Related papers: Optical measurements of phase steps in segmented m…
A wide variety of imaging systems have been designed to measure phase variations, with applications from physics to biology and medicine. In this work, we theoretically compare the precision of phase estimations achievable with classical…
Phase estimates in adaptive-optics systems are computed by use of wavefront sensors such as Shack-Hartmann or curvature sensors. In either case the standard error of the phase estimates is proportional to the standard error of the…
Precision measurement has been an important research area in sensing and metrology. In classical physics, the Fisher information determines the maximum extractable information from statistically unknown signals, based on a joint probability…
In this paper we use the Cramer-Rao lower uncertainty bound to estimate the maximum precision that could be achieved on the joint simultaneous (or 2D) estimation of photometry and astrometry of a point source measured by a linear CCD…
Context: Ground-based telescopes are susceptible to seeing, an atmospheric phenomenon that reduces the resolving power of large observatories to that of a home telescope. Compensating these effects is therefore critical to realizing the…
The problem of measuring a time-varying phase, even when the statistics of the variation is known, is considerably harder than that of measuring a constant phase. In particular, the usual bounds on accuracy - such as the $1/(4\bar{n})$…
We show that the quantum Cram\'er-Rao bound on the precision of measurements of the optical phase gradient, or the wavefront tilt, with a beam of finite width is consistent with the Heisenberg uncertainty principle for a single-photon…
The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramer-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as…
A recently proposed phase-estimation protocol that is based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that Cram\'{e}r-Rao bound sensitivity can be obtained [P.\ M.\…
Estimation of the properties of a physical system with minimal uncertainty is a central task in quantum metrology. Optical phase estimation is at the center of many metrological tasks where the value of a physical parameter is mapped to the…
A proposed phase-estimation protocol based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that the Cram\'{e}r-Rao sensitivity is sub-Heisenberg [Phys.\ Rev.\ Lett.\ {\bf104},…
We experimentally demonstrate optomechanical motion and force measurements near the quantum precision limits set by the quantum Cram\'er-Rao bounds (QCRBs). Optical beams in coherent and phase-squeezed states are used to measure the motion…
The ultimate precision of phase estimation is limited by the Heisenberg scaling $\Delta\phi_0 = K/N$, where $K\sim1$ is a numerical prefactor and $N$ is the mean number of photons interacting with the phase shifting object(s). However,…
The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously…
The quantum Cram\'er-Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We…
We investigate the phase sensitivity of a Mach-Zehnder interferometer using a special class of generalized coherent states constructed from generalized Heisenberg and deformed $su(1,1)$ algebras. These states, derived from a perturbed…
Based on the conventional Mach-Zehnder interferometer, we propose a metrological scheme to improve phase sensitivity. In this scheme, we use a coherent state and a squeezed vacuum state as input states, employ multi-photon-subtraction…
The ultimate sensitivity of optical measurements is a key element of many recent works. Classically, it is mainly limited by the shot noise limit. However, a measurement setup that incorporates quantum mechanical principles can surpass the…
While adaptive optical systems are able to remove moderate wavefront distortions in scintillated optical beams, phase singularities that appear in strongly scintillated beams can severely degrade the performance of such an adaptive optical…
Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods…