400 nm ∼750 nm). In this work, two common dielectric materials, i.e. $\textrm{A}{\textrm{l}_2}{\textrm{O}_3}$ (inner layer, n = 1.6979) and $\textrm{Si}{\textrm{O}_2}$ (outer layer, n = 1.4737), are selected to compose the thin films. Simulation results prove that two layers of thin films are sufficient because the area of Newton’s rings corresponds to a small range of reflection angles at the bottom spherical surface. Considering actual imaging experimental conditions, where a 50 µm barium titanate glass (BTG) microsphere (n = 1.9) is fully immersed in polydimethylsiloxane (PDMS, n = 1.444), the final optimized thicknesses of $\textrm{A}{\textrm{l}_2}{\textrm{O}_3}$ and $\textrm{Si}{\textrm{O}_2}$ layers are 70 nm and 92 nm, respectively. Subsequently, full-wave imaging simulation is conducted to verify that the optimized bilayer thin films can diminish the Newton’s rings (see detailed simulation settings in Supplement 1, sec. 2). Firstly, the Lumerical FDTD software is used to directly simulate the process of light illumination across the microsphere boundaries and reflection from the sample surface. The simulated reflected light field ${E_r}({x,y} )$ is collected in $x\textrm{y}$ plane 1 µm above the microsphere and recorded for subsequent calculations. Secondly, the virtual image ${P_v}({x,y} )$ is retrieved by the backward propagation of the reflected light field ${E_r}({x,y} )$ based on the Fourier optics theory. ${P_v}({x,y} )$ is calculated by the following formulas [29,30]:
Virtual imaging simulation is performed for PDMS-immersed 50 µm BTG microspheres under three conditions, i.e. without thin films, with a single-layer thin film, and with bilayer optimized thin films. Fully coated microsphere models are adopted in the simulation (see details in Supplement 1, sec. 2). Limited by the running memory, 2D simulation in $xz$ plane is conducted, where z is the propagation direction of reflected light, and data along x direction is recorded. The sample used is a silicon substrate with the sample surface set at $z = 0$. The retrieved light field in z direction is presented in Figs. 3(a)-(c). Figure 3(a) shows obvious interference fringes in the image formed through a microsphere. When a single layer of 62 nm $\textrm{A}{\textrm{l}_2}{\textrm{O}_3}$ film is deposited on the microsphere surface, the contrast between bright and dark interference fringes moderately decreases as shown in Fig. 3(b), indicating that an optimized single-layer thin film cannot completely remove the Newton’s rings. Figure 3(c) displays the image obtained via a microsphere decorated with the optimized bilayer thin film. In this image, most interference fringes disappear, and more uniform brightness in the virtual image is exhibited. Optical field intensity profiles along the dashed lines in Fig. 3(a)-(c) are plotted in Fig. 3(d) in blue, purple and red colors, respectively. The imaging simulation results demonstrate the feasibility of using bilayer thin films to substantially reduce interface reflection and thus diminish the Newton’s rings in microsphere nano-imaging. Besides, the optimized bilayer film can also slightly reduce the reflection of microsphere in focusing applications and does not affect the size of the focal spot (see details in Supplement 1, sec. 3).
Fig. 3. Full-wave imaging simulation for 50 µm BTG microspheres (a) without coating, (b) with a layer of 62 nm Al2O3 thin film and (c) with a bilayer (70 nm Al2O3 and 92 nm SiO2) thin film. (d) Optical field intensity profiles of the white dashed lines in (a)-(c).
Experiments are carried out to verify the practical capacity of the optimized bilayer thin film on interface reflection suppression. The major difficulty in the experiment is fixing the microspheres for film deposition, such that the thin film deposited area later can be precisely oriented towards the sample surface for imaging. A strategy for surface modification on microspheres is proposed to solve the problem, as shown in Fig. 4. Firstly, a layer of photoresist (AZ1512) film with ∼1 µm thickness is spin-coated onto the silicon substrate. Next, 50 µm BTG microspheres are dispersed onto the photoresist, and the microspheres are allowed to sink in the photoresist because the density of the microsphere (4.38 g/cm3) is larger than that of AZ1512 photoresist (1.038 g/cm3). To speed up the sinking process and make sure that microspheres are in contact with the silicon substrate, a glass slide (thickness 1 mm) is put on microspheres to apply a downward pressure. Therefore, the depth of sinkage is almost equal to the thickness of the photoresist. After baking the AZ1512 photoresist at 115°C for 1 minute, the PDMS is drop-casted on the photoresist to cover the microspheres and cured by heating at 70 °C. After that, the PDMS is peeled off from the substrate, and the bottom parts of microspheres are exposed. A 70 nm Al2O3 film and a 92 nm SiO2 film are then deposited onto the exposed parts of microspheres through the electronic beam evaporator. To ensure that the thin films decorated microsphere is fully immersed for imaging, a thin layer of PDMS was coated on the silicon substrate, and a heavy mass is employed to apply pressure on the PDMS membrane during curing. After the PDMS has been cured, the fully immersed decorated microspheres are transferred onto samples for nano-imaging. From the experimental setting, the actual thin film decorated area on the microsphere is calculated to be ∼14 µm in diameter.
Figures 5(a) and (b) show the virtual image of a Blu-ray disc captured through an uncoated microsphere and a bilayer thin film decorated microsphere, respectively. The corresponding stacked optical field distributions are obtained through z scanning and presented in Figs. 5(c) and (d), respectively. By comparing Figs. 5(a) & (c) with Figs. 5(b) & (d), it can be found that the Newton’s rings pattern (or interference fringes) in the virtual image is significantly diminished and the brightness of the image becomes more uniform when the bilayer thin film decorated microsphere is employed. To better exhibit the effect of Newton’s rings on virtual images and the improvements on imaging when Newton’s rings are diminished by bilayer film, the central part of Fig. 5(a), where the Newton’s rings effect is most severe, is enlarged and displayed in Fig. 5(e). As shown in Fig. 5(e), in the central dark ring region, the line pattern is not clearly seen. The intensity profile along the blue line is plotted and presented in Fig. 5(g), while no structure information can be distinguished. Due to the destructive interference, light carrying information about the line features is suppressed within the dark ring regions and becomes invisible. On the contrary, Fig. 5(f) is the enlarged image of the central part in Fig. 5(b), without interference fringes, the line structures in the center can be recognized. The normalized intensity profile along the red line in Fig. 5(f) is plotted in Fig. 5(h), showing the line structures can be well resolved with good contrast. By comparing Figs. 5(e) & (g) with Figs. 5(f) & (h), it is proved that the thin film coated microsphere can improve imaging contrast in a region where Newton’s rings effect is obvious.
Fig. 5. A Blu-ray disc is imaged by a 50 µm BTG microsphere (a) without or (b) with bilayer thin films. (c) and (d) measured light intensity distributions in $yz$ plane. (e) and (f) the enlarged images of the white squares surrounded area in (a) and (b), respectively. (g) and (h) the normalized intensity profile of the blue and red lines in (e) and (f), respectively. I: normalized optical intensity and P: relative position in the blue or red line from bottom to up.
The film modifications on the microsphere do not change the overall FOV of the microsphere as shown in Fig. 5(a) and (b). However, when the Newton’s rings effect is severe, some sample features within the overall FOV is covered by the interference pattern and cannot be visualized. In this situation, the actual visible area under the microsphere in which all features can be discernible is reduced. Here, such an actual visible area is called “effective FOV”. Figures 5(e)-(h) demonstrate that the thin film decorated microsphere can improve effective FOV. Specifically, a dark ring exists in the center of Figs. 5(e) and no clear line pattern can be observed. So, the effective FOV of this microsphere does not include this dark ring area. As a comparison, no rings patten exists in Figs. 5(f). Line structures in the central area are still well resolved as shown in Figs. 5(h). So, this region is counted as part of the effective FOV of the bilayer-film-decorated microsphere. For a common microsphere with severe Newton’s rings effects, its effective FOV is smaller than its overall FOV due to the existence of some areas where sample features are invisible. The bilayer-film-decorated microsphere diminishes the effect of Newton’s rings on such areas, thus its effective FOV is enhanced to be close to the overall FOV. So, the effective FOV of the bilayer-film-decorated microsphere is increased compared with the common microsphere. In addition, as indicated by the purple dashed lines in Fig. 5(c) and (d), the position of the virtual image plane is almost the same after the microsphere is decorated with bilayer thin films. The magnifications of the two images are both ∼3.5×. This experiment demonstrates that the Newton’s rings are diminished through the decoration of bilayer thin films without altering the nano-imaging properties of microspheres.
Other than reducing interface reflection, there is an alternative method to diminish the Newton’s rings in microsphere imaging, i.e. taking advantage of the short coherent length of the light source to prevent interference. An 83 µm (BTG) microsphere (n = 1.9) fixed on a tip holder is used to image a micro-pattern array on a silicon substrate (see SEM images in Supplement 1, sec. 4) in n = 1.4 oil immersion at different working distances from the sample surface. The virtual images captured by the microsphere when the gap is 0 µm and 8.3 µm are presented in Fig. 6(a) and (b), respectively. Interference fringes are apparent when the microsphere is in contact with the sample surface. When the gap increases and approaches the coherent length (∼9.7 µm) of the light source, the Newton’s rings in the virtual image are almost invisible. Similar results are also obtained in the solid immersion circumstance (See more details in Supplement 1, sec. 5).
Fig. 6. An array of micro-patterns on silicon substrate imaged by an 83 µm BTG microsphere (n = 1.9) in oil (n = 1.4) when the distance between microsphere and silicon surface is (a) 0 µm and (b) 8.3 µm.
As the distance between microsphere and sample increases, the resolution of the microsphere deteriorates because of the reduced effective numerical aperture. However, the practical system resolution is not only determined by the resolving power of the microsphere but also subjected to the magnification of the microscope system because the pixel size of the cameral in a microscope must be taken into account (see detailed discussion and more quantitative information in Supplement 1, sec. 6). Due to the longer object distance from the microsphere, Fig. 6(b) and S7(b) exhibit higher magnifications and better image resolution than those in Fig. 6(a) and S7(a). The better image resolution of Fig. 6(b) and S7(b) mainly attribute to that they are magnified larger and occupy more pixels at the camera sensor plane, which makes the resolved images clearer and thus appear as more distinguishable patterns (see detailed discussion and more quantitative information in Supplement 1, sec. 6). However, an introduced gap results in a reduced microsphere resolution, thus there is a prerequisite for this method to be adopted, i.e. the size of the sample feature is larger than the resolution limit of the microsphere working at a given distance. Such a prerequisite limits the applicable situations for this method to diminish the Newton’s rings. When super-resolving power is required, it is necessary to use the thin films decorated microsphere to suppressed interface reflection and thus achieve enhanced nano-imaging performance.
There are other potential methods to diminish the interference, such as imaging processing with purely computational methods and modulated illumination. Advantages of the imaging processing method are low cost and no need for modifications on microsphere. However, the demand for post-processing is not suitable for real-time imaging. In terms of the modulated illumination method, it requires direct modification on the optical microscope system, which loses an important advantage of microsphere nano-imaging, i.e. compatible with a conventionally available wide-field microscope. Compared with them, the proposed bilayer-film-decorated microsphere keeps the operation manner of common microspheres and thus maintains their advantages, including super-resolving power on imaging, compatible with a conventional wide-field microscope and real-time imaging. Thus, the proposed bilayer-film-decorated microsphere design is a competitive scheme.
4. Conclusion
In summary, a new surface engineering method for microsphere using bilayer thin films deposition is proposed to suppress interface reflection and is demonstrated by diminishing Newton’s rings in microsphere nano-imaging. A model to study the relationship between the interface reflection of microsphere and Newton’s rings in virtual images is presented. The particle swarm optimization algorithm is performed with a full-wave simulation to refine the reflection-reduced engineered microsphere design. Such microspheres decorated with optimized bilayer thin films are also realized with a novel experimental scheme and are demonstrated to be effective on interface reflection suppression through imaging experiments, in which the Newton’s rings pattern is substantially diminished. As such, both the imaging contrast and effective FOV are improved. The combination of microspheres and multilayer thin films paves the way to a new type of optical device with promising potentials in diverse applications, such as improving the signal-to-noise ratio of microsphere-assisted confocal microscopes and increasing the efficiency of the pulse energy coupling into the targeted sample in microsphere laser processing.
Funding
Ministry of Education - Singapore (MOE2019-T2-2-147).
Acknowledgments
This research is supported by the Ministry of Education, Singapore, under Academic Research Fund Tier 2 (Award MOE2019-T2-2-147).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. Z. Wang, W. Guo, L. Li, B. Luk’Yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2(1), 218 (2011). [CrossRef]
2. Y. Zhou and M. Hong, “Realization of noncontact confocal optical microsphere imaging microscope,” Microsc. Res. Tech. 84(10), 2381–2387 (2021). [CrossRef]
3. T. Zhang, H. Yu, P. Li, X. Wang, F. Wang, J. Shi, Z. Liu, P. Yu, W. Yang, and Y. Wang, “Microsphere-based super-resolution imaging for visualized nano-manipulation,” ACS Appl. Mater. Interfaces 12(42), 48093–48100 (2020). [CrossRef]
4. C. Xing, Y. Yan, C. Feng, J. Xu, P. Dong, W. Guan, Y. Zeng, Y. Zhao, and Y. Jiang, “Flexible microsphere-embedded film for microsphere-enhanced Raman spectroscopy,” ACS Appl. Mater. Interfaces 9(38), 32896–32906 (2017). [CrossRef]
5. Z. Lin and M. Hong, “Femtosecond Laser Precision Engineering: From Micron, Submicron, to Nanoscale,” Ultrafast Sci. 2021, 1–22 (2021). [CrossRef]
6. L. Li, W. Guo, Y. Yan, S. Lee, and T. Wang, “Label-free super-resolution imaging of adenoviruses by submerged microsphere optical nanoscopy,” Light: Sci. Appl. 2(9), e104 (2013). [CrossRef]
7. L. Chen and M. Hong, “Functional nonlinear optical nanoparticles synthesized by laser ablation,” Opto-Electron. Sci. 1(5), 210007 (2022). [CrossRef]
8. T. Zhang, P. Li, H. Yu, F. Wang, X. Wang, T. Yang, W. Yang, W. J. Li, Y. Wang, and L. Liu, “Fabrication of flexible microlens arrays for parallel super-resolution imaging,” Appl. Surf. Sci. 504, 144375 (2020). [CrossRef]
9. L. Chen, Y. Zhou, M. Wu, and M. Hong, “Remote-mode microsphere nano-imaging: new boundaries for optical microscopes,” Opto-Electron. Adv. 1(1), 17000101 (2018). [CrossRef]
10. F. Wang, L. Liu, H. Yu, Y. Wen, P. Yu, Z. Liu, Y. Wang, and W. J. Li, “Scanning superlens microscopy for non-invasive large field-of-view visible light nanoscale imaging,” Nat. Commun. 7(1), 13748 (2016). [CrossRef]
11. G. Huszka, H. Yang, and M. A. Gijs, “Microsphere-based super-resolution scanning optical microscope,” Opt. Express 25(13), 15079–15092 (2017). [CrossRef]
12. K. W. Allen, N. Farahi, Y. Li, N. I. Limberopoulos, D. E. Walker Jr., A. M. Urbas, and V. N. Astratov, “Super-resolution imaging by arrays of high-index spheres embedded in transparent matrices,” in NAECON 2014 - IEEE National Aerospace and Electronics Conference (IEEE, 2014), pp. 50–52.
13. K. W. Allen, “Waveguide, photodetector, and imaging applications of microspherical photonics,” Ph.D. dissertation (University of North Carolina at Charlotte, 2014), Chapter 4: Super-Resolution Imaging through Arrays of High-Index Spheres Embedded in Transparent Matrices, pp. 98–122. http://gradworks.umi.com/36/85/3685782.html
14. G. Wu and M. Hong, “Optical nano-imaging via microsphere compound lenses working in non-contact mode,” Opt. Express 29(15), 23073–23082 (2021). [CrossRef]
15. J. Zhou, B. Zeng, S. Bi, and Y. Wang, “Enhanced magnification factors in super-resolution imaging using stacked dual microspheres,” J. Opt. 22(8), 085605 (2020). [CrossRef]
16. H. Luo, H. Yu, Y. Wen, T. Zhang, P. Li, F. Wang, and L. Liu, “Enhanced high-quality super-resolution imaging in air using microsphere lens groups,” Opt. Lett. 45(11), 2981–2984 (2020). [CrossRef]
17. S. Perrin, Y. J. Donie, P. Montgomery, G. Gomard, and S. Lecler, “Compensated microsphere-assisted interference microscopy,” Phys. Rev. Appl. 13(1), 014068 (2020). [CrossRef]
18. Y. Zhou, Y. Tang, Q. Deng, L. Zhao, and S. Hu, “Contrast enhancement of microsphere-assisted super-resolution imaging in dark-field microscopy,” Appl. Phys. Express 10(8), 082501 (2017). [CrossRef]
19. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59(3), 427–471 (1996). [CrossRef]
20. A. Darafsheh, “Influence of the background medium on imaging performance of microsphere-assisted super-resolution microscopy,” Opt. Lett. 42(4), 735–738 (2017). [CrossRef]
21. K. W. Allen, N. Farahi, Y. Li, N. I. Limberopoulos, D. E. Walker Jr, A. M. Urbas, V. Liberman, and V. N. Astratov, “Super-resolution microscopy by movable thin-films with embedded microspheres: resolution analysis,” Ann. Phys.-Berlin 527(7-8), 513–522 (2015). [CrossRef]
22. S. Perrin, H. Li, A. Leong-Hoi, S. Lecler, and P. Montgomery, “Illumination conditions in microsphere-assisted microscopy,” J. Microsc. 274(1), 69–75 (2019). [CrossRef]
23. B. Jia, P. Li, F. Wang, H. Y. Chan, G. Zhang, and W. J. Li, “Determination of Microsphere-Lens Magnification Using Micro-Robotic Scanning Superlens Nanoscopy,” IEEE Open J. Nanotechnol. 1, 65–76 (2020). [CrossRef]
24. H. S. S. Lai, F. Wang, Y. Li, B. Jia, L. Liu, and W. J. Li, “Super-resolution real imaging in microsphere-assisted microscopy,” PLoS One 11(10), e0165194 (2016). [CrossRef]
25. S. Yang, Y. Cao, Q. Shi, X. Wang, T. Chen, J. Wang, and Y.-H. Ye, “Label-free super-resolution imaging of transparent dielectric objects assembled on a silver film by a microsphere-assisted microscope,” J. Phys. Chem. C 123(46), 28353–28358 (2019). [CrossRef]
26. S. Yang, X. Wang, J. Wang, Y. Cao, F. Wang, T. Chen, and Y. H. Ye, “Reduced distortion in high-index microsphere imaging by partial immersion,” Appl. Opt. 57(27), 7818–7822 (2018). [CrossRef]
27. H. Cory, C. J. M. Zach, and O. T. Letters, “Wave propagation in metamaterial multi-layered structures,” Microw. Opt. Technol. Lett. 40(6), 460–465 (2004). [CrossRef]
28. K. Pfeiffer, L. Ghazaryan, U. Schulz, and A. Szeghalmi, “Wide-angle broadband antireflection coatings prepared by atomic layer deposition,” ACS Appl. Mater. Interfaces 11(24), 21887–21894 (2019). [CrossRef]
29. J. Goodman, Introduction to Fourier Optics, 4W. H (Freeman, New York, 2017).
30. X. Liu, C. Kuang, X. Hao, C. Pang, P. Xu, H. Li, Y. Liu, C. Yu, Y. Xu, and D. Nan, “Fluorescent nanowire ring illumination for wide-field far-field subdiffraction imaging,” Phys. Rev. Lett. 118(7), 076101 (2017). [CrossRef]
31. A. V. Maslov and V. N. Astratov, “Imaging of sub-wavelength structures radiating coherently near microspheres,” Appl. Phys. Lett. 108(5), 051104 (2016). [CrossRef]
32. A. V. Maslov and V. N. Astratov, “Optical nanoscopy with contact Mie-particles: Resolution analysis,” Appl. Phys. Lett. 110(26), 261107 (2017). [CrossRef]
33. A. Maslov and V. Astratov, “Resolution and reciprocity in microspherical nanoscopy: Point-spread function versus photonic nanojets,” Phys. Rev. Appl. 11(6), 064004 (2019). [CrossRef]
