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E. Khan and E. Narimanov
based imaging methods inherently slow, but the fluorescent labels may modify the
dynamics of the process that is being investigated, induce an unwanted chemical
reaction or may even be toxic to the biological sample.
As a result, there is an increasing demand in an alternative approach to optical
imaging that is inherently label-free but offers the resolution comparable to that of
the fluorescent microscopy. One possible solution for this objective is offered by the
imaging systems that are based on metamaterials—artificial composite structures
with the emergent properties that are different from conventional media. The present
chapter reviews recent progress in this line of research.
14.2 Super-Resolution Microscopy
When an object is illuminated, its fine structure information is carried by evanescent
waves [1] which rapidly decay away from the target and therefore do not reach a
detector in the far field. Originally proposed in 1928, [8] near-field scanning optical
microscopy (NSOM) techniques [9] capture these evanescent waves or scatter them
into the far field, using a probe with a subwavelength tip, positioned at a very short
distance from the object [10]. Even though high lateral resolution can be achieved, the
shallow depth of field and long scanning time limit the applicability of this approach.
An alternative imaging method of the structured illumination [6, 11], uses a coherent grid pattern formed by light through interference, that is superimposed on the
object. The resulting scattered signal is detected in the far field, followed by computational reconstruction of the structure of the original object from these data. This
approach can be understood as the optical analogue of the detection and “reconstruction” of the signal that was encoded in the modulation of a carrier wave [12].
In this approach, the resulting reconstructed image involves high spatial frequency
information outside the diffraction limit, with the extended range that is defined by
the periodicity of the illumination pattern. In the standard implementation of structured illumination approach, the diffraction-limited resolution can be improved by
the factor of two, [6, 11] down to one-quarter of the light wavelength in the medium
surrounding the object, λ 0 /4.
Super-resolution can also be achieved by bandwidth extrapolation techniques [13,
14]. Electromagnetic field scattered by a finite object, can be represented as a Fourier
transform of a function with a finite spatial support, [1] and is therefore an analytical
function of the wavevector. As a result, by virtue of its convergent Taylor series that
only involves the derivatives at a single point (albeit of exceedingly high orders), the
entire spectrum can be obtained from its finite part, no matter how limited in range.
In the actual implementation of this approach, the necessary data post-processing
can be facilitated by finding the point spread function of the optical system and
deconvolving the image and using multiple images of the same object, with certain
a priori information about the target, such as sparsity [15, 16]. While this approach
can lead to retrieval of information not originally captured by the imaging sensors,
E. Khan and E. Narimanov
based imaging methods inherently slow, but the fluorescent labels may modify the
dynamics of the process that is being investigated, induce an unwanted chemical
reaction or may even be toxic to the biological sample.
As a result, there is an increasing demand in an alternative approach to optical
imaging that is inherently label-free but offers the resolution comparable to that of
the fluorescent microscopy. One possible solution for this objective is offered by the
imaging systems that are based on metamaterials—artificial composite structures
with the emergent properties that are different from conventional media. The present
chapter reviews recent progress in this line of research.
14.2 Super-Resolution Microscopy
When an object is illuminated, its fine structure information is carried by evanescent
waves [1] which rapidly decay away from the target and therefore do not reach a
detector in the far field. Originally proposed in 1928, [8] near-field scanning optical
microscopy (NSOM) techniques [9] capture these evanescent waves or scatter them
into the far field, using a probe with a subwavelength tip, positioned at a very short
distance from the object [10]. Even though high lateral resolution can be achieved, the
shallow depth of field and long scanning time limit the applicability of this approach.
An alternative imaging method of the structured illumination [6, 11], uses a coherent grid pattern formed by light through interference, that is superimposed on the
object. The resulting scattered signal is detected in the far field, followed by computational reconstruction of the structure of the original object from these data. This
approach can be understood as the optical analogue of the detection and “reconstruction” of the signal that was encoded in the modulation of a carrier wave [12].
In this approach, the resulting reconstructed image involves high spatial frequency
information outside the diffraction limit, with the extended range that is defined by
the periodicity of the illumination pattern. In the standard implementation of structured illumination approach, the diffraction-limited resolution can be improved by
the factor of two, [6, 11] down to one-quarter of the light wavelength in the medium
surrounding the object, λ 0 /4.
Super-resolution can also be achieved by bandwidth extrapolation techniques [13,
14]. Electromagnetic field scattered by a finite object, can be represented as a Fourier
transform of a function with a finite spatial support, [1] and is therefore an analytical
function of the wavevector. As a result, by virtue of its convergent Taylor series that
only involves the derivatives at a single point (albeit of exceedingly high orders), the
entire spectrum can be obtained from its finite part, no matter how limited in range.
In the actual implementation of this approach, the necessary data post-processing
can be facilitated by finding the point spread function of the optical system and
deconvolving the image and using multiple images of the same object, with certain
a priori information about the target, such as sparsity [15, 16]. While this approach
can lead to retrieval of information not originally captured by the imaging sensors,