50,428 research outputs found
Conservative classical and quantum resolution limits for incoherent imaging
I propose classical and quantum limits to the statistical resolution of two
incoherent optical point sources from the perspective of minimax parameter
estimation. Unlike earlier results based on the Cram\'er-Rao bound, the limits
proposed here, based on the worst-case error criterion and a Bayesian version
of the Cram\'er-Rao bound, are valid for any biased or unbiased estimator and
obey photon-number scalings that are consistent with the behaviors of actual
estimators. These results prove that, from the minimax perspective, the
spatial-mode demultiplexing (SPADE) measurement scheme recently proposed by
Tsang, Nair, and Lu [Phys. Rev. X 6, 031033 (2016)] remains superior to direct
imaging for sufficiently high photon numbers.Comment: 12 pages, 2 figures. v2: focused on imaging, cleaned up the math,
added new analytic and numerical results. v3: restructured and submitte
Exploring plenoptic properties of correlation imaging with chaotic light
In a setup illuminated by chaotic light, we consider different schemes that
enable to perform imaging by measuring second-order intensity correlations. The
most relevant feature of the proposed protocols is the ability to perform
plenoptic imaging, namely to reconstruct the geometrical path of light
propagating in the system, by imaging both the object and the focusing element.
This property allows to encode, in a single data acquisition, both
multi-perspective images of the scene and light distribution in different
planes between the scene and the focusing element. We unveil the plenoptic
property of three different setups, explore their refocusing potentialities and
discuss their practical applications.Comment: 9 pages, 4 figure
Mapping Atomic Motions with Electrons: Toward the Quantum Limit to Imaging Chemistry
Recent advances in ultrafast electron and X-ray diffraction have pushed imaging of structural dynamics into the femtosecond time domain, that is, the fundamental time scale of atomic motion. New physics can be reached beyond the scope of traditional diffraction or reciprocal space imaging. By exploiting the high time resolution, it has been possible to directly observe the collapse of nearly innumerable possible nuclear motions to a few key reaction modes that direct chemistry. It is this reduction in dimensionality in the transition state region that makes chemistry a transferable concept, with the same class of reactions being applicable to synthetic strategies to nearly arbitrary levels of complexity. The ability to image the underlying key reaction modes has been achieved with resolution to relative changes in atomic positions to better than 0.01 Å, that is, comparable to thermal motions. We have effectively reached the fundamental space-time limit with respect to the reaction energetics and imaging the acting forces. In the process of ensemble measured structural changes, we have missed the quantum aspects of chemistry. This perspective reviews the current state of the art in imaging chemistry in action and poses the challenge to access quantum information on the dynamics. There is the possibility with the present ultrabright electron and X-ray sources, at least in principle, to do tomographic reconstruction of quantum states in the form of a Wigner function and density matrix for the vibrational, rotational, and electronic degrees of freedom. Accessing this quantum information constitutes the ultimate demand on the spatial and temporal resolution of reciprocal space imaging of chemistry. Given the much shorter wavelength and corresponding intrinsically higher spatial resolution of current electron sources over X-rays, this Perspective will focus on electrons to provide an overview of the challenge on both the theory and the experimental fronts to extract the quantum aspects of molecular dynamics
Superresolution without Separation
This paper provides a theoretical analysis of diffraction-limited
superresolution, demonstrating that arbitrarily close point sources can be
resolved in ideal situations. Precisely, we assume that the incoming signal is
a linear combination of M shifted copies of a known waveform with unknown
shifts and amplitudes, and one only observes a finite collection of evaluations
of this signal. We characterize properties of the base waveform such that the
exact translations and amplitudes can be recovered from 2M + 1 observations.
This recovery is achieved by solving a a weighted version of basis pursuit over
a continuous dictionary. Our methods combine classical polynomial interpolation
techniques with contemporary tools from compressed sensing.Comment: 23 pages, 8 figure
Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
Rayleigh's criterion for resolving two incoherent point sources has been the
most influential measure of optical imaging resolution for over a century. In
the context of statistical image processing, violation of the criterion is
especially detrimental to the estimation of the separation between the sources,
and modern farfield superresolution techniques rely on suppressing the emission
of close sources to enhance the localization precision. Using quantum optics,
quantum metrology, and statistical analysis, here we show that, even if two
close incoherent sources emit simultaneously, measurements with linear optics
and photon counting can estimate their separation from the far field almost as
precisely as conventional methods do for isolated sources, rendering Rayleigh's
criterion irrelevant to the problem. Our results demonstrate that
superresolution can be achieved not only for fluorophores but also for stars.Comment: 18 pages, 11 figures. v1: First draft. v2: Improved the presentation
and added a section on the issues of unknown centroid and misalignment. v3:
published in Physical Review
Quantum metrology and its application in biology
Quantum metrology provides a route to overcome practical limits in sensing
devices. It holds particular relevance to biology, where sensitivity and
resolution constraints restrict applications both in fundamental biophysics and
in medicine. Here, we review quantum metrology from this biological context,
focusing on optical techniques due to their particular relevance for biological
imaging, sensing, and stimulation. Our understanding of quantum mechanics has
already enabled important applications in biology, including positron emission
tomography (PET) with entangled photons, magnetic resonance imaging (MRI) using
nuclear magnetic resonance, and bio-magnetic imaging with superconducting
quantum interference devices (SQUIDs). In quantum metrology an even greater
range of applications arise from the ability to not just understand, but to
engineer, coherence and correlations at the quantum level. In the past few
years, quite dramatic progress has been seen in applying these ideas into
biological systems. Capabilities that have been demonstrated include enhanced
sensitivity and resolution, immunity to imaging artifacts and technical noise,
and characterization of the biological response to light at the single-photon
level. New quantum measurement techniques offer even greater promise, raising
the prospect for improved multi-photon microscopy and magnetic imaging, among
many other possible applications. Realization of this potential will require
cross-disciplinary input from researchers in both biology and quantum physics.
In this review we seek to communicate the developments of quantum metrology in
a way that is accessible to biologists and biophysicists, while providing
sufficient detail to allow the interested reader to obtain a solid
understanding of the field. We further seek to introduce quantum physicists to
some of the central challenges of optical measurements in biological science.Comment: Submitted review article, comments and suggestions welcom
Optimal measurements for quantum spatial superresolution
We construct optimal measurements, achieving the ultimate precision predicted
by quantum theory, for the simultaneous estimation of centroid, separation, and
relative intensities of two incoherent point sources using a linear optical
system. We discuss the physical feasibility of the scheme, which could pave the
way for future practical implementations of quantum inspired imaging.Comment: 7 pages. 3 color figures. Title change
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