Resolution limit of label-free far-field microscopy
Evgenii Narimanov*
Purdue University, School of Electrical Engineering, Birck Nanotechnology Center, West Lafayette, Indiana, United States
Abstract. The Abbe diffraction limit, which relates the maximum optic al reso lution to the numerical aperture of
the lenses involved and the optical wavelength, is generally considered a practical limit that cannot be
overcome with conventional imaging systems. However, it does not represent a fundamental limit to
optical resolution, as demonstrated by several new imaging techniques that prove the possibility of finding the
subwavelength information from the far field of an optical image. These include super-resolution fluorescence
microscopy, imaging systems that use new data processing algorithms to obtain dramatically improved
resolution, and the use of super-oscillating metamaterial lenses. This raises the key questi on of whether
there is in fact a fundamental limit to the optical resolution, as opposed to practical limitations due to
noise and imperfections, and if so then what it is. We derive the fundamental limit to the resolution of
optical imaging and demonstrate that while a limit to the resolution of a fundamental nature does exist,
contrary to the conventional wisdom it is neither exactly equal to nor necessarily close to Abbe’s estimate.
Furthermore, our approach to imaging resolution, which combines the tools from the physics of wave
phenomena and the methods of information theory, is general and can be extended beyond optical
microscopy, e.g., to geophysical and ultrasound imaging.
Keywords: imaging; super-resolution.
Received Sep. 17, 2019; accepted for publication Oct. 15, 2019; published online Nov. 1, 2019.
© The Author. Published by SPIE and CLP under a Creative Commons Attribution 4.0 Unported License. Distribution or re-
production of this work in whole or in part requires full attribution of the original publication, including its DOI.
[DOI: 10.1117/1.AP.1.5.056003]
1 Introduct ion
High-resolution optical imaging holds the key to the under-
standing of fundamental microscopic processes both in nature
and in artificial systems—from the charge carrier dynamics
in electronic nanocircuits
1
to the biological activity in cellular
structures.
2
However, optical diffraction prevents the “squeez-
ing” of light into dimensions much smaller than its wavelength,
3
leading to the celebrated Abbe diffraction limit.
4–7
This does not
allow a straightforward extension of the conventional optical
microscopy to the direct imaging of such subwavelength struc-
tures as cell membranes, individual viruses, or large protein
molecules. As a result, recent decades have seen an increasing
interest in developing “super-resolution” optical methods that
allow to overcome this diffraction barrier—i.e., near-field opti-
cal microscopy,
8
structured illumination imaging,
9
metamateri-
als-based super-resolution,
10
two-photon luminescence and
stimulated emission-depletion microscopy,
11
stochastic optical
reconstruction imaging,
12
and photoactivated localization
microscopy.
13
In particular, there is an increasing demand for the approach
to optical imaging that is inherently label-free and does not rely
on fluorescence, operates on the sample that is in the far field of
all elements of the imaging syst em, and offers resolution com-
parable to that of fluorescent microscopy. Although seemingly a
tall order, this task has recent ly found two possible solutions that
approach the problem from the “hardware” and “algorithmic”
sides, respectively. The former approac h relies on the phenom e-
non of “super-oscillations”—where the band-limited function
can and—when properly designed—does oscillate faster than
its fastest Fourier component. The super-oscillatory lenses that
implement this behavior have been designed and fabricated,
14,15
and optical resolution exceeding the conventional Abbe limit
has been demonstrated in experiment.
14
The second app roach
relies on methods of processing the “diffraction-limited” data,
taking full advantage of the fact that actual targets (and espe-
cially biological samples) are often inherently sparse.
3
The re-
sulting resolution improvement beyond the Abbe limit, due to
this improved data processing, has been demonstrated both in
numerical simulations and in experiment.
16–18
Far-field optical resolution beyond the Abbe limit in a scat-
tering rather than fluorescence-based approach, observed in
*Address all correspondence to Evgenii Narimanov, E-mail: evgenii@purdue.edu
Research Article
Advanced Photonics 056003-1 Sep∕Oct 2019
•
Vol. 1(5)