Microsphere-assisted microscopy Free

Light microscopy is one of the most powerful techniques for nondestructive real-time imaging of specimens at a resolution beyond the reach of human eyes. However, the spatial resolution of any conventional microscope is fundamentally limited by the diffraction of light waves at the lens aperture. The resolution limit is approximately 200 nm in conventional white-light microscopes. Microscopy with a resolution beyond this limit would have a profound impact on a myriad of applications in life and material sciences, so it has been the subject of intense investigation. Various microscopy techniques based on scanning near-field probes,¹ molecular fluorescence,^2–4 microscale and nanoscale solid immersion lenses,^5–8 structured illumination,⁹ plasmonic structures,¹⁰ and metamaterials¹¹ have been proposed to improve microscopy resolution. Each of these techniques has its own advantages and limitations. For example, fluorescent-based super-resolution techniques, such as stimulated emission depletion (STED) microscopy¹² and photo-activated localization microscopy (PALM),¹³ are only applicable to specimens already labeled with a fluorophore.

Evanescent waves containing high spatial frequencies corresponding to the sub-wavelength structures of the specimen play an important role in near-field techniques. In scanning near-field optical microscopy (SNOM or NSOM)^1,14,15 technique, developed in the 1970s and 1980s, typically a single mode fiber optic whose tip is tapered and metal-coated is coupled to a laser light source and used as a near-field probe. Such a probe, maintained at the immediate vicinity (a few nanometers) of the specimen, is raster-scanned over the specimen's surface and collects the evanescent scattered field from the specimen, thanks to the sub-wavelength size of the tip. An accurate and precise feedback system is crucial to maintain the extremely short distance between the tip and specimen in order to secure capturing of evanescent waves. SNOM's resolution is not restricted by the wavelength of light; however, it is restricted by the tip's size. Typically, resolution in the range of 10 s of nm is achievable through SNOM at the optical spectrum. The scanning process leads to an extremely slow acquisition time. The light throughput (∼10⁻⁶–10⁻³)¹⁶ in SNOM is considerably lower than that in solid immersion lenses (∼0.1–1).⁷ 

The use of metamaterials, i.e., engineered materials with a negative refractive index, to overcome the diffraction limit in microscopy was met with significant interest and vigorous debate in the early 21st century. Historically, in 1968, Veselago¹⁷ demonstrated theoretically that a negative-index flat lens can produce an image; however, Pendry¹⁸ in 2000 pointed out that a negative-index material can as well cancel the decay of evanescent waves acting like a “perfect lens.” Fabrication of such a lens at visible spectrum turned out to be very challenging associated with design complexities and engineering limitations. Those challenges can be overcome to some extent in some metamaterials;^19–22 nevertheless, they have their own restrictions: limited operational frequency range and absorption issues.

In this context, microsphere-assisted microscopy (MAM) emerged in the past decade as an interestingly simple, yet efficient approach to improve microscopy resolution.^23–28 In MAM, a microsphere is placed in the immediate vicinity of the object acting as a “magnifying glass” to improve the resolution. Much of this enhancement is due to the higher index of the lens material (the immersion effect); however, additional boost appears to arise because of the geometrical shape and meso-scale dimension of the microsphere. MAM can be used in conjunction with white-light, wide-field, bright-field,^23–25 dark-field, confocal,^24,26 fluorescent,^27,29,30 second harmonic generation, two-photon,³¹ interferometric,^32,33 and digital holographic^34,35 microscopies. It can be employed in reflection and transmission modes.^23,24

Here, we present a comprehensive and critical review of the progress in MAM in the past decade. In Sec. II, background information regarding classic resolution criteria is given to provide a suitable context for the discussions in the paper. Liquid and solid immersion microscopy techniques are discussed in Sec. III. Section IV deals with various configurations of MAM, including low-index and high-index MAM and critical analysis of the achievable resolution. Microscopy aided by microcylinders is presented in Sec. IV as well. The standing questions and challenges in MAM are stated in Sec. V.

The diffraction limit is manifested when a point in the object appears as a spot with a finite size in the image plane with a certain irradiance profile named the point-spread function (PSF). The PSF is the Fourier transform of the transmittance function of the aperture.³⁷ 

In a light microscope, resolution hinges on the illumination properties, including object-space wavelength, state of polarization,³⁸ degree of coherence,³⁹ and condenser lens,^40,41 and aperture-specific properties, such as size, shape, and apodization.^42,43

For a diffraction-limited optical system, an aberration-free system whose performance is restricted only by the diffraction phenomenon, several classic criteria exist for resolution, including Abbe,⁴⁴ Rayleigh,⁴⁵ Sparrow,⁴⁶ and Houston.⁴⁷ These criteria were proposed in order to determine the minimum physical distance between two point sources of equal intensities (as the objects) so that they can be distinguished as two separate objects in the image. At smaller distances between the two point sources, it was assumed that recognizing them unambiguously as individual point sources is not possible. We consider incoherent image formation unless otherwise is stated.

According to Eq. (3), a decrease in the illumination wavelength (λ₀), an increase in the object-space index (n), or an increase in the acceptance angle of the light collection objective (θ_max) will improve the resolution. For a conventional visible light (λ ∼ 400–600 nm) microscope, the theoretical Abbe limit is ∼200–250 nm. Enhancing the imaging resolution further than the Abbe limit, without reducing the working wavelength or increasing the form factor of the instrument, has been labeled as super-resolution techniques in the literature.⁵⁰ In label-free super-resolution techniques, the involvement of the near-field components of the object's scattered field is crucial because the evanescent components of the scattered field carry the high spatial frequencies corresponding to sub-wavelength information of the object. Super-resolution without engaging evanescent waves can be reached through optical super-oscillation,^51–53 a phenomenon in which a bandlimited function locally oscillates faster than the highest Fourier component in its spectrum.⁵¹ 

Several classic resolution criteria, that are connected to the width of the main lobe of the PSF of the imaging aperture, are reviewed here.⁴² It is worth noting that a fundamental difference exists between Abbe's limit, which is derived from a physical model, and the Rayleigh, Sparrow, and Houston criteria which are rather heuristic estimates of the resolution limit.^45,54

As presented in Figs. 2(a) and 2(b), at the Rayleigh limit, the central local minimum (saddle) in the double-peak composite irradiance distribution in the image is 81.1% (square aperture) and 73.5% (circular aperture) of the peak value. The contrast, defined as $( I max - I min)/( I max + I min)$⁠, is related to the saddle-to-peak ratio; a lower saddle-to-peak ratio indicates a higher contrast in distinguishing the adjacent point sources in the image.

The Rayleigh criterion was generalized in the context of spectroscopy based on the saddle-to-peak ratio in the composite profile.⁵⁵ Since, for a sinc-like irradiance profile, the saddle-to-peak ratio is 0.81 [see Fig. 2(a)], it was generalized to other systems (e.g., Fabry–Pérot interferometers) and it was assumed that any two spectral lines can be resolved when the saddle-to-peak ratio is <0.81.⁵⁵ Nevertheless, the choice of this value is rather arbitrary.⁵⁵ Sparrow⁴⁶ mentioned that this somewhat arbitrarily chosen number makes performance comparison of two devices subjective, and a fair and objective assessment can only be achieved based on an “actual limit of resolution.”^46,55

As mentioned in Sec. II, the minimum feature resolvable by a conventional microscope is $k λ 0/ NA$⁠, where k is a coefficient (⁠ $k=0.5,0.609,0.473, and 0.515$ according to the Abbe, Rayleigh, Sparrow, and Houston criteria for resolution, respectively), $λ 0$ is the free-space wavelength of light, and $NA$ is the numerical aperture. The maximum theoretically achievable NA for an objective lens working in air (n = 1) is restricted by its maximum acceptance half-angle, $θ max= π 2$⁠. Theoretically, the maximum value for NA is 1; practically for high-NA objectives, we have NA ∼ 0.95. Nevertheless, it is possible to enhance the NA by filling the object space with a liquid, such as water or oil, as proposed by Hooke in the 17th century.⁵⁸ Then, the resolution gain will hinge on the immersion medium's index. Liquid immersion microscopy requires objective lenses that are specially designed for operation in a liquid environment. It is also important that the specimen holds sufficient index contrast with the immersion medium.

Improving conventional microscopy resolution by using solid immersion lenses (SILs) was reported in 1990 and further developed in the last decade of the 20th century.⁵⁹ The principle of SIL and liquid immersion microscopies is similar in a way that in the former the liquid is substituted with a hemispherical⁵⁹ or super-spherical⁶⁰ solid dielectric medium that is placed directly over the specimen. The effective imaging wavelength is reduced to λ₀/n due to the presence of the SIL with index n, enhancing the resolution. Magnification and collection efficiency are also enhanced when a SIL is used. The important difference between SIL and liquid immersion microscopies is that the former relies on evanescent coupling;⁶¹ in order to secure coupling of the near-field scattered field of the specimen into the SIL, the distance between the SIL's base and specimen's surface must be shorter than the penetration depth of the evanescent field (∼λ/10), which can be secured by gently pressing the SIL against the specimen or by filling the gap by using an index-matching liquid.

The SIL idea stems from a theory by Born and Wolf³⁶ stating the existence of two aplanatic points (spherical aberration-free focal points) in a dielectric sphere.⁸ Hence, when a sphere is cut by a plane, parallel to its equatorial plane, passing through either one of the aplanatic points, then a spherical aberration-free focal spot is formed just at the flat base of the truncated sphere. Therefore, morphologically, two categories of conventional SILs exist: hemispherical SILs (h-SILs)⁵⁹ and super-spherical SILs (s-SILs).⁶⁰ 

Figure 3(b) illustrates an h-SIL that is basically a dielectric hemisphere⁵⁹ since one of the aplanatic points is just at the sphere's center. The effective NA is increased by a factor of n due to the presence of h-SIL, but the collection angle remains the same. Hence, using a higher NA objective lens would maximize the resolution provided by an h-SIL. An h-SIL forms a virtual image just at the surface of the specimen as shown in Fig. 3(b). Geometrical optics magnification factor for an h-SIL is equal to n (n is the SIL's index).

Figure 3(c) illustrates an s-SIL, also referred to as Weierstrass SIL, which is a truncated sphere with height $( 1 + 1 / n)r$⁠, in which r is the sphere's radius.⁶⁰ This specific thickness corresponds to the distance between one of the aplanatic points of the sphere and the distal pole of the sphere. An s-SIL forms a virtual image underneath the specimen at distance $( n − 1 / n)r$ from the base of the SIL as shown in Fig. 3(c). Geometrical optics magnification factor of an s-SIL is n². An s-SIL increases the collection angle of the objective lens (θ₂ > θ₁) as well as the object-space index. Hence, it has a higher relative resolution gain compared to an h-SIL under the same objective lens. The maximum achievable NA in an s-SIL is n.

In 2010, Mason et al.⁵ through finite-difference time-domain (FDTD) simulation demonstrated that ∼25% sharper focusing of light can be achieved by a micrometer-scale SIL-type lens, irradiated by a linearly polarized focused light through a high-NA lens, compared to a millimeter-scale SIL suggesting superior resolving power of the former. The fact that the small wavelength-scale lenses or microlenses have better resolution than their enlarged counterparts plays an important, yet not completely understood role in different imaging and focusing applications.

Near-field microscopy using nanolenses,⁶² microdroplets,⁶³ and particularly microspheres^23–25,64 emerged as a surprisingly simple approach for enhancing microscopy resolution. In 2011, Wang et al.²³ demonstrated MAM by using silica (n ∼ 1.46) microspheres for far-field imaging of sub-diffraction-limited features of various specimens by refocusing the objective lens (bringing that closer to the specimen) to look “through the microsphere” into a virtual image formed by the microsphere underneath the specimen, as illustrated in Fig. 3(d). They suggested that the microsphere can convert high spatial frequencies of the evanescent field into propagating modes enabling resolution enhancement. They performed MAM of serval samples with different features' shape and size using silica microspheres with diameters D ∼ 2–9 μm.²³ One interesting imaging specimen, that later found a wide-spread use in the MAM literature, was a commercial Blu-ray® disk (BD) whose structure was composed of stripes with 200 nm width separated 100 nm apart. The 100-μm-thick protective layer of the BD was peeled off prior to the experiment to place the microsphere in direct contact with the surface of the BD. They reported that conventional microscopy, and silica h-SILs with 0.5 and 2.5 mm diameters were not able to discern the structure of the BD specimen [Figs. 4(a)–4(c)]; however, the BD structure was resolved using a 4.74-μm-diameter silica microsphere [Fig. 4(d)]. A similar observation was reported for specimens containing feature sizes between 50 and 130 nm. The authors concluded that silica microspheres with diameters between 2 and 9 μm overperform their macro h-SIL counterparts in nanoimaging.²³ 

Wang et al.²³ suggested that the super-resolution imaging of micrometer-scale spheres and the “photonic nanojet” effect, the ability of microspheres to focus light down to sub-diffraction-limited dimensions, are fundamentally connected based on the optical reciprocity principle.⁶⁵ Photonic nanojets and their applications have been recently reviewed in more detail in Ref. 66. Wang et al.²³ defined “super-resolution strength” of a microsphere as (focus spot size − Rayleigh limit)/(radius of the sphere), according to which a negative value would indicate a resolution surpassing the Rayleigh limit. Figure 5(a) shows the simulation results for super-resolution strength as a function of size parameter $q=2πr/λ$ for several indices. It can be seen that at n = 1.8, the super-resolution strength is the strongest among other studied indices and would be preserved over a wide window of spheres' size (up to $q∼250$⁠). It was stated that the super-resolution strength would be decreased for n > 1.8, as well as the size window of microspheres (i.e., smaller q) where this effect is expected. Further, simulation revealed that the focused light at a gold-coated substrate is sharper compared to that in a freestanding sphere [Figs. 5(b) and 5(c)]; hence, the resolution improvement could be impacted by the substrate material.²³ 

It was found that β = 0.34 provides the best fit that links the geometrical optics field enhancement factor to the geometrical optics magnification. Although Eqs. (9) and (10) show that under the geometrical optics assumptions the field enhancement factor does not depend on the sphere size and only depends on the refractive index, the authors showed that for the micrometer-scale spheres, the Mie theory approximations would show size dependency of their field enhancement factors. They used a relationship of the form $M≈ ( I m a x / I 0 ) 0.34$ to theoretically estimate the magnification of microspheres (with n = 1.46) within the super-resolution window (size range where spheres with a given index have “super-resolution strength”). Figure 5(d) shows their calculated magnification factors as a function of sphere diameter (D = 2–9 μm and n = 1.46) based on the abovementioned assumptions, which qualitatively agreed with their experimental data showing higher magnification factors in the 9 μm-diameter sphere (M ∼ 7) compared to the 2 μm-diameter sphere (M ∼ 4). However, later it was found that the behavior of the magnification as a function of the sphere size is more complicated.²⁵ 

Hao et al.⁶⁸ showed that when a low-index microsphere is partially immersed in microdroplet of liquid, MAM images with sharper contrast but with smaller magnification can be obtained compared to those obtained using a dry microsphere counterpart. Even though imaging in the presence of a liquid is valuable for applications in life sciences, utilizing semi-immersed microspheres is associated with technical complications due to the dynamics of the droplet's evaporation that gradually varies the resolution and magnification of the optical setup. This dynamic process in some scenarios may possibly be used for rapid inspection of a specimen. However, many biomedical specimens contain a permanent fraction of water, and allowing evaporation of water may be harmful. In such cases, the consistent presence of water is required. It was argued, however, that the super-resolution effect cannot be expected when a microsphere is completely immersed in the liquid droplet.⁶⁸ 

As mentioned in Sec. IV A, it was argued that MAM was not practical with high-index (n_p > 1.8) spheres²³ or when microspheres were completely submerged in a liquid,⁶⁸ which was disappointing for MAM of biological specimens and in cases where imaging needed to be performed in a liquid environment. Darafsheh²⁴ extensively studied MAM using high-index (n_p ∼ 1.9–2.2) microspheres immersed in a liquid medium. It was demonstrated that the combination of high refractive index microspheres and total immersion in a liquid in fact permits MAM.^24,25 Feasibility of MAM with high-index barium titanate glass (BTG) microspheres surrounded by a background medium with a significantly lower index than that of the sphere [e.g., isopropanol (IPA) with n_bg = 1.37] was demonstrated for applications in which imaging must be performed in a liquid environment.^24,25,69 Figure 6 illustrates MAM with high-index BTG spheres submerged in isopropanol. It can be seen in Fig. 6(e) that the 150-nm distance in the specimen, whose SEM is presented in Fig. 6(c), can be resolved using MAM whereas it cannot be resolved using conventional microscopy [cf. Fig. 6(d)]. Pincushion distortion can be noted in Fig. 6(e). Similarly, the structure of a BD [Fig. 6(f)] was not resolved using conventional microscopy [Fig. 6(g)] while it was resolved using BTG microspheres as shown in Fig. 6(h). Interestingly, Fig. 6(h) suggests that in principle an array of microspheres can be used for wide field-of-view (FoV) imaging provided that the spheres are translated over the specimen.

Equation (11) shows the dependence of the magnification on the gap between a sphere-lens and the specimen's surface. It can be seen that an increase in the gap, g, would lead to an increase in the magnification as long as the object lies within the focal length of the lens. Such a trend in the magnification as a function of the gap size has been observed in MAM (for example, in Refs. 71 and 72). However, it should be noted that once the gap increases, the resolution deteriorates due to the significant reduction in the coupling efficiency of evanescent waves from the specimen's surface to the microsphere. This behavior is expected in analogy with SIL microscopy in which in order to secure coupling of the near-field scattered field of the specimen into the SIL, the distance between the SIL's base and specimen's surface has to be kept under the penetration depth of the evanescent field (∼λ/10).

Another example of MAM is presented in Fig. 8. Figure 8(a) shows the conventional micrograph of a specimen consisting of silver nanowires dispersed over a silica substrate.⁷³ Due to their micrometer-scale length, the nanowires can be seen through conventional microscopy by a 100 × (NA = 0.9) objective lens. The diffraction limit is ∼300 nm at $λ∼550 nm$ wavelength for that objective lens. The FWHM of the irradiance profile in the image of the nanowire along the dashed line in Fig. 8(a) was measured at ∼390 nm. The MAM image of the same wire through a BTG microsphere (n_p ∼ 1.91 and D ∼ 9.6 μm) submerged in IPA is presented in Fig. 8(b). The image size was scaled by the magnification factor of the microsphere (3.6×) so a straightforward comparison between the MAM image and its conventional micrograph counterpart can be made. The identical triangles with dashed lines link the same features in both images, showing that both images have the same size scale. The FWHM in the nanowire's MAM image in Fig. 8(b) was measured at ∼230 ± 30 nm, demonstrating resolution enhancement by a factor of 1.7. The actual thickness of the wire was believed to be ∼200 nm based on SEM imaging of the ensemble of nanowires on the substrate.⁷³ Since, in general, the use of smaller microspheres can further increase the resolution [e.g., Figs. 7(b)–7(d)], it was suggested that further resolution gain in imaging nanowires could be realized by using microspheres with ∼4–5 μm diameters.

Darafsheh et al.²⁶ compared MAM with SIL and confocal microscopies. Figures 9(a) and 9(b) show resolution comparison between an h-SIL (D = 2 mm, n = 2) and a BTG microsphere (D ∼ 10 μm, n_p ∼ 1.91) immersed in IPA. It can be seen that the structure shown as the top inset in Fig. 9 cannot be resolved by SIL microscopy using the NA = 0.6 objective lens, while MAM can discern that under the same objective lens. Figures 9(c)–9(h) show the influence of the numerical aperture of the objective lens. The gaps in the structure shown in Fig. 9(c) were barely resolved using the NA = 0.9 objective lens. Using the NA = 0.7 lens leads to a degradation of the image quality [Fig. 9(g)]. The image was not resolved when the objective lens with NA = 0.5 was used [Fig. 9(f)]. However, the MAM image obtained with the lowest NA objective lens, NA = 0.4(20× ), was well-resolved [Fig. 9(d)]. This can be explained by the enhancement of the acceptance cone in MAM [see θ₃ in Fig. 3(d)] compared to that in conventional microscopy.

The comparison of the magnification of SIL microscopy and MAM is presented in Figs. 9(i)–9(o). The BD sample and a conventional upright white-light microscope were used; MAM was performed with a 220-μm-diameter BTG sphere (n_p ∼ 2.1) submerged in IPA; 2-mm-diameter h-SILs made of fused silica (n ∼ 1.458), N-BK7 (n ∼ 1.51), sapphire (n ∼ 1.77), and S-LAH79 (n ∼ 2) were studied in that work. It can be seen in Fig. 9(o) that M increases as SIL's index increases, which is expected for mm-scale lenses, which is in excellent agreement with the geometrical optics prediction. Such agreement to some degree was observed for the relatively large (D = 220 μm) BTG sphere submerged in IPA with $n p/ n b g∼1.4$⁠. It should be reemphasized that for meso-scale spheres, M is not exactly obtained from the geometrical optics approximation.

It should be mentioned that the formation of real images in MAM has also been reported for both low-index and high-index microspheres.^34,71

Since the demonstration of the feasibility of MAM with low-index microspheres by Wang et al.²³ and high-index microspheres by Darafsheh et al.,^24–27 microsphere-based approaches have been the subject of wide-spread investigation by many groups for imaging, sensing, patterning, spectroscopy, and profilometry applications.^72,74–106 Characterization of the imaging properties,^107–115 fundamental understanding of the imaging mechanism,^116–123 enhancing the imaging FoV,^124–131 and novel applications were among the most studied topics in the MAM-related literature.

Darafsheh et al.²⁷ demonstrated the feasibility of MAM with high-index microspheres embedded in a polymer film by imaging various samples including biological specimens using BTG microspheres (n_p = 1.9–2.2) embedded in a polydimethylsiloxane (PDMS) film (n_bg = 1.41). Advantages of positioning the microspheres in a solidified film instead of submerging them in a liquid, in particular for biological specimens, are that an inverted microscope can also be used for the imaging; and any possible impact of dynamics of liquid evaporation on image properties would be minimized. This discovery was promising for making novel optical devices, such as microscope slides and accessories, that can improve the resolution for applications in life and material sciences.^29,132,133 Such microscope accessories are composed of an individual or array of microspheres embedded in a transparent medium, e.g., an elastomer layer.

Figure 10(a) shows the schematic illustration of the spin coating method used to fabricate arrays of microspheres embedded in PDMS with a controllable thickness of polydimethylsiloxane (PDMS) layer.²⁷ BTG microspheres with diameter ∼10–100 μm were used. PDMS elastomer (SYLGARD® 170 silicone elastomer, Dow Corning) with proportion 1:10 of cure compound was extended over the microspheres by using spin-coating. The spinner speed and duration controlled the thickness of the final product. The compound was baked for 1 h at 65 °C to dry the mixed compound and form a removable microsphere-embedded film. Successful fabrication of slides with a controllable thickness of 30–300 μm was demonstrated. The practical lower limit of the thickness was defined by the thickness of the microspheres and the upper limit was imposed by the working distance of the objective lens. The thickness of the PDMS layer would also impact the imaging FoV.

Figures 10(b) and 10(c) show the experimental MAM setup with BTG spheres embedded in a PDMS film. The structure of the BD, used as the imaging sample, was not resolved using conventional microscopy, i.e., without a microsphere. However, it was resolved using MAM with an ∼60-μm-diameter sphere with n_p = 1.9 and n_p = 2.1, respectively, as shown in Figs. 10(d) and 10(e). Similar to the case of liquid-immersed microspheres, the magnification was reduced as the sphere's size increased; for the largest spheres (D = 125 μm and n_p = 1.9) reported in that paper, the magnification was M ∼ 2.4. The geometrical optics calculation using Eq. (12) yields M ∼ 2.1. The FoV increased with the sphere's size in general agreement with that of the liquid-immersed microspheres.

It has been suggested that the performance of MAM can be optimized by optimizing the photonic nanojet properties of the microspheres and possibly their whispering gallery modes (WGMs). The index of the medium surrounding the microspheres (⁠ $n b g$⁠) influences the focusing and imaging properties of microspheres, indicating that it can be used as an optimization parameter.^28,134 For example, it has been shown that for the spheres with equal index contrast (i.e., the same $n p/ n b g$⁠) the case of higher index sphere provides better imaging quality due to its more confined and intense photonic nanojet.²⁸ 

MAM is a versatile technique capable of integration with various microscopy systems; fluorescent (FL) MAM has been demonstrated for imaging fluorescence nanobeads,³⁰ cells,^27,30 and tissue sections.²⁹  Figures 11(a)–11(d) compare conventional FL microscopy with MAM through a BTG sphere (n_p = 1.9, D = 60 μm) submerged in water (n_bg = 1.33). Figure 11(b) shows that MAM offers 5.4× magnification in imaging a 1-μm-diameter FL polystyrene microsphere (λ = 680 nm) whose conventional FL micrograph is shown in Fig. 11(a). Figure 11(d) shows that the 100-nm-diameter FL beads were visualized using MAM, whereas they were not visualized through conventional FL microscopy as shown in Fig. 11(c).³⁰ 

Figures 11(f) and 11(h) demonstrate MAM using BTG spheres (n_p = 2.1) embedded in a PDMS layer (n_bg = 1.41), in imaging cancerous cells irradiated with radiotherapy beams. Ionizing radiation used in radiotherapy creates DNA double-strand breaks in the cells' nuclei that by immunofluorescent staining can be observed using an FL microscope. The comparison between Figs. 11(f) and 11(e) shows ∼2.3× magnification in MAM of imaging U87 glioblastoma cells stained with DAPI (4′,6-diamidino-2-phenylindole) (λ = 440 nm). γ-H2AX can be used as an assay for characterization of the DNA double-strand breaks in cells; there is a correlation between the number of the γ-H2AX foci and the radiation damage to the cell. Enhancing the imaging resolution to distinguish between an individual focus or cluster of foci is an important task. Figure 11(h) shows MAM in imaging of the γ-H2AX foci in the irradiated cells—with immunofluorescent staining with γ-H2AX antibodies that reveal nuclear foci formation (λ = 620 nm). Compared to Fig. 11(g), the γ-H2AX foci can be better visualized using MAM through the same 20× (NA = 0.4) objective lens.²⁹ 

FL MAM for imaging mouse kidney sections²⁹ immunostained with antibodies against podocyte protein markers ZO-1 (Alexa 488, green) and Myo1c (Alexa 568, red) is shown in Figs. 11(i)–11(p). The tissue sections were mounted with gold antifade solution containing 80-μm-diameter BTG microspheres (n ∼ 2.1) following the staining. FL MAM was performed using an oil immersion objective lens with NA = 0.8(25×). Conventional FL microscopy images of glomeruli stained for Myo1c, ZO-1, and DAPI, respectively, are shown in Figs. 11(i)–11(k); Fig. 11(l) is the composite image of the three panels. Figures 11(m)–11(p) are the corresponding FL MAM imaging through the microsphere which demonstrate the improvements obtained by using MAM. For example, in Fig. 11(l), the colocalization of Myo1c with ZO-1 is difficult to be noticed, whereas in Fig. 11(p), the colocalization of Myo1c with ZO-1 at the podocyte cell membrane within the glomerulus is clearly observed. Since MAM can possibly improve the capability of a standard microscope to visualize the affected regions in the tissue, it may be helpful in diagnosing the disease economically without subjecting the tissue to a more extensive imaging analysis.²⁹ From a research viewpoint, MAM looks very promising for analyzing changes in the distribution pattern of proteins inside the various cell types of a glomerulus. However, precise positioning of the microsphere is very challenging. Other challenging issues include limited FoV of a single sphere, correcting optical aberrations, and maintaining minimal distance between the sphere and the specimen.

Kassamakov et al.³² demonstrated the integration of MAM with Mirau interference microscopy for label-free 3D optical profilometry. Their scanning white-light interferometry (SWLI) setup is shown in Fig. 12(a). A BD, whose protective polymer layer was peeled off, was used as the specimen. The surface structure of the BD was measured with atomic force microscopy (AFM), which revealed grooves with depth in the range 21.0–24.8 nm. The groove's width and the inter-groove distances, measured through SEM, were 112 ± 2.5 and 323 ± 2.5 nm, respectively. A monolayer of melamine formaldehyde microspheres (n = 1.68) with 11 μm diameter was formed on a BD specimen via self-assembly. A Mirau-type interferometric objective, NA = 0.55(50×), with white-light illumination centered at λ = 600 nm was utilized.

The objective lens was scanned along the optical axis while imaging the sample through the microsphere. The axial scan range was selected to cover all the interference patterns produced by the microsphere, limiting the scan to a range of 20 μm. Precise movement and positioning of the objective lens during the frame grabbing process were achieved by a high-precision scanner. The interference data were analyzed on a pixel-by-pixel basis in terms of the light intensity as a function of the relative height and a 3D data map was constructed by applying an improved vertical-scanning interferometry algorithm.¹³⁵ A commercial software (MountainsMap®, Digital Surf) was used to produce a 3D image. The lateral image magnification due to the microsphere was corrected by using a magnification factor calculated from the ratio between the measured pitch to the nominal pitch of the BD. Figure 12(b) shows the corrected image of the BD surface profile. The FoV was approximately 2–3 μm. The groove's depth was measured between 17.2 and 23.8 nm in agreement with the AFM measurement. It should be noted that without the microsphere, the classical interferometric system cannot resolve the BD grooves.

Aakhte et al.⁷² demonstrated the integration of MAM with Mirau digital holographic microscopy. Their experimental setup is shown in Fig. 12(d). A Mirau-type interferometric objective, NA = 0.3(10×), and a He-Ne laser source (λ = 632.8 nm) were utilized. In order to reduce the speckle noise, the laser beam was passed through a rotating diffuser. A silica microsphere (n = 1.46) with a diameter in the range of 100–530 μm was attached to an optical fiber (as a holder) connected to a micro-positioner and placed between the objective lens and the specimen. Digital holograms were formed by recording the interference pattern of the object beam (reflected from the object and passed through the microsphere) and the reference beam using a digital camera.

They proved the concept for 3D profilometry using a standard resolution target and a commercial digital versatile disk (DVD). It was found that smaller spheres provided higher magnification in agreement with previous works; however, the magnification of the smaller spheres was much more sensitive to the gap size between the sphere and the specimen's surface compared to that in their larger counterparts. Then, the authors applied their technique for 3D imaging and identification of healthy red blood cells (RBCs) and thalassemia minor red blood cells (tRBCs). Identification was done by comparing the volumetric measurements with those of healthy RBCs. Holograms of RBCs obtained without and with a microsphere are shown in Figs. 12(e) and 12(f), respectively. A typical phase map of healthy RBC and tRBC is shown in Figs. 12(g) and 12(h), respectively. By attributing the phase changes to the variations in the cell thickness, the volume of the cells was calculated. Figure 12(i) shows the volume of ∼140 RBCs, demonstrating the distinction between the healthy and thalassemia cells, which may not be achieved by the use of a conventional high-magnification microscope. The histogram of the volume distribution of the cells is shown in Fig. 12(j).

Due to the limited imaging FoV of the microspheres (∼D/4–D/6), their precise positioning on the specimen is critical for practical applications of MAM. Several techniques have been used for microsphere positioning over the specimen.

In this technique, microspheres in liquid suspensions or in the form of powder are deposited over the specimen. The placement of the microspheres is random and relies on the self-assembly of the microspheres over the specimen. This method is suitable for imaging large samples with periodic structures for the fundamental characterization of MAM, for example, to measure the magnification and FoV. On a coarse level by applying an air flow or tilting the sample, the microspheres can be redistributed over the sample.

When the microspheres are deposited over the specimen, they can be further displaced in fine steps by using a microneedle or tapered fiber tip connected to a 3D micromanipulator, somewhat similar to a cue stick and billiard balls. Darafsheh²⁴ used that method to characterize the imaging properties of BTG microspheres with 1–300 μm diameters immersed in IPA. Another approach is to permanently attach a microsphere to a rigid shaft (e.g., pipet and fiber tip) connected to the micromanipulator to precisely position the microsphere over the specimen. Krivitsky et al.¹²⁶ demonstrated attaching a 6-μm-diameter dry silica glass sphere to a pipet tip using vacuum suction (negative air pressure was created in the micropipet by pulling the syringe's plunger) or a UV-curable optical adhesive. The other end of the pipet was connected to a nano-manipulator providing 20 nm positioning spatial resolution in x, y, and z directions [see Figs. 13(a)–13(c)]. Attaching the microspheres to a rigid shaft allows studying the dependence of the imaging properties of MAM (e.g., magnification, resolution, and FoV) on the distance between the microsphere and specimen's surface.

Wang et al.¹²⁸ demonstrated a scannable platform for MAM by gluing a 7.5-μm-diameter silica microsphere (n = 1.46) to the tip of an atomic force microscope (AFM) cantilever, which was mounted on a 3D stage allowing locomotion of the microsphere across the specimen. Duocastella et al.¹³⁶ showed a scanning probe MAM composed of a 4.7-μm-diameter silica microsphere electrostatically attached to an AFM cantilever, which was precisely controlled using the AFM piezoelectric motors [see Figs. 13(d)–13(f)]. Wang et al.¹²⁴ showed a scanning and stitching approach to obtain wide FoV images using the MAM technique. They glued a 57-μm-diameter BTG sphere to an AFM cantilever immersed in water. The vertical distance between the sphere and the sample's surface was tuned using AFM principles, permitting scanning and imaging over a relatively large region. The raster scanning spacing and the interval of the triggering signal for the camera to capture the images during scanning were determined according to the size of the aberration-free FoV of the microsphere. A commercial software (Topostitch, Image Metrology) or ImageJ software with the Stitching plugin¹³⁷ based on a phase correlation algorithm¹³⁸ was utilized to stitch the acquired images. Figures 13(g)–13(j) illustrate the scanning-and-stitching method.

The use of an optical tweezer to manipulate the microspheres in MAM has been investigated.^139,140 This technique works in a liquid environment and combines optical trapping with optical imaging. One main challenge in this technique is to maintain the minimal gap between the microsphere and the specimen because the imaging magnification and resolution strongly depend on the distance between the sphere and specimen's surface (e.g., Ref. 70). The image quality and the magnification factor are also affected by the index contrast between the microsphere and the immersion medium.

Arrays of microspheres embedded in polymer films can be fabricated and used as microscope accessories (e.g., coverslip).^27,29,132 Yan et al.¹⁴¹ showed the feasibility of MAM when a high-index BTG microsphere was glued to the objective lens using PDMS, together working as a unibody compound objective lens.

The surface of Janus particles¹⁴² has two or more distinct physical properties allowing them autonomous chemical locomotion when placed in an aqueous solution. Li et al.¹³⁰ fabricated Janus microspheres by partially coating polystyrene (n = 1.59) or TiO₂ (n = 2.1) microspheres (D = 2–20 μm) with a thin Ti/Ni/Pt (2/5/5 nm) metallic trilayer. They showed that the autonomous movement and magnetic steering of microspheres allowed large-area, parallel, and nondestructive imaging.¹³⁰ However, since the distance between the microsphere and the specimen's surface is a critical factor impacting resolution and magnification, it is vital that the same minimal distance is preserved during the imaging across the specimen.

Enhancement in spatial resolution in MAM stems from several factors. For a wide window of spheres' size, resolution enhances as a result of the growth of the effective numerical aperture. Geometrical optics yields $N A s= n sin θ 2 − n$ for the combination of the objective lens (with collection half-angle $θ$⁠) and a sphere with index n. However, the maximum theoretically possible $N A s$ is n. For spheres with meso-scale dimensions, the resolution is presumably additionally enhanced because of the shape-dependent and size-dependent nanophotonic mechanisms in microspheres.^23,24,66

Darafsheh et al.¹³² have pointed out that there is an inconsistency in the MAM literature regarding the resolution improvement claims. This inconsistency mostly stems from using arbitrary and subjective criteria to express the imaging resolution. For example, Yan et al.¹⁴³ stated λ/17 (λ = 408 nm) “resolution” by mere observation of a 25 nm edge-to-edge distance in a specimen whose structure consisted of 135-nm-diameter gold quintuplet nanodisks (with 25 nm distance between them), using a confocal microscope [Figs. 14(a) and 14(b)]. Wang et al.²³ stated λ/8–λ/14 (λ = 400–750 nm) “resolution” by merely observing 50-nm-diameter pores distanced 50 nm apart in a gold-coated fishnet array used as the imaging specimen [Figs. 14(c) and 14(d)]. Darafsheh et al.²⁵ realized the complexity of the issue and used a different terminology; they stated “ability to discern the features” as small as λ/7 (λ ∼ 550 nm) in their work.

The resolution of a lens depends on several parameters, such as the numerical aperture of the lens, the wavelength, and the coherence properties of the light. The performance of an imaging system can be characterized by two means; the PSF and the transfer function method. The former is related to the image of a single point object, whereas the latter is obtained through imaging structures with varying spatial frequencies.

In order to find the resolution gain in MAM, it is crucial to follow a method compatible with definition of resolution. As mentioned in Sec. II, there exist several criteria for resolution; among them the Houston criterion (the FWHM of the system's PSF) is more practical. The PSF can be measured by deconvolution of the object and image functions. However, it is important to realize the fundamental difference between coherent and incoherent image formation. The former is linear in amplitude such that the amplitude image of each point in the object is added to give the final amplitude image for which the intensity image is given by the amplitude modulus square, whereas the latter is linear in intensity in which the intensities of individual point images add to give the final intensity image. This leads to two fundamentally different mathematical formalism based on convolution integrals. The convolution formalism for incoherent and coherent image formation are $I=|h | 2⊗| U o | 2$ and $I=| h ⊗ U o | 2$⁠, respectively, where $⊗$ denotes the convolution, $U o$ is the amplitude of the ideal geometrical-optics image of the object, and h represents the complex point-spread function (APSF) of the system (i.e., it gives the complex amplitude of the light field response of the system to an impulse stimulus) whose modulus square, $|h | 2$⁠, gives the intensity or irradiance point-spread function (IPSF).^37,144 As an aside, note that a coherent image, due to constructive interference, may display bright spots in the field-of-view which do not correspond to the object pattern that requires a priori knowledge of the object in order to correctly interpret the image.

Textbook definition of resolution is based on two point sources with equal intensities as the object, while in reality objects with finite sizes are used. Ignoring the influence of the physical size of the object and claiming a specific distance in the object, for example, edge-to-edge or center-to-center distance between two features, the attained “resolution” has led to exaggerated resolution claims in the MAM literature as mentioned above. In the following, this point is demonstrated via computational examples provided in Ref. 132.

A structure similar to that of a BD (i.e., a pair of 200-nm-wide steps distanced apart by a 100-nm gap), which has been commonly used in many MAM-related experiments, was considered the object function. The image of this profile was calculated through convolution with an Airy profile PSF with 230 and 100 nm FWHM, respectively, in Figs. 15(m) and 15(n). This example shows that even a system with 230 nm resolution can discern the 100 nm distance between the structures in the object. The difference between the calculated image profiles is that the saddle-to-peak ratio is smaller (i.e., higher image contrast) in the system with narrower PSF. In the next example, the gap between the steps was reduced to 20 nm and each step's width was increased to 240 nm. The corresponding image was calculated for a system with PSF with 97 and 20 nm FWHM, respectively, in Figs. 15(o) and 15(p). It is evident in Fig. 15(o) that ∼100 nm (not necessarily 20 nm) resolution is sufficient in order to merely visualize the 20-nm gap in the object. This is a critical point that has been overlooked frequently in the MAM literature with regard to resolution claims, especially in the earlier works. It demonstrates that significant exaggeration (fivefold in the latter example) could happen if by mere visualization of the 20-nm distance between the object features one claims 20-nm “resolution.”

Figure 16 shows the “required resolution” in order to resolve the $g$-nm-gap between the two parallel steps with width w as a function of the gap size (⁠ $g=500 -2w$⁠). The required resolution was calculated as the FWHM of a PSF that produced an image with 0.81 saddle-to-peak ratio. The choice of 0.81 was based on the generalized Rayleigh criterion for resolution.⁴² It can be seen that the ratio between the resolution and gap size is not linear and a gross error (2–5 fold in that example) in resolution claim happens if just by discerning the gap, one claims the gap size as the system's resolution.

The abovementioned examples obviously demonstrate that for measuring the imaging resolution extreme caution must be exercised when instead of “point source” objects, objects with finite sizes, such as the BD, are used as the imaging specimen. In fluorescent microscopy, the PSF can be measured through imaging fluorescent nanobeads (often treated as point sources). In label-free MAM, however, measuring the PSF is not a trivial task. The deconvolution method, however, can potentially offer a robust platform for measuring the attained resolution in MAM or any other technique, provided that the impact of digital image processing and contrast adjustment is carefully mitigated. In this method, the PSF of the system is obtained through deconvolving the image profile from the object profile. The object profile can be obtained through the scanning electron microscopy of the specimen. Proper selection of the convolution formalism for incoherent and coherent image formation is critical in this method. Another approach to quantify the resolution as suggested by Luk’yanchuk et al.¹⁴⁵ is to fabricate ad hoc nanoscale resolution targets, for example, something analogous to the 1951 USAF resolution test chart, which is commonly used for characterization of optical imaging instruments.

In Ref. 27, Darafsheh et al. used the deconvolution approach for resolution measurement; they reported ∼λ/4–λ/3 resolution for high-index BTG spheres embedded in PDMS using a conventional white-light wide-field microscope. In their previous work, Darafsheh et al.²⁶ reported ∼λ/6 resolution for MAM using a confocal microscope. Allen et al.¹⁴⁶ also reported ∼λ/6–λ/7 resolution in imaging gold nanostructures using MAM in a confocal arrangement. However, it should be noted that a confocal microscope per se, taking advantage of the pinholes, narrows down the PSF and enhances the lateral resolution typically by a factor up to ∼1.4.^147,148 Therefore, using a confocal arrangement to measure the inherent resolution gain provided by the microspheres in MAM is not optimum and makes the measurement multifaceted because what is measured as the imaging resolution is an intertwined consequence of the confocal setup and the microspheres that cannot be exclusively credited to the microsphere. In addition to the impact of the microscope setting (e.g., confocal arrangement and partial coherence), other factors such as specimen-specific effects^43,119 may be involved in resolution enhancement when metallic (e.g., Au and Ag) nanostructures are used as the imaging specimen. Furthermore, the impact of digital image processing and contrast adjustment in digital cameras must be carefully examined and removed from the resolution analysis. In order to reach a plausible objective conclusion regarding the resolution of MAM, caution must be exercised in using an imaging apparatus and specimen that rules out extra affecting parameters in resolution analysis. A critique on an ill-considered method for analyzing inherent resolution in MAM is provided in Ref. 70 and it was stated that for the inherent resolution of a microsphere (with index n), a value significantly better than λ/(2n) is not to be expected.

Duan et al.¹²¹ performed numerical calculations using Mie theory to study the imaging resolution in MAM for a selected case, a standalone microsphere with D = 4.74 μm and n_p = 1.46 (and n_bg = 1) to mimic the microsphere that was experimentally used in Ref. 23. Two separated point sources were considered the object and their virtual image was calculated in the far-field. The calculation results showed that the resolution cannot reach sub-100 nm and other physical phenomena may be involved to further improve the resolution. Sundaram and Wen¹²⁰ performed full wave finite element method simulations to study the resolution in a system composed of a 6-μm-diameter sphere and a pair of lenses to mimic an objective lens of a microscope. A dipole in contact with the microsphere was selected as a point source. They calculated λ/2.63 resolution at n_p = 1.45 (and n_bg = 1). Note that the theoretical solid immersion resolution for that case is λ/(2 × 1.45) = λ/2.9. The authors studied the substrate effect in three cases: air, fused silica, and aluminum oxide as the substrates' material; it was found that the highest resolution λ/3.33 (λ/4.17) occurs when a transverse (longitudinal) dipole was placed on an aluminum oxide substrate.

Duocastella et al.¹³⁶ performed modulation transfer function (MTF) measurement for an NA 0.5 (50×) objective lens with and without using a 4.6-μm-diameter silica microsphere (n = 1.46) to determine the cutoff spatial frequency. A series of gold gratings with periodicities in the range of 100–1000 nm fabricated on a glass substrate were imaged with a blue LED (λ = 405 nm) as the light source. Figures 17(a) and 17(b) show the images of different spatial frequencies without and with using the microsphere, respectively. It can be seen that the samples with spatial frequencies shown in Fig. 17(b) could not be resolved without using the microsphere. The MTF for both configurations is shown in Fig. 17(c). The Rayleigh resolution limit corresponds to 10% of the MTF, which in their experiment with the microsphere indicated 260 nm resolution. This value corresponds to an effective NA around 0.95 [cf. Eq. (5)], indicating a factor of 1.9 gain in the effective NA of the objective lens. The theoretical Rayleigh limit of an NA = 0.5 objective lens working in air is 0.61λ/NA = 494 nm. However, if one assumes immersion effect for a material with n = 1.46, then the maximum theoretical NA becomes 1.46, leading to Rayleigh limits of 169 nm.

Vlad et al.¹⁴⁹ fabricated wavelength-scale polystyrene SILs by thermal reshaping of spherical colloidal particles with diameters in the range of 1–10 μm. They showed that such SILs overperform their microsphere counterparts in terms of imaging resolution. It should be noted, however, that the choice of the microspheres' index (n = 1.59) used in that work might not be optimal. Although fabrication of micrometer-scale SILs made of arbitrary materials may not be easily possible, a direct comparison of the imaging performance of micro-SILs and microspheres, made of common materials used in MAM studies, would shed more light on the actual resolution limit and resolution enhancement mechanism in MAM. Zhu et al.¹⁵⁰ have shown that novel microspheres with a controllable refractive index (n = 1.590–1.685) can be fabricated through a nanoparticle-hybrid suspension polymerization approach. Fan et al.¹⁵¹ have shown that novel micro-SILs can be fabricated using the nano-solid-fluid assembly of TiO₂ (n = 2.55) nanoparticles as building blocks. Such advancement in microsphere and micro-SIL fabrication would provide a platform to further investigate and optimize the MAM.

Darafsheh et al. demonstrated that microcylinders, such as chemically etched optical fibers and polymer microwires, can be utilized to enhance the microscopy resolution.^24,152,153 For example, in Ref. 153, they made microwires with uniform size (5 and 10 μm diameter) from several transparent polymers [MD700 (n ∼ 1.337), NOA61 (n ∼ 1.556–1.575), and SU-8 (n ∼ 1.56–1.66)] by capillary force lithography followed by photopatterning. Figure 18(a) shows the bird's eye-view of an array of microwires made from NOA61. Figure 18(b) shows the harvested microwires dispersed over a BD specimen. Figure 18(c) demonstrates the microscopy setup with the microwires using a conventional upright wide-field microscope in reflection mode. A thin layer of IPA was poured over the specimen to provide contact with the microwire. Conventional microscopy using a 100× (0.95 NA) objective lens was not able to resolve the BD structure as presented in Fig. 18(d); however, it was resolved by using the microwire as demonstrated in Fig. 18(e) in which the 100 nm grooves in the BD are seen. Due to the long length of the microwires (∼100 μm), the FoV along the length of the wire was ∼100 μm. However, due to the one-dimensional character of the microcylinder's focal spots, which are only along the axis perpendicular to the cylinder's axis of symmetry, the direction of the magnification provided by the microcylinder is perpendicular to the cylinder's axis. Because of that, only when the orientation of the microwire was parallel to the BD features, as schematically shown in Fig. 18(c), the structure of the BD was resolved.

Later, Monks et al.¹⁵⁴ used the same concept and performed microscopy of a BD specimen aided by spider's silk as a microcylinder [see Fig. 18(f)]; the minor ampullate silk had an index of ∼1.55 with a diameter of ∼6.8 μm in their experiment. Figure 18(g) shows their experimental setup with an erect microscope equipped with a 100× (0.9 NA) objective lens. The spider silk was taped over the BD specimen and a thin layer of IPA was poured to fill any possible gap between the silk and specimen. Figure 18(h) shows that the BD structure can be resolved using the spider silk with magnification factor M ∼ 2.1. The stripes observed outside of the silk were believed to be false images formed due to interference between the incident light and scattered light from the silk and BD surface.

Microscopy assisted by microcylinders provides a useful research tool to investigate fundamental dependency of imaging characteristics on different microwires' parameters (e.g., size, index, and etc) because the fabrication of microwires with different diameters and from different materials is—in general—easier than that for microspheres. Also, numerical simulation (e.g., FDTD) is easier and less time consuming to run for a 2D case compared to a 3D case, especially when the dimension of the microelements and the number of different scenarios that need to be investigated increase.

The exact principle behind resolution improvement in MAM is still under intense investigation. The following effects have been suggested in the literature as potential contributors to the MAM process. These effects are not necessarily mutually exclusive and it is possible that multiple effects are involved in resolution enhancement in MAM.

The microspheres due to their curved boundary increase the collection angle of the rays scattered from the specimen, which together with the moderate-to-high refractive index of the sphere, would lead to an increase in the effective numerical aperture of the imaging system. However, in analogy to the SIL effect, the maximum theoretical resolution for a sphere with index n would be $λ/( 2 n)$⁠.

Transformation of evanescent waves to propagating waves through the microspheres has been pointed out as a contributing factor in resolution improvement by the microspheres.^{23,25,68,155,156} The proximity of the microsphere to the specimen's surface allows capturing of the evanescent waves from the specimen; hence, it is critical that minimal gap exists between the specimen and the sphere to secure efficient evanescent wave coupling. This condition also influences the imaging FoV of the microsphere.⁶⁸ 

A fundamental connection between imaging properties of microspheres and the size of their photonic nanojets has been suggested by several investigators^23,25,118 based on the optical reciprocity principle;^65,157 however, in most scenarios, the size of a typical photonic nanojet rarely beats the solid immersion limit of $λ/( 2 n)$⁠. Microspheres with different materials and sizes can be tested in order to establish the dependency of the imaging properties on the nanojet characteristics of the spheres. Similarly, the background material around a high-index microsphere can be changed in order to tune the nanojet properties of the microsphere. Such data will shed more light on the extent of the influence of the nanojets on imaging properties of microspheres.

It is known that the WGMs, when the wavelength of light is in resonance with the cavity modes of the sphere, can lead to the formation of smaller focal spots by the microsphere compared to their conventional off-resonance photonic nanojets.¹⁵⁸ The involvement of WGMs has been suggested^24,159 as a possible contributing factor in resolution improvement in MAM. The other resonance-based hypothesis is the “super-resonance” effect. Super-resonance refers to a giant optical field enhancement due to the excitation of a special order of internal partial waves temporarily trapped inside the microsphere.^119,160 In contrast to WGMs that can occur in both cylindrical and spherical cavities, super-resonance only occurs in microspheres. The super-resonance can lead to the formation of hot spots with significantly smaller FWHM (∼λ/5) and higher intensity compared to the off-resonance photonic nanojets. It has been shown theoretically that the microsphere is more efficient in converting evanescent waves to propagating waves when the incident light is in super-resonance with the cavity modes of the sphere.¹¹⁹ However, it should be noted that most of the MAM experimental results have been obtained using broadband light sources. Experimental data obtained with laser sources with precise wavelength control are needed to investigate the resonance-based hypotheses in MAM.

It is well-known that two point sources can be better resolved when they are in phase opposition (i.e., φ = π); in that case, the saddle-to-peak ratio reaches zero.³⁷ Coherent effects, described in Refs. 32 and 161, can be manifested due to the object complexity (profile and material heterogeneity) as a result of the destructive phase difference between two adjacent points in the object that may contribute to the separation of those points in the image plane. The low difference in optical pathway due to the small size of the sphere may enhance this phenomenon even with low coherent sources.

The impact of the substrate material on imaging resolution has been suggested by several investigators. As mentioned before, simulation results have shown that the focused light at a gold-coated substrate is sharper compared to that in a freestanding sphere; hence, the resolution could be improved due to the substrate material.²³ Another simulation work showed that the imaging resolution is higher when the substrate material is aluminum oxide instead of silica or air.¹²⁰ Different imaging targets made from different materials (e.g., Au, Ag, and Si) can be made to investigate to what extent the resolution is impacted by the material properties of the imaging target.

It should be mentioned that a set of robust, systematic, and reproducible rigorous experimental data quantitatively evaluating these series of hypotheses in a controlled fashion is currently missing in the literature.

Another challenge in MAM is connected to the imaging FoV. The FoV of an individual microsphere is small (a fraction of its diameter). Intense research effort is directed toward making MAM applicable for wide FoV imaging. Various approaches have been proposed to achieve this goal; among them, scanning-and-stitching technique either through an individual sphere or an array of spheres seems more compelling. Novel optical devices such as microscope accessories can be made with microspheres embedded in a background medium. Microsphere-based applications go beyond microscopy extending to spectroscopy, sensing, profilometry, nano-patterning, and so on. Due to the meso-scale dimension of the microspheres, an optimum solution strongly depends on the desired application, and an ad hoc optimization of the involving parameters seems necessary.

Microsphere-assisted microscopy can be incorporated with various microscopy systems to enhance the imaging resolution. The imaging properties of micrometer-scale spheres do not exactly follow geometrical optics assumptions due to their meso-scale dimension. The resolution gain and magnification in MAM depend on several parameters including the index of the sphere and surrounding medium, sphere's size, degree of immersion of the microsphere in the background medium, and illumination properties as well as specimen-specific properties (e.g., material and size).

The resolution gain on a fundamental level mainly stems from the enhancement of the system's effective NA and evanescence wave collection and possibly additionally from the nanojet properties of the microspheres. Other possible contributing factors include coherent effects, and whispering gallery modes and super-resonance effects when the imaging wavelength is in resonance with the cavity modes of the microsphere. Intense research effort has been directed toward understanding the “super-resolution” mechanism of MAM; a series of hypotheses have been proposed mostly based on theoretical assumptions. A meticulously obtained set of quantitative experimental data, instead of “anecdotal evidence,” is required in order to verify the asserted hypotheses. Adherence to the classic definition of resolution and a specimen-agnostic method is necessary in order to conduct a fair comparison between resolution gain in MAM and that in other imaging modalities.

In some of the works in the MAM-related literature, the imaging resolution is still limited by the diffraction; hence—technically speaking—the “super-resolution” label must be inappropriately used. Nevertheless, semantic aside, the advantage (or disadvantage) of MAM over other microscopy techniques must be evaluated on a case-by-case basis depending on the application which provides an appropriate context. For example, fabrication of individual or arrays of micro-SILs with a given material is not as straightforward as that for microspheres. The use of macro SILs, on the other hand, is not convenient due to the significantly sub-mm working distance of most of the high-NA objective lenses. The inherent simplicity, relatively low economic cost, being a label-free method, and its highly versatile and broadband nature are some unbeatable traits of MAM. Limited FoV and imaging aberrations are the main drawbacks of MAM, which need to be overcome in a sustainable manner.

The author has no conflict to disclose.

This work does not contain experiments on animals or human subjects.

The data that support the findings of this study are available within the article.