1. Introduction

Exploration of intracellular or intratissue activities in biological systems, inspection of buried or embedded nanostructures in material engineering, localization of defect or dopant sites in semiconductor devices, verification of drug or reagent nanotoxicology in pharmaceutical products and manipulation of molecular or atomic behaviours in microscopic world are of tremendous importance in modern science and technology. Non-destructive, high-resolution and real-space imaging techniques are comparatively effective methods to realize the identification, quantification and analyzation of such nanoscale subsurface features and structures [1, 2]. The main ideas of these techniques are through the improvement of conventional electron microscopy (EM) and scanning probe microscopy (SPM) [3–5]. Due to the introduction of ultrasound excitation and the utilization of cantilever probe, electronic crosstalk, mechanical instability, complex principle, expensive apparatuses and slow image acquisition time are the insurmountable obstacles and restrictions of EM- and SPM-based subsurface nano-imaging techniques. The corresponding detection depth beneath the surface is usually no more than one micron [6, 7]. Although, on the one hand, near-field scanning optical microscopy and its variants are still confronted with these relative adverse factors in imaging the nano-sized subsurface details [8–10]. On the other hand, fluorescently-labelled nano-imaging approaches may probably cause the damage or change of original function of the studied samples since the conjugation of fluorophores [11]. Optical methods (OMs) hold great promise for subsurface characterization benefit from their easy integration with high numerical aperture (NA) lens and other highly attractive advantages including non-invasive radiation, label-free interaction, wide-field excitation, real-time monitoring and far-field imaging [12–14].

Because of the existence of classical diffraction limits, OM-based subsurface nano-imaging technique remains a poorly explored area [15]. The obtainment of good resolution depends on the substrate and the high-NA lens with the same refractive indices, while too much refractive index difference (RID) with the addition of fabrication imperfection between two interfaces brings about high reflection and leads to large aberration. Intense absorption and chromatic dispersion are accompanied by incorporating a high refractive index adscititious lens. There is a strong demand to develop an optical superlens that can directly visualize the nano-sized subsurface fine features and be composed by two different materials with small RID.

The discovered microsphere nanoscopy, of which capturing image in a virtual mode and improving resolution to the sub-diffraction-limited size, has paved a way to apply low-refractive-index microparticle to realize nano-imaging [16]. Some pioneer works have revealed the potentials for imaging spatially separated objects with microsphere nanoscopy [17–19]. However, on account of the image formation relying on the morphology feature and refractive index of the microsphere particle, the field of view (FOV) is generally confined to a few microns [16, 20, 21]. The truncated face-down microsphere can broaden the FOV and make use of more focal depth, which is naturally adopted as an excellent candidate to form the superlens of wide view fields and observable subsurface nanostructures [22, 23]. Such microparticle superlens can be regularly shaped with a self-assembly method based on the equilibrium of surface tension at solid/liquid/gas interface [24–26]. Among the rest, polystyrene [22], polymethyl methacrylate [27] and photocurable polymer [23, 28] are the frequently utilized materials which can self-assemble superlens under the surface tension and the subsequent thermal-forming or photopolymerization technology. Super-hydrophobic surface with ultra-low adhesive force prompts the microscale structures induced by surface tension quickly and possessing nearly atomic-scale surface finish [29–31]. In line with the imaging theory presented by Abbe, the projection of an object’s image are mainly related to the interference of various components of electromagnetic waves emitted or scattered from the object. This fact is helpful towards the creation of subsurface nano-imaging facilities due to the smoother surface showing lower energy loss and less invalid scattering.

Here, we successfully constructed a spherical cap optical nanoscopy (SCON) subsurface nano-imaging system (SNIS), where a bio-compatible and chemically-inert polydimethyl siloxane (PDMS) elastomer is coated onto the subsurface object as the artificial substrate and a commercially available, optically transparent and low-refractive-index UV-curable adhesive is used to self-assemble the nanoscopy. SCON-SNIS is considered as a bridge of the subsurface details and the ordinary optical microscope, which can directly convert subsurface nanofeature information to the far-field optical imaging system. The SCON is formed above the PDMS substrate without immersion or semi-immersion in a medium. By this approach, nanoscale objects of several micrometres below the substrate and less than Rayleigh resolution limit or the space far below the diffraction limit (as small as 100 nm) were clearly resolved under a white light microscopy. It shows that the FOV of SCON-SNIS, in the radial direction, is approximate one-half of the SCON’s equatorial diameter (ED). With the decline of microscope’s focal plane, the FOV extends from the centre out to the periphery and the virtual image magnifications synchronously increase. This cost-effective and easily implementable nanoscopy is made possible to develop a high-resolution, label-free and dynamic real-time on-chip image projection tool by integrating with other microsystems.

2. SCON-SNIS preparation

Two nanoscale structures, Si-nanodisk array and Blu-ray DVD disk, are used as the subsurface specimens. Si-nanodisk arrays are fabricated through laser interference lithography and metal assisted chemical etching [32]. Norland UV-curable adhesive (NOA 61, produced by Norland Inc), with the attributes of broad transparency, small viscosity, low shrinkage, long-term stability and excellent UV-curability, is chosen to prepare the SCON. The refractive index of NOA 61 is approximate 1.56 (n_N) in the visible spectral region, which is far less than the refractive index of solid immersion lens (SIL) and NA increasing lens [12–14]. A structural rigidity and thermally curable material used for the artificial substrate is Sylgard 184 liquid PDMS elastomer with refractive index n_P = 1.41 and one-tenth weight curing agent purchased from Dow Corning. The SCON is self-assembled upon the PDMS substrate by super-hydrophobic effect and surface tension [33].

The preparation process flow is composed of four steps: spin-coating with PDMS, NOA 61 prepolymer transfer to the PDMS substrate, NOA 61 liquids self-assembling into spherical cap microparticles and SCON formed upon UV irradiation. As shown in Fig. 1(a), the process details are as follows. In the first place, a prefabricated Si-nanodisk cleaned by deionized water or a pretreated Blu-ray disk peeled off its protective layer is spin-coated with unseasoned PDMS matrix and cured at 60 °C for 24 hours in a temperature controlled oven [Figs. 1(a)-i to 1(a)-ii]. Multiple thicknesses of PDMS substrate layers are fabricated by setting different spinning duration and coating speed. After the PDMS substrate layer is fully baked, a good super-hydrophobic property would emerge [28]. As a result of the adhesive action of PDMS to Si-nanodisk (or Blu-ray disk), it is able to ensure close proximity between PDMS substrates and subsurface objects. Then, a half-tapered optical fiber, obtained by a heating-and-pulling method, is used to transfer the NOA 61 adhesive to the PDMS substrate layer on the basis of the wettability of NOA 61 towards optical fiber [Fig. 1(a)-iii] [34]. Due to the effect of surface tension, NOA 61 microspherical cap particles are self-assembled on the super-hydrophobic PDMS layer [Fig. 1(a)-iv].

 

Fig. 1 (a) Diagram illustrating the process used to fabricate SCON-SNIS. (b) Self-assembling process of SCON on PDMS substrate as a function of time.

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Figure 1(b) (i to vi) demonstrate the self-assembly process, which is monitored and recorded by a microscope equipped with a charge-coupled device (CCD) camera, as a function of time. At the beginning, a long cylinder shape of NOA 61 liquid composed by a series of closely adjacent bottle-like micro-segments is created on the flat PDMS substrate surface [Fig. 1(b)-i]. In a very short period of time, the cylinder fleetly breaks into several short bottle-like micro-segments [Fig. 1(b)-ii]. As can be seen in Fig. 1(b)-iii, all the micro-segments are completely broke apart in less than two seconds. In the following two seconds, these micro-segments gradually shrink to each center with a slight movement and self-assemble into circular microdroplets [Fig. 1(b)-iv]. After about four seconds, the NOA 61 microdroplets gather together to form the final spherical cap microparticles [Fig. 1(b)-v]. There are almost no changes in the shape of spherical cap microparticles observed in the last two seconds during the monitoring period. Owning to surface tension action and super-hydrophobic effect, the whole self-assembling process takes about eight seconds.

Next, the liquid spherical cap microparticles are exposed under a Norland UVC splice lamp with light intensity output of 2.5 W/cm² in UV spectrum to attain solid and constitutionally stable SCONs. It is important to note that the shape of the SCON is almost unchanged after the curing resulting from the highly UV-transparent PDMS and low shrinkage nature of NOA 61 [35, 36].

3. Subsurface nano-imaging

To investigate the subsurface nano-imaging of SCON-SNIS, a schema of the experimental setup is depicted in Fig. 2. The SCON-SNIS is directly placed under an upright Nikon microscopy (ECLIPSE LV100) in reflection mode. The white light is focused by a 100 × (NA = 0.9) objective lens and used to illuminate the SCON-SNIS and the underlying subsurface object. Near-field nanofeatures of the specimen are captured and projected to the far-field imaging equipment to form a magnified virtual image. This process can be observed by adjusting the microscope objective to the virtual image plane below the subsurface specimen plane and recorded with a CCD camera.

 

Fig. 2 Schematic illustration of the experimental setup. Imaging of subsurface objects by a SCON-SNIS in combination with a conventional far-field optical microscope under reflection mode.

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According to Rayleigh's criterion, the resolution limit is 303 nm for point objects (R = 0.61λ/n_PNA) and 248 nm for line objects (R = 0.5λ/n_PNA), where in the central wavelength of halogen light source is λ = 630 nm. As illustrated in Fig. 3(a)-i, the Si-nanodisk array has periodic lines of 260 nm space and 220 nm diameter, which is apparently less than the Rayleigh resolution limit and close to Abbe diffraction limit and can be roughly discerned by an optical microscope. In the case of Blu-ray disk, it is a one-dimensional array structure of 300 nm track pitch with 100 nm line spacing and is indistinguishable with the Nikon microscopy. Figure 3(b)-i shows the scanning electron microscopy (SEM) image of the Blu-ray disk, the 100 nm spacing is far less than the Rayleigh resolution limit and the theoretical ∼200 nm diffraction limit as well.

 

Fig. 3 (a)-i Microscopic image of an Si-nanodisk array with periodic sizes of 480 nm consisting of 260-nm-diameters disk separated by 220 nm spaces; (a)-ii Self-assembled SCON with equatorial diameter (ED) of 7.6 μm and 1 μm above the subsurface object of Si-nanodisk array; (a)-iii Image of the subsurface Si-nanodisk array generated by 7.6 μm SCON at the position of d = −0.5 μm. (b)-i SEM image of a Blu-ray disk with a line width of 200 nm and a spacing of 100 nm; (b)-ii Self-assembled SCON with ED of 20 μm and 3 μm above the subsurface object of Blu-ray disk; (b)-iii Image of the subsurface Blu-ray disk generated by 20 μm SCON at the position of d = −6 μm.

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With the employment of self-assembly method, two SCONs with equatorial diameters (EDs) of 7.6 μm and 20 μm are accordingly formed on PDMS-coated Si-nanodisk array and Blu-ray disk. These two cases are named as Case 1 and Case 2 in this work. The thicknesses of the PDMS substrates are 1 μm for Fig. 3(a)-ii and 3 μm for Fig. 3(b)-ii. The symbol “d” marked in Fig. 3 denotes the locations relative to the surface of the subsurface specimen, where the horizontal subsurface here is assigned to zero along z-axis direction of the 3-dimensional rectangular coordinate system. As for the Si-nanodisk array, a clear and magnified image is produced at the position of d = −0.5 μm [Fig. 3(a)-iii]. The bright spots within the spherical cap are the virtual images of discoidal body. The lateral magnification of the virtual image is m ≈1.4. For the Blu-ray disk, the virtual image with a higher magnification factor (m ≈2) and nearly no obvious distortion is situated at a lower position of 6 μm beneath the surface of subsurface object [Fig. 3(b)-iii].

The subsurface nano-imaging could be regarded as the electromagnetic wave propagation through SCON-SNIS, interaction with subsurface object and fractional light feeding back to the signal acquisition system to form the image. A finite element method (FEM) based numerical technique (COMSOL Multiphysics software package) combing with classical ray optics approach is employed to study the imaging mechanism. The light source used for the ray-tracing analysis and full-wave simulation is a monochromatic plane wave with wavelength λ = 630 nm and intensity I = 1. For the simulation model, perfectly matched layer (PML) absorbing boundary condition is set to all exterior boundaries. A non-uniform mesh with a refractive-index-dependent element size (50 nm in the air) is small enough for the computational accuracy.

When the plane wave emits from the top and reaches the interface of air and SCON, it refracts towards the round and optically dense microspherical cap. The constringent and high-intensity electromagnetic beam propagates into the substrate and illuminate the buried subsurface object of interest. As shown in Figs. 4(a) and 4(b), SCONs are supposed hemispheric shapes. Four rectangles with different colors in Fig. 4(a) denote ambient air, NOA 61 SCON, PDMS substrate and subsurface object. The red ray trajectories travel following the dark black arrows with a convergence trend. This tendency can be confirmed by the flow and distribution of Poynting vector in Fig. 4(b). The calculated and simulated illumination size of electric field intensity distribution on the subsurface specimen plane are 10.44 μm and 10.86 μm in diameters. The deviation lies in that the diffraction effect occurred in the physical optics numerical model, when the light beam propagates from one surface to another, is not considered in the geometrical optics of using imaginary straight lines to represent the ray tracing.

 

Fig. 4 (a) Ray tracing analysis of plane wave transmitting through SCON-SNIS. (b) Full-wave simulation of SCON-SNIS illuminated by a monochromatic plane wave. The arrows denote the distribution of Poynting vector field. (c) Illumination sizes comparison of SCON with (c)-i θ = 90° and (c)-ii θ> 90°. ED: equatorial diameter, r: half of ED, h (height): distance from bottom surface to top vertex of face-down SCON, θ: contact angle, t: thickness, O: center of SCON. The regions within the black dashed boxes stand for the illumination area. Insert: principle scheme of a liquid NOA 61 SCON in contact with the PDMS substrate surface in the state of equilibrium, the contact angle is related to the surface energy of gas/solid (σ_g-s), solid/liquid (σ_s-l) and gas/liquid (σ_g-l). (d) Ray-tracing and FEM-simulation results of illumination sizes with respect to the height (h) in the cases of (d)-i ED = 20 μm and (d)-ii ED = 7.6 μm. Transparent green rectangular boxes: the observed experimental FOVs, Grey dotted line: illumination size at h = r.

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FOV is a significant performance for imaging application which is defined here as the diameter of the observed and recognized circular area of the subsurface specimen. Though the FOV is frequently mentioned in previous studies of microsphere nanoscopy, the physical origin was rarely explored [16, 37, 38]. In our research, it is found that the FOV is related to the illumination cross section. The experimental results of the FOV are approximate 3.84-4.8 μm for Case 1 and 9-10.2 μm for Case 2, which are smaller than the simulation results of 4.83 μm and 10.86 μm. Referring to the theory of interfacial chemistry, when the retracted NOA 61 liquid reaching the ultimate equilibrium shape, the contact angle (θ) can be estimated via Young’s equation [39]. As shown in the inset of bottom-middle position between Figs. 4(c)-i and 4(c)-ii, σ_g-s, σ_s-l and σ_g-l stand for the surface energy values of gas/solid, solid/liquid and gas/liquid interfaces. Since PDMS has a low surface energy of ∼20 dynes∙cm⁻¹ [40], which is smaller than the surface energy of NOA 61 (40 dynes∙cm⁻¹) [34]. The liquid NOA 61 spherical cap microparticles, in equilibrium, do not wet the solid PDMS substrate layer and the corresponding contact angles (θ) are larger than 90° [Fig. 4(c)-ii]. Figure 4(c)-i shows the schema of the situation of hemispheric shape, of which the contact angle θ = 90° and the height (h) from the bottom surface to the top vertex equals half of the ED (r). By comparison of Fig. 4(c)-i with Fig. 4(c)-ii, it is clear to see that the illumination size (labelled with black dashed boxes in the figures) of SCON with the case of θ> 90° is smaller than the case of θ = 90°. With this line of thinking, the illumination sizes of SCON-SNIS with the variation of SCON height for Case 1 and Case 2 are investigated under the conditions of θ> 90° and h>r. It can be seen from Figs. 4(d), the simulation and calculation values both decreases with the increase of h. As a result, the observed experimental FOVs match the illumination sizes of SCON with specific height of higher than r (ie, the contact angle over 90 degree).

It is obvious that this spherical cap shaped nanoscopy provides a wide FOV (∼ED/2) and thereby it is easy to reach positioning of the imaging. Whereas a limited FOV may cause the entire view of an object not obtainable or the whole image displayed with blurring edge. Though the spherical and chromatic aberrations inevitably result in some edge-blur of the image and the degradation of contrast, as can be seen in Figs. 3(a)-ii and 3(b)-ii, small refractive index mismatch between NOA 61 SCON and PDMS substrate can maximally reduce the disruption of the image quality induced from the discontinuity at the substrate-SCON boundary itself. A relative better imaging effect of Si-nanodisk than Blu-ray disk could be attributed to larger feature sizes and less longitudinal and transverse geometrical aberrations.

As to the Si-nanodisk arrays with sizes slightly more than diffraction limit, a model of PDMS-immersion combination with NOA 61 SCON acting as a SIL is adequate for the explanation of such nanoscale resolution. However, the highest diffraction-limited resolution, with this estimation method, is ∼λ/(2n_N)/n_P = 143 nm for λ = 630 nm, n_N = 1.56 and n_P = 1.41. This limit value is insufficient to resolve the Blu-ray disk of containing 100 nm spacing. The widely used phenomenological explanation upon super-focusing effect of photonic nanojet can only gain a full-width at half-maximum (FWHM) down to minimum value of ∼λ/3 [41]. An image treatment method on the basis of classic Houston criterion and convolution of an object with the point spread function (PSF) is well adopted to analyse nanoscale spatial resolution of over or under diffraction limit [42–44].

Even though ray optics, especially for the research objects with dimensions comparable to the optical wavelengths, are not effective methodologies to quantitatively determine the virtual image characteristic and magnification factor of micro- or nano-sized particle imaging systems, it can provide a reasonable way to qualitatively indicate the rule and trend [16, 20, 22, 42, 45]. Figure 5(a) shows the ray-tracing of a magnified virtual image formed under the subsurface specimen by SCON-SNIS. r, t, h, n_N, n_P and m express the same meanings as earlier presented in this paper. n_A = 1 is the refractive index of ambient air, d_e and d_c are respective the observed image plane in the experiment and the calculated image plane through the ray optics analysis. l, m₁l and ml stand for the length of object and magnified virtual images at the positions of experimental image plane (d_e) and calculational image plane (d_c). For SCON-SNIS with ED = 20 μm, t = 3 μm and taking the height value h = 11.4 μm (of which the simulated FOV completely overlaps with the experimental FOV) into account, the calculated magnification factors (m_c) with the image plane positions in the range of −6.7 μm to −4.8 μm below the substrate are around 2 [violet circle line in Fig. 5(b)-i]. It is a fairly approximate value to the experimentally measured magnification factor (m_e ≈2) that marked in Fig. 5(b)-i as a red asterisk at d_e = −6 μm.

 

Fig. 5 Virtual image formation of subsurface specimen with a SCON-SNIS by ray tracing method. (b)-i and (b)-ii Magnification factors with (r, t, h) = (10, 3, 11.4) and (r, t, h) = (3.8, 1, 4.1) at different position range of −6.7 to −4.8 μm and −2.78 to −2.62 μm of calculated image planes. Red asterisks show the observed magnification factors at the experimental image plane. m₁∼1.2 is the calculated magnification factor with a comparatively small value.

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A similar analytic process is implemented to the SCON-SNIS with small size (ED = 7.6 μm) and thin thickness (t = 1 μm). As illustrated in Fig. 5(b)-ii, the calculated m at the image plane positions of ∼-2.7 μm lower than the substrate plane are higher than the experimental result of m_e ≈1.4 at image plane position of d_e = −0.5 μm. This indicates that ray optics approximation is not an accurate method for predicting the image plane position and magnification factor, from the quantitative point of view, as the SCON size reducing to a certain level. Nevertheless, when the position of the calculated image plane is set to the value of d_c = d_e = −0.5 μm, as can be seen from the lavender dumbbell-like shaped virtual image in Fig. 5(a)-i, the image is formed in the state of the light beams without converging to an ideal point. The magnification factor m₁∼1.2 is less than the theoretical prediction value m_c> 2. In consequence, the experimental result (m_e ≈1.4) of the magnification factor falls in between and much closer to the value at the real observed virtual image plane.

The following investigations further confirm the experimental phenomenon of which conform to the above theoretical predictions. When the focal plane positions of the microscope objective are going down, no matter large-sized Si-nanodisk array or small-sized Blu-ray disk, the magnification times of the virtual images increases. In order to clarify, the half of the virtual images for case 2, illustrated in Figs. 6(a)-i, 6(a)-ii and 6(a)-iii, are marked with white arc-shaped lines. The white lines show the magnified images containing pincushion distortion. Due to the existence of image plane composed by ideal focal points, there must be an optimal imaging positions of which the image showing the best optical contrast. As can be seen from the intensity distribution profiles in the insets of Figs. 6(a)-i to 6(a)-iii, the maximal ratios of adjacent peak and trough values is emerged in the inset of Fig. 6(a)-ii. Thus, the virtual image plane at the position of d_e = −5.4 μm has the clearest image among the three. The relatively low definition out of the scope of SCON hides the concomitantly enlarged FOV. This situation is reflected in the case of imaging large-sized Si-nanodisk array specimen through a SCON-SNIS of ED = 20.9 μm and t = 6 μm [Fig. 6(b)]. With the reduction of image plane positions, the expansion of the FOVs and the enlargement of the magnification factors are apparent [Figs. 6(b)-i to 6(b)-iii]. The optical contrasts, on the whole, change with the same rule as the case of imaging Blu-ray disk specimen. In the middle part of the SCON, the optical contrast of the images at d_e = −9 μm is a little less than the image formed at d_e = −7.4 μm. At the position of d_e = −11 μm, the images of the array points within the SCON disappear, and the reserved peripheral part of the image becomes breezing. Figures 6(b)-iv to 6(b)-vi give relevant evidences with intensity profile of the labelled lines in each microscopic images. By contrast with the case of Blu-ray disk, the generated images show a sharper contrast and a wider image plane positions for collecting images.

 

Fig. 6 Virtual images of subsurface Blu-ray disk with a SCON-SNIS of ED = 21.4 μm and t = 4.1 μm at the image plane positions of (a)-i d_e = −5 μm, (a)-ii d_e = −5.4 μm and (a)-iii d_e = −6 μm. The insets in (a)-i, (a)-ii and (a)-iii, respectively, are the irradiance intensity distributions along the red, green and blue short lines. The white arc-shaped lines are artificial markers for more clearly indicating the virtual images formed unearth the specimen surface and pincushion distortion to a certain degree. Virtual images of subsurface Si-nanodisk array with a SCON-SNIS of ED = 20.9 μm and t = 6 μm at the image plane positions of (b)-i d_e = −7.4 μm, (b)-ii d_e = −9 μm and (b)-iii d_e = −11 μm. (b)-iv to (b)-vi are the intensity distribution profiles along the red, green and blue dashed lines.

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The magnification factors relative to EDs and t of the SCON-SNISs in these two cases are experimentally studied. Figures 7(a) and 7(b), respectively, show the three dimensional bivariate (ED and t) graph and two dimensional univariate (ED) graph. The ED and t values are mainly distributed in the ranges of ∼10 μm to ∼30 μm and ∼1 μm to ∼6 μm. The variation law of rising first and then falling with respect to EDs for point object of Si-nanodisk array is similar to the research finding of imaging nanoparticle dimer array with liquid-immersed barium titanate glass microspheres in Ref. 20. In the case of Blu-ray disk, there are no clear images observed with SCON’s EDs less than 10 μm in our study. The magnification factors, as the same as case 1, decrease with the increase of EDs. Since the curvature (1/r) of a micro/nano-sized particle lens exhibiting an important role in the formation of optical image [46], as illustrated in Fig. 7(c), m_e is gradually increasing with the decrease of 1/r when the substrate thickness is set to t = 4 μm. The increasing trends are also observed in the cases of t = 3 μm and t = 4.2 μm [two insets in Fig. 7(c)]. Figure 7(d) shows the theoretical calculation results of m_c depending on 1/r. The m_c curves reveal the same variation tendency at different SCON heights, which agrees well with the experimental results. A higher height of SCON brings about a narrower convergence light illuminated to the surface of the subsurface specimen, which accordingly leads to the returned signal captured by the acquisition system of the optical microscope possessing a larger magnification factor.

 

Fig. 7 (a) Experimental measurement values (m_e) of magnification factors as a function of equatorial diameter (ED) and substrate thickness (t) with the specimens of Si-nanodisk array and Blu-ray disk. (b) Two dimensional univariate graph of m_e relative to EDs for these two cases. (c) The changing relationship of magnification factors (m_e) and curvature (1/r) under a fixed substrate thickness (t) in the case of Blu-ray disk. Insets: Relationship of m_e and 1/r with t = 3 μm and t = 4.2 μm. (d) Theoretical analysis of magnification factors (m_c) versus to curvature (1/r) with the heights equalling r + 0.1, r + 0.3, r + 0.6, r + 0.9 and r + 1.2, respectively.

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4. Conclusions

A non-invasive, label-free, real-time and far-field subsurface nano-imaging technique at wide-field excitation mode, from both theoretical and experimental aspects, is demonstrated in this work. The SCON is constructed by using a self-assembly method on the basis of surface tension action and super-hydrophobic effect with two low RID materials of UV-curable adhesive and PDMS elastomer. Typical point shaped subsurface structures of below Rayleigh resolution limit (∼0.35λ) and the space of line shaped subsurface structures of beyond Abbe diffraction limit (∼0.16λ) situated under the artificial substrate can be clearly imaged and resolved in such conventional microscopy combined SCON-SNIS. The imaging mechanism, through FEM-based full-wave simulation and geometrical optics based ray-tracing analysis, indicates, firstly, that the SCON-SNIS has a FOV is approximate one-half of its ED in the radial direction and the FOV is related to the illumination cross section; secondly, the virtual image characteristics and magnification factors are qualitatively determined by employing ray optics approximation. With the decrease of image plane positions, magnification factors are increased and the corresponded FOVs are enlarged. There exists an optimal imaging position of presenting the best optical contrast and the clearest structure profile. For the case of the substrate thickness taking a fixed value, the magnification factors have an inverse relationship to the curvature.