Rayleigh Criterion Research Articles

What is resolution? A statistical minimax testing perspective on superresolution microscopy

As a general rule of thumb the resolution of a light microscope (i.e., the ability to discern objects) is predominantly described by the full width at half maximum (FWHM) of its point spread function (psf)—the diameter of the blurring density at half of its maximum. Classical wave optics suggests a linear relationship between FWHM and resolution also manifested in the well-known Abbe and Rayleigh criteria, dating back to the end of the 19th century. However, during the last two decades conventional light microscopy has undergone a shift from microscopic scales to nanoscales. This increase in resolution comes with the need to incorporate the random nature of observations (light photons) and challenges the classical view of discernability, as we argue in this paper. Instead, we suggest a statistical description of resolution obtained from such random data. Our notion of discernability is based on statistical testing whether one or two objects with the same total intensity are present. For Poisson measurements, we get linear dependence of the (minimax) detection boundary on the FWHM, whereas for a homogeneous Gaussian model the dependence of resolution is nonlinear. Hence, at small physical scales modeling by homogeneous gaussians is inadequate, although often implicitly assumed in many reconstruction algorithms. In contrast, the Poisson model and its variance stabilized Gaussian approximation seem to provide a statistically sound description of resolution at the nanoscale. Our theory is also applicable to other imaging setups, such as telescopes.

P‐16.8: Research on anti‐visibility characteristics of OGM touch screen

This paper mainly studies the influence factors and the theoretical model of OGM anti‐visibility. The factor experiment is performed by controlling the Mesh Space, the double‐layer metal reflectance difference |Rd|%, and the metal reflectivity R%. Though the research on the relationship between the factor and the level of anti‐visibility of the touch screen, Mesh Space, |Rd|%, and R% have a negative correlation with Anti visibility ability. To improve anti‐visibility ability, it is necessary to reduce Mesh Space, |Rd|% and R%. By establishing the OGM anti‐visibility theoretical model, the visibility of the human eye to the OGM metal mesh is equivalent to the human eye's ability to distinguish the smallest unit of metal mesh line. When mesh Space and |Rd|% increases, which is equivalent to the larger the resolution line distance of the mesh , it is easier for human eye to recognize metal mesh according to the Rayleigh criterion, so that the metal mesh is visible and anti‐ visibility ability decreases. When R% increases, metal reflection energy increases, and the background difference from the display module increases, making it easier to be recognized.

A Sparse Denoising-Based Super-Resolution Method for Scanning Radar Imaging

Scanning radar enables wide-range imaging through antenna scanning and is widely used for radar warning. The Rayleigh criterion indicates that narrow beams of radar are required to improve the azimuth resolution. However, a narrower beam means a larger antenna aperture. In practical applications, due to platform limitations, the antenna aperture is limited, resulting in a low azimuth resolution. The conventional sparse super-resolution method (SSM) has been proposed for improving the azimuth resolution of scanning radar imaging and achieving superior performance. This method uses the L1 norm to represent the sparse prior of the target and solves the L1 regularization problem to achieve super-resolution imaging under the regularization framework. The resolution of strong-point targets is improved efficiently. However, for some targets with typical shapes, the strong sparsity of the L1 norm treats them as strong-point targets, resulting in the loss of shape characteristics. Thus, we can only see the strong points in its processing results. However, in some applications that need to identify targets in detail, SSM can lead to false judgments. In this paper, a sparse denoising-based super-resolution method (SDBSM) is proposed to compensate for the deficiency of traditional SSM. The proposed SDBSM uses a sparse minimization scheme for denoising, which helps to reduce the influence of noise. Then, the super-resolution imaging is achieved by alternating iterative denoising and deconvolution. As the proposed SDBSM uses the L1 norm for denoising rather than deconvolution, the strong sparsity constraint of the L1 norm is reduced. Therefore, it can effectively preserve the shape of the target while improving the azimuth resolution. The performance of the proposed SDBSM was demonstrated via simulation and real data processing results.

Algorithms for Digital Processing of Measurement Data Providing Angular Superresolution

Incorrect one- and two-dimensional inverse problems of reconstructing images of objects with angular resolutionexceeding the Rayleigh criterion are considered. The technique is based on the solution of inverse problems of source reconstruction signals described Fredholm integral equations. Algebraic methods and algorithms for processing dataobtained by measuring systems in order to achieve angular superresolution are presented. Angular superresolution allows you to detail images of objects, solve problems of their recognition and identification on this basis. The efficiency of using algorithms based on developed algebraic methods and their modifications in parameterization the inverse problems under study and further reconstructing approximate images of objects of various types is shown. It is shown that the noise immunity of the obtained solutions exceeds many known approaches. The results of numerical experiments demonstrate the possibility of obtaining images with a resolution exceeding the Rayleigh criterion by 2-6 times at small values of the signal-to-noise ratio. The ways of further increasing the degree of superresolution based on the intelligent analysis of measurement data are described. On the basis of the preliminary information on a source of signals algorithms allow to increase consistently the effective angular resolution before achievement greatest possible for a solved problem. Algorithms of secondary processing of the information necessary for it are described. It is found that the proposed symmetrization algorithm improves the quality of solutions to the inverse problems under consideration and their stability. The examples demonstrate the successful application of modified algebraic methods and algorithms for obtaining images of the objects under study in the presence of a priori information about the solution. The results of numerical studies show that the presented methods of digital processing of received signals allow us to restore the angular coordinates of individual objects under study and their elements with super-resolution with good accuracy. The adequacy and stability of the solutions were verified by conducting numerical experiments on a mathematical model. It was shown that the stability of solutions, especially at a significant level of random components, is higher than that of many other methods. The limiting possibilities of increasing the effective angular resolution and the accuracy of image reconstruction of signal sources, depending on the level of random components in the data utilized, are found. The effective angular resolution achieved in this case is 2—10 times higher than the Rayleigh criterion. The minimum required signal-to-noise ratio for obtaining adequate solutions with super-resolution is 13—16 dB for the described methods, which is significantly less than for the known methods. The relative simplicity of the presented methods allows you to use inexpensive computing devices and work in real time.

Three-dimensional transfer function of optical microscopes in reflection mode.

Three-dimensional (3D) transfer functions build the basis for a comprehensive characterization of optical imaging systems in the spatial frequency domain. Utilizing the projection-slice theorem, the 2D modulation transfer function of an incoherent imaging system can be derived from a 3D transfer function by integration with respect to the axial spatial frequency. For a diffraction limited microscope with homogeneous incoherent pupil illumination, the modulation transfer function equals the 2D autocorrelation function of a circular disc. However, until now to the best of our knowledge no 3D transfer function has been published, which exactly leads to the 2D modulation transfer function of a diffraction limited microscope in reflection mode. In this article, we derive a formula, which after integration with respect to the axial spatial frequency coordinate perfectly fits to the diffraction limited 2D modulation transfer function. The inverse three-dimensional Fourier transform of the 3D transfer function results in a complex-valued 3D point spread function, from which the depth of field, the lateral resolution and, in addition, the corresponding 3D point spread function of both, a conventional and an interference microscope, can beobtained.

Achieving Angular Superresolution of Control and Measurement Systems in Signal Processing

Algebraic methods of processing data obtained by control and measurement systems to achieve angular superresolution are presented. The efficiency of using the methods in the formation of approximate images of objects at low signal-to-noise ratios is shown. The results of numerical experiments demonstrate the possibility of obtaining images with a resolution exceeding the Rayleigh criterion by 3-10 times. The robustness of the solutions obtained by the methods of algebraic exceeds many well-known approaches. The relative simplicity of the presented methods allows the use of inexpensive computing devices and perform real-time measurement processing.

변형 코노스코픽 홀로그래피의 해상도에 관한 기초연구

In this paper, the optical path lengths(OPL) of ordinary and extraordinary waves in an uniaxial crystal were obtained in modified conoscopic holography, and the phase difference between the two waves was calculated using OPL. Using the complex hologram considering the phase difference, the intensity of light in the lateral and longitudinal directions of the reconstructed image was obtained by changing the size of the hologram and the uniaxial crystal, and wavelength. According to the Rayleigh criterion, the lateral and longitudinal resolutions of the reconstructed image are proportional to the size of the hologram and the uniaxial crystal, and are inversely proportional to the length of wavelength.

Quantum-accelerated imaging of N stars.

Imaging point sources with low angular separation near or below the Rayleigh criterion are important in astronomy, e.g., in the search for habitable exoplanets near stars. However, the measurement time required to resolve stars in the sub-Rayleigh region via traditional direct imaging is usually prohibitive. Here we propose quantum-accelerated imaging (QAI) to significantly reduce the measurement time using an information-theoretic approach. QAI achieves quantum acceleration by adaptively learning optimal measurements from data to maximize Fisher information per detected photon. Our approach can be implemented experimentally by linear-projection instruments followed by single-photon detectors. We estimate the position, brightness, and the number of unknown stars 10∼100 times faster than direct imaging with the same aperture. QAI is scalable to a large number of incoherent point sources and can find widespread applicability beyond astronomy to high-speed imaging, fluorescence microscopy, and efficient optical read-out of qubits.

Preconditioned deconvolution method for high-resolution ghost imaging

Ghost imaging (GI) can nonlocally image objects by exploiting the fluctuation characteristics of light fields, where the spatial resolution is determined by the normalized second-order correlation function g ( 2 ) . However, the spatial shift-invariant property of g ( 2 ) is distorted when the number of samples is limited, which hinders the deconvolution methods from improving the spatial resolution of GI. In this paper, based on prior imaging systems, we propose a preconditioned deconvolution method to improve the imaging resolution of GI by refining the mutual coherence of a sampling matrix in GI. Our theoretical analysis shows that the preconditioned deconvolution method actually extends the deconvolution technique to GI and regresses into the classical deconvolution technique for the conventional imaging system. The imaging resolution of GI after preconditioning is restricted to the detection noise. Both simulation and experimental results show that the spatial resolution of the reconstructed image is obviously enhanced by using the preconditioned deconvolution method. In the experiment, 1.4-fold resolution enhancement over Rayleigh criterion is achieved via the preconditioned deconvolution. Our results extend the deconvolution technique that is only applicable to spatial shift-invariant imaging systems to all linear imaging systems, and will promote their applications in biological imaging and remote sensing for high-resolution imaging demands.

Evaluation of Nonparametric SAR Tomography Methods for Urban Building Reconstruction

Recently, the synthetic aperture radar tomography (TomoSAR) technique has attracted significant attention owing to its 3-D reconstruction capability of complex urban environments. The availability of a high number of images is usually a requirement for nonparametric spectral estimation methods. This letter evaluates the potential of four nonparametric spectral estimation algorithms, that is: 1) linear prediction (LP); 2) minimum norm (MN); 3) singular value decomposition (SVD); and 4) Capon for improved tomographic reconstruction of the third dimension of built-up areas with a small number of observations. The performance analysis is carried out for both simulated and real SAR datasets. The returns from the employed techniques indicate the efficient and low-computational estimator of LP by minimizing the average output signal power at the array of antenna elements and make it possible to separate multiple scatters at a distance below the Rayleigh resolution and clean sidelobes’ phenomena in the elevation profiles. The experimental results of a dataset acquired by the TerraSAR-X sensor verify the effectiveness of the LP spectral estimator algorithm in the reconstruction of urban buildings. The estimated height of scatterers with the LP method is considerably similar to the ground-observed data.

Design and analysis of segmented-mirror primary mirror system

with the development of space exploration, the resolution of optical system is required to be higher and higher. According to the Rayleigh criterion, the resolution of the optical system is directly proportional to the aperture. However, due to the influence of processing capacity and size of the rocket fairing, it is difficult to achieve one single large aperture. Therefore, the scheme of using small size segmented-mirror to achieve one large aperture becomes an effective form. Because location difference between the deployment and the ideal position, the imaging quality will be affected, and cannot be imaged in serious case. For the analysis of influence of the position error on the imaging quality, the traditional method is to analyze on the optical transfer function and Strehl ratio in theory, ignoring the influence of various aberrations that cannot be corrected by the optical system itself. In this paper, the segmented-mirror primary mirror system model is established to analyze the influence of the position error and the real influence of the various aberrations of the system, so as to complete the analysis of the influence more comprehensively. Through the analysis of different position errors, we can get the final wave-front aberration and Strehl ratio of the system under the influence of position error, which can be used as a reference for the analysis of position error influence of segmented-mirror primary mirror form and sparse aperture form of large aperture optical system in the future.

Generalized Rayleigh criterion for signal resolution on coherent Doppler wind measurements

Speed range is an important specification of coherent Doppler wind lidar (CDWL). However, it is difficult to identify the lower speed bound of CDWL, because the Doppler signal is often overlapped or covered by relative intensity noise (RIN) at the low-frequency end of the spectrum. Therefore, how to distinguish the Doppler signal and the RIN at the low frequency is always an important issue. In the optical information processing, Rayleigh criterion specifies the spatial resolution limit, which is the minimum distance between the two distinguishable Airy disks. Due to the rigorous one-to-one correspondence between optical signals and electrical signals in photoelectric conversion, Rayleigh criterion can be extended to the electrical signal processing. We mapped the Doppler signal and RIN into the Airy disk profile and used the generalized Rayleigh criterion to study the signal resolution limit to define the lower speed bound of the system. The comparative experiments were carried out and the results were consistent with the generalized Rayleigh criterion. It shows that the generalized Rayleigh criterion is available and effective and can be used as a new method for the signal resolution on coherent Doppler wind measurements.

Preparation method for polyimide films with imaging potential

Polyimide (PI) film is widely used in aerospace, microelectronics, and other fields because of its excellent thermal stability and mechanical strength. However, there are very few reports about its application in the direction of optical imaging. To use PI film for imaging, the requirements for the optical homogeneity of the PI film are extremely demanding. The optical homogeneity of the stretch-resistant PI film proposed in this paper with 100 mm diameter and low thermal expansion coefficient meets the Rayleigh criterion, which has the potential for applications in the imaging field. In addition, the tensile strength of this PI is 285 MPa, which is ~2.6 times that of the PMDA-ODA type PI; the coefficient of thermal expansion is about 3.2 ppmK-1, which is comparable to that of the Novastrat®905 type PI and is one order of magnitude lower than that of the commercial PI films. These excellent basic properties reserve more space to further improve the space adaptability of the PI film. The solution of the optical homogeneity of the PI film will lay the foundation for its application in thin film diffractive optical elements.

Generalization of Rayleigh's criterion on parameter estimation with incoherent sources

The basic idea behind Rayleigh's criterion on resolving two incoherent optical point sources is that the overlap between the spatial modes from different sources would reduce the estimation precision for the locations of the sources, dubbed Rayleigh's curse. We generalize the concept of Rayleigh's curse to the abstract problems of quantum parameter estimation with incoherent sources. To manifest the effect of Rayleigh's curse on quantum parameter estimation, we define the curse matrix in terms of quantum Fisher information and introduce the global and local immunity to the curse accordingly. We further derive the expression for the curse matrix and give the necessary and sufficient condition on the immunity to Rayleigh's curse. For estimating the one-dimensional location parameters with a common initial state, we demonstrate that the global immunity to the curse on quantum Fisher information is impossible for more than two sources.

Experimental Study on Dynamic Combustion Characteristics in Swirl-Stabilized Combustors

An experimental study was performed to investigate the combustion instability characteristics of swirl-stabilized combustors. A premixed gas composed of ethylene and air was burned under various flow and geometric conditions. Experiments were conducted by changing the inlet mean velocity, equivalence ratio, swirler vane angle, and combustor length. Two dynamic pressure sensors, a hot-wire anemometer, and a photomultiplier tube were installed to detect the pressure oscillations, velocity perturbations, and heat release fluctuations in the inlet and combustion chambers, respectively. An ICCD camera was used to capture the time-averaged flame structure. The objective was to understand the relationship between combustion instability and the Rayleigh criterion/the flame structure. When combustion instability occurred, the pressure oscillations were in-phase with the heat release oscillations. Even if the Rayleigh criterion between the pressure and heat release oscillations was satisfied, stable combustion with low pressure fluctuations was possible. This was explained by analyzing the dynamic flow and combustion data. The root-mean-square value of the heat release fluctuations was observed to predict the combustion instability region better than that of the inlet velocity fluctuations. The bifurcation of the flame structure was a necessary condition for combustion instability in this combustor. The results shed new insight into combustion instability in swirl-stabilized combustors.

Acoustic Energy Balance During the Onset, Growth, and Saturation of Thermoacoustic Instabilities

Abstract Thermoacoustic instabilities can occur in a wide range of combustors and are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, it does not provide any physical insight in terms of the acoustic energy balance of the system. On the other hand, Rayleigh's criterion may be used to quantify the losses, sources and transfers of acoustic energy within and at the boundaries of a combustor. However, this approach is cumbersome for most applications because it requires computing volume and surface integrals and averaging over an oscillation cycle. In this work, a new methodology for studying the acoustic energy balance of a combustor during the onset, growth and saturation of thermoacoustic instabilities is proposed. The two cornerstones of this new framework are the acoustic absorption coefficient Δ and the cycle-to-cycle acoustic energy ratio λ, both of which do not require computing integrals. Used along with a suitable acoustic network model, where the flame frequency response is described using the weakly nonlinear Flame Describing Function (FDF) formalism, these two dimensionless numbers are shown to characterize: 1) the variation of acoustic energy stored within the combustor between two consecutive cycles, 2) the acoustic energy transfers occurring at the combustor's boundaries, and 3) the sources and sinks of acoustic energy located within the combustor. The acoustic energy balance of the well-documented Palies burner is then analyzed during the onset, growth and saturation of thermoacoustic instabilities using this new methodology. It is demonstrated that this new approach allows a deeper understanding of the physical mechanisms at play. For instance, it is possible to determine when the flame acts as an acoustic energy source or sink, where acoustic damping is generated, and if acoustic energy is transmitted through the boundaries of the burner.

Measuring the Behavioral Effects of Intraocular Scatter.

Intraocular scatter, with its associated functional manifestations, is a leading cause of automotive accidents and a significant biomarker of covert and overt ocular disease (e.g., diseases of the cornea and lens). Nearly all current methods of measuring the behavioral consequences of light scatter, however, suffer from various limitations mostly reflecting a lack of construct and content validity: to wit, the measures do not adequately reflect real world conditions (e.g., artificial light vs. sunlight) or everyday tasks (e.g., recognition under visually demanding conditions). This protocol describes two novel, ecologically valid methods of measuring the behavioral effects of intraocular scatter by quantifying scatter geometry and visual recognition under glare conditions. The former was measured by assessing the diameter of halos and spokes that resulted from a bright point source. Light spread (essentially, the point spread function determined using Rayleigh criteria) was quantified by determining the minimum perceivable distance between two small points of broad-band light. The latter was done based on the identification of letters formed using apertures through which bright light was shone.

Measuring the Behavioral Effects of Intraocular Scatter

Intraocular scatter, with its associated functional manifestations, is a leading cause of automotive accidents and a significant biomarker of covert and overt ocular disease (e.g., diseases of the cornea and lens). Nearly all current methods of measuring the behavioral consequences of light scatter, however, suffer from various limitations mostly reflecting a lack of construct and content validity: to wit, the measures do not adequately reflect real world conditions (e.g., artificial light vs. sunlight) or everyday tasks (e.g., recognition under visually demanding conditions). This protocol describes two novel, ecologically valid methods of measuring the behavioral effects of intraocular scatter by quantifying scatter geometry and visual recognition under glare conditions. The former was measured by assessing the diameter of halos and spokes that resulted from a bright point source. Light spread (essentially, the point spread function determined using Rayleigh criteria) was quantified by determining the minimum perceivable distance between two small points of broad-band light. The latter was done based on the identification of letters formed using apertures through which bright light was shone.

Microwave Correlation Forward-Looking Super-Resolution Imaging Based on Compressed Sensing

Forward-looking correlated imaging plays an increasingly important role in modern radar imaging systems. It overcomes disadvantages of traditional side or squint synthetic aperture radar (SAR) which is dependent on specific relative motion between the radar and target scene. A new microwave forward-looking correlated 3-D imaging method based on random radiation field combined with sparse reconstruction is proposed in this article. Firstly, phased array radar (PAR) is adopted to form different and random antenna patterns. Then, combined with the compressed sensing (CS) theory, the target image can be recovered with very few samples which can break through Rayleigh resolution limitation. Furthermore, the proposed method can achieve resolution at least 5.5 times higher than real aperture imaging. To raise computation efficiency of sparse reconstruction, an improved quasi-Newton iteration method based on graphics processing unit (GPU) platform is developed. Meanwhile, a GPU-based (NVIDIA Tesla K40c) accelerated computing method can significantly reduce the processing time compared with the time given by a personal computer (PC). Both simulation and field experiment verify the validity of the proposed method.

Viscoelastic Taylor–Couette instability in the Keplerian regime

Instability modes of viscoelastic Taylor–Couette flow in the Keplerian regime are investigated using both linear stability analysis and experimental detection of critical states. A generalised Rayleigh criterion has been derived and it allows to separate the zone of potential purely elastic instability modes and the zone of stability. The analogy between the instability of viscoelastic Taylor–Couette flow in the Keplerian regime and the magnetorotational instability (MRI) of conducting magnetic fluids is established. Viscoelastic stress tensor can be represented by a tensor product of magnetic-like vectors. This allows to use the Velikhov-Chandrasekhar criterion of the MRI to predict the elasto-rotational instability (ERI). ERI modes obtained in linear stability and in the experiments are assumed to represent the MRI analogue modes as they are observed in the stable zone according to generalised Rayleigh discriminant.