Model-based two-object resolution from observations having counting statistics

Bettens, E.; Dyck, D. Van; Dekker, Arnold J. den; Sijbers, Jan; Bos, A. van den

doi:10.1016/s0304-3991(99)00006-6

Cited by 66 publications

(70 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…TheÊS(x, y) component is separated again into symmetric (Ê3(x, y)) and antisymmetric (Ê2(x, y)) components with respect to reflection about the x-axis, which are detected using bucket detectors. The set of binary outcomes, g (1) , g (2) and g (3) , observed in the detectors over a series of M measurements is processed to give estimatesďX andďY of the components of the separation. The required field transformations are realized by the extra reflection at an appropriately aligned plane mirror in one arm of the balanced Mach-Zehnder interferometers, which are indicated by the evolution of the letters 'A' and 'B' through the system.…”

Section: Linear-optics Schemes For Estimating the Separation Vectormentioning

confidence: 99%

Quantum limit for two-dimensional resolution of two incoherent optical point sources

2017

View full text Add to dashboard Cite

We obtain the multiple-parameter quantum Cramér-Rao bound for estimating the transverse Cartesian components of the centroid and separation of two incoherent optical point sources using an imaging system with finite spatial bandwidth. Under quite general and realistic assumptions on the point-spread function of the imaging system, and for weak source strengths, we show that the Cramér-Rao bounds for the x and y components of the separation are independent of the values of those components, which may be well below the conventional Rayleigh resolution limit. We also propose two linear optics-based measurement methods that approach the quantum bound for the estimation of the Cartesian components of the separation once the centroid has been located. One of the methods is an interferometric scheme that approaches the quantum bound for sub-Rayleigh separations. The other method using fiber coupling can in principle attain the bound regardless of the distance between the two sources.

show abstract

Section: Linear-optics Schemes For Estimating the Separation Vectormentioning

confidence: 99%

Quantum limit for two-dimensional resolution of two incoherent optical point sources

2017

View full text Add to dashboard Cite

show abstract

“…1). That is, the signal model is (1) We consider the following two-dimensional (2-D) model for the measured (discrete) signal (2) where is the blurring kernel 1 (representing the overall point spread function (PSF) of the imaging system) and is assumed to be a zero-mean Gaussian white noise 2 process with variance .…”

Section: Introductionmentioning

confidence: 99%

“…This can be posed as a hypothesis testing problem, i.e., One point source Two point sources (3) or equivalently (see (4) at the bottom of the page). The problem of resolution from the statistical viewpoint has been well studied in the past [25], [2], [1], [7], [9]. The majority of researchers have used the Cramér-Rao bound to analyze the problem of resolution to study the mean-square error of unbiased estimators for the distance between the sources [8], [9], [1], [21], [22], [13], [16].…”

Section: Introductionmentioning

confidence: 99%

Statistical and Information-Theoretic Analysis of Resolution in Imaging

Shahram

Milanfar

2006

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

Abstract-In this paper, some detection-theoretic, estimation-theoretic, and information-theoretic methods are investigated to analyze the problem of determining resolution limits in imaging systems. The canonical problem of interest is formulated based on a model of the blurred image of two closely spaced point sources of unknown brightness. To quantify a measure of resolution in statistical terms, the following question is addressed: "What is the minimum detectable separation between two point sources at a given signal-to-noise ratio (SNR), and for prespecified probabilities of detection and false alarm ( and )?". Furthermore, asymptotic performance analysis for the estimation of the unknown parameters is carried out using the Cramér-Rao bound. Although similar approaches to this problem (for one-dimensional (1-D) and oversampled signals) have been presented in the past, the analyzes presented in this paper are carried out for the general two-dimensional (2-D) model and general sampling scheme. In particular the case of under-Nyquist (aliased) images is studied. Furthermore, the Kullback-Liebler distance is derived to further confirm the earlier results and to establish a link between the detection-theoretic approach and Fisher information. To study the effects of variation in point spread function (PSF) and model mismatch, a perturbation analysis of the detection problem is presented as well.

show abstract

“…Under the modern advent of rigorous statistics and image processing, Rayleigh's criterion remains a curse. When the image is noisy, necessarily so owing to the quantum nature of light [2], and Rayleigh's criterion is violated, it becomes much more difficult to estimate the separation accurately by conventional imaging methods [3][4][5]. Modern superresolution techniques in microscopy [6][7][8] can circumvent Rayleigh's criterion by making sources radiate in isolation, but such techniques require careful control of the fluorescent emissions, making them difficult to use for microscopy and irrelevant to astronomy.…”

mentioning

confidence: 99%

Quantum information for semiclassical optics

Tsang

Nair

2016

Quantum and Nonlinear Optics IV

View full text Add to dashboard Cite

Using a semiclassical model of photodetection with Poissonian noise and insights from quantum metrology, we prove that linear optics and photon counting can optimally estimate the separation between two incoherent point sources without regard to Rayleigh's criterion. The model is applicable to weak thermal or fluorescent sources as well as lasers.Lord Rayleigh suggested in 1879 that two incoherent optical point sources should be separated by a diffraction-limited spot size for them to be resolved [1]. This criterion has since become the most influential measure of imaging resolution. Under the modern advent of rigorous statistics and image processing, Rayleigh's criterion remains a curse. When the image is noisy, necessarily so owing to the quantum nature of light [2], and Rayleigh's criterion is violated, it becomes much more difficult to estimate the separation accurately by conventional imaging methods [3][4][5]. Modern superresolution techniques in microscopy [6][7][8] can circumvent Rayleigh's criterion by making sources radiate in isolation, but such techniques require careful control of the fluorescent emissions, making them difficult to use for microscopy and irrelevant to astronomy.Here we show that, contrary to conventional wisdom, the separation between two incoherent optical sources can be estimated accurately via linear optics and photon counting (LOPC) even if Rayleigh's criterion is severely violated. Our theoretical model here is based on the semiclassical theory of photodetection with Poissonian noise, which is a widely accepted statistical model for lasers [2] as well as weak thermal [9,10] or fluorescent [5,11] light in astronomy and microscopy. The semiclassical model is consistent with the quantum model proposed in Ref. [12] for weak incoherent sources and the mathematical formalisms are similar, but the semiclassical model has the advantage of being applicable also to lasers, which are important sources for remote-sensing, testing, and proof-of-concept experiments. The semiclassical theory also avoids a quantum description of light and offers a more pedagogical perspective. Compared with the full semiclassical theory in Ref. [13], the Poissonian model is invalid for strong thermal sources but more analytically tractable.Consider J optical modes and a column vector of complex field amplitudes α = (α 1 , . . . , α J ) ⊤ within one coherence time interval. The amplitudes are normalized such that |α j | 2 is equal to the energy in each mode in units of quanta. The central quantity in statistical optics is the mutual coherence matrix [2, 9]where † denotes the complex transpose and E denotes the statistical expectation. We also define ε ≡ E α † α = tr Γ as the mean total energy, tr as the trace, andas the correlation matrix. g is positive-semidefinite with unit trace and typically called g (1) in statistical optics. Suppose that we process the optical fields with lossless passive linear optics, the input-output relations of which are characterized by a unitary scattering matrix F. The output mutu...

show abstract

Model-based two-object resolution from observations having counting statistics

Cited by 66 publications

References 8 publications

Quantum limit for two-dimensional resolution of two incoherent optical point sources

Quantum limit for two-dimensional resolution of two incoherent optical point sources

Statistical and Information-Theoretic Analysis of Resolution in Imaging

Quantum information for semiclassical optics

Contact Info

Product

Resources

About