Quantum-limited estimation of the axial separation of two incoherent point sources

Improving axial resolution is crucial for three-dimensional optical imaging systems. Here we present a scheme of axial superresolution for two incoherent point sources based on spatial mode demultiplexing. A radial mode sorter is used to losslessly decompose the optical fields into a radial mode basis set to extract the phase information associated with the axial positions of the point sources. We show theoretically and experimentally that, in the limit of a zero axial separation, our scheme allows for reaching the quantum Cram\'er-Rao lower bound and thus can be considered as one of the optimal measurement methods. Unlike other superresolution schemes, this scheme does not require neither activation of fluorophores nor sophisticated stabilization control. Moreover, it is applicable to the localization of a single point source in the axial direction. Our demonstration can be useful to a variety of applications such as far-field fluorescence microscopy.Comment: Comments are welcom

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

MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

Gravitational waves: search results, data analysis and parameter estimation

The Amaldi 10 Parallel Session C2 on gravitational wave (GW) search results, data analysis and parameter estimation included three lively sessions of lectures by 13 presenters, and 34 posters. The talks and posters covered a huge range of material, including results and analysis techniques for ground-based GW detectors, targeting anticipated signals from different astrophysical sources: compact binary inspiral, merger and ringdown; GW bursts from intermediate mass binary black hole mergers, cosmic string cusps, core-collapse supernovae, and other unmodeled sources; continuous waves from spinning neutron stars; and a stochastic GW background. There was considerable emphasis on Bayesian techniques for estimating the parameters of coalescing compact binary systems from the gravitational waveforms extracted from the data from the advanced detector network. This included methods to distinguish deviations of the signals from what is expected in the context of General Relativity

Development of a fusion adaptive algorithm for marine debris detection within the post-Sandy restoration framework

Recognition of marine debris represent a difficult task due to the extreme variability of the marine environment, the possible targets, and the variable skill levels of human operators. The range of potential targets is much wider than similar fields of research such as mine hunting, localization of unexploded ordnance or pipeline detection. In order to address this additional complexity, an adaptive algorithm is being developing that appropriately responds to changes in the environment, and context. The preliminary step is to properly geometrically and radiometrically correct the collected data. Then, the core engine manages the fusion of a set of statistically- and physically-based algorithms, working at different levels (swath, beam, snippet, and pixel) and using both predictive modeling (that is, a high-frequency acoustic backscatter model) and phenomenological (e.g., digital image processing techniques) approaches. The expected outcome is the reduction of inter-algorithmic cross-correlation and, thus, the probability of false alarm. At this early stage, we provide a proof of concept showing outcomes from algorithms that dynamically adapt themselves to the depth and average backscatter level met in the surveyed environment, targeting marine debris (modeled as objects of about 1-m size). The project relies on a modular software library, called Matador (Marine Target Detection and Object Recognition)