16 Theoretical Foundations of Super-Resolution in Microspherical Nanoscopy
413
in the experiments. An entire microsphere-based microscope system, including both
the focusing (illumination) and imaging subsystems, was studied in [77] using multipole and plane wave expansions. The resolution of about λ/4 was obtained in the
regime in which the resonant modes of the microsphere are excited.
Coherent effects may affect resolution as well. In the total internal reflection darkfield microscopy, coherent illumination can give rise to the resolution higher than
the classical limit [78]. The origin of enhancement is related to the out-of-phase
excitation of closely spaced objects and their subsequent re-radiation. Coherent reradiation, however, introduces image distortions and artifacts [79]. The problem of
imaging coherent currents through microspheres was considered in [80], where it
was shown that one obtains deeply subwavelength resolution accompanied by image
distortion. Modeling of coherent emission of several closely spaced point sources
located near a microsphere (in 2D model) using COMSOL Multiphysics also showed
the capability of their resolution when the emission phase is shifted by π between
the neighbors [81, 82].
Using microspheres that provide a high- index contrast relative to the environment,
such as n = 2 microspheres in the air, gives rise to some interesting effects. In
particular, one obtains images of objects when focusing the microscope objective
just above the particle in the upright system. The resolution can reach about λ/4 if
the illumination is tuned at the wavelengths of the internal microparticle resonances
[83]. This means that the resolution enhancement does not come only from the
immersion effect.
In this chapter, we present an analysis of the performance of microspherical
nanoscopy using various models. In Sect. 16.2 we begin with a simple geometrical
optics. In Sect. 16.3 we move to imaging point sources emitting near microspheres,
as in the classical approach used for resolution definition. In Sect. 16.4 we quantify
the resolution in terms of the SIL concept. We also discuss the possible role of coherence. In Sect. 16.5, we consider the combinations of microspherical nanoscopy with
nanoplasmonics and plasmonic metasurfaces, which represent the most advanced
way of increasing the resolution far beyond the classical diffraction limit.
16.2 Geometrical Optics of Contact Microspheres
Geometrical optics provides the basic understanding of imaging and, therefore, it
is useful to apply it to microspherical nanoscopy. Certainly, its results have to be
treated with caution. While the size 2−20 µm of typical microspheres exceeds the
typical operating wavelengths λ ∼ 600 nm, it may not be sufficiently larger than λ for
the geometrical optics approximations. On the other hand, rather large microspheres
with sizes ∼60 µm are also used [58].
In the approximation of geometrical optics, a point-like source near a microsphere
emits rays, see Fig. 16.1b. The ray paths can be found directly using the Fresnel
refraction formulas. Upon exiting the microsphere, the rays are focused by the lens
on the detector. Extending the exiting rays backwards, the location of the virtual
413
in the experiments. An entire microsphere-based microscope system, including both
the focusing (illumination) and imaging subsystems, was studied in [77] using multipole and plane wave expansions. The resolution of about λ/4 was obtained in the
regime in which the resonant modes of the microsphere are excited.
Coherent effects may affect resolution as well. In the total internal reflection darkfield microscopy, coherent illumination can give rise to the resolution higher than
the classical limit [78]. The origin of enhancement is related to the out-of-phase
excitation of closely spaced objects and their subsequent re-radiation. Coherent reradiation, however, introduces image distortions and artifacts [79]. The problem of
imaging coherent currents through microspheres was considered in [80], where it
was shown that one obtains deeply subwavelength resolution accompanied by image
distortion. Modeling of coherent emission of several closely spaced point sources
located near a microsphere (in 2D model) using COMSOL Multiphysics also showed
the capability of their resolution when the emission phase is shifted by π between
the neighbors [81, 82].
Using microspheres that provide a high- index contrast relative to the environment,
such as n = 2 microspheres in the air, gives rise to some interesting effects. In
particular, one obtains images of objects when focusing the microscope objective
just above the particle in the upright system. The resolution can reach about λ/4 if
the illumination is tuned at the wavelengths of the internal microparticle resonances
[83]. This means that the resolution enhancement does not come only from the
immersion effect.
In this chapter, we present an analysis of the performance of microspherical
nanoscopy using various models. In Sect. 16.2 we begin with a simple geometrical
optics. In Sect. 16.3 we move to imaging point sources emitting near microspheres,
as in the classical approach used for resolution definition. In Sect. 16.4 we quantify
the resolution in terms of the SIL concept. We also discuss the possible role of coherence. In Sect. 16.5, we consider the combinations of microspherical nanoscopy with
nanoplasmonics and plasmonic metasurfaces, which represent the most advanced
way of increasing the resolution far beyond the classical diffraction limit.
16.2 Geometrical Optics of Contact Microspheres
Geometrical optics provides the basic understanding of imaging and, therefore, it
is useful to apply it to microspherical nanoscopy. Certainly, its results have to be
treated with caution. While the size 2−20 µm of typical microspheres exceeds the
typical operating wavelengths λ ∼ 600 nm, it may not be sufficiently larger than λ for
the geometrical optics approximations. On the other hand, rather large microspheres
with sizes ∼60 µm are also used [58].
In the approximation of geometrical optics, a point-like source near a microsphere
emits rays, see Fig. 16.1b. The ray paths can be found directly using the Fresnel
refraction formulas. Upon exiting the microsphere, the rays are focused by the lens
on the detector. Extending the exiting rays backwards, the location of the virtual