Point Emitters Research Articles

Universal inverse modeling of point spread functions for SMLM localization and microscope characterization.

The point spread function (PSF) of a microscope describes the image of a point emitter. Knowing the accurate PSF model is essential for various imaging tasks, including single-molecule localization, aberration correction and deconvolution. Here we present universal inverse modeling of point spread functions (uiPSF), a toolbox to infer accurate PSF models from microscopy data, using either image stacks of fluorescent beads or directly images of blinking fluorophores, the raw data in single-molecule localization microscopy (SMLM). Our modular framework is applicable to a variety of microscope modalities and the PSF model incorporates system- or sample-specific characteristics, for example, the bead size, field- and depth- dependent aberrations, and transformations among channels. We demonstrate its application in single or multiple channels or large field-of-view SMLM systems, 4Pi-SMLM, and lattice light-sheet microscopes using either bead data or single-molecule blinking data.

Beam shaping elements for single photon sources based on 3D printed micro-optics

Multiple researchers have explored the use of 3D printed micro-optical components as interfaces to quantum point emitters by considering different designs and configurations. Typically, these designs involve parametric structures optimized in combination with idealized point source models following the principles of imaging optics. In this work, we propose a different approach based on the use of well-known numerical routines developed in the field of illumination optics. We compare the obtained design to reference parametric 3D printed based interfaces, which have been used in the context of 3D printed micro-optical interfaces to single photon sources.

ТРАНСПОРТНЫЕ РЕШЕНИЯ УРАВНЕНИЙ МАКСВЕЛЛА В БИКВАТЕРНИОННОМ ПРЕДСТАВЛЕНИИ ПРИ ДОСВЕТОВЫХ СКОРОСТЯХ

The most common movable radiation sources of electromagnetic waves among the operating ones located on the platforms of various vehicles. It is obvious that the speed of movement affects the processes of wave propagation in an environment with such electrical conductivity and magnetic permeability, as does the shape of the source itself and the nature of its operation. In this work are constructed and studied transport solutions of the biquaternion wave equation, which is a biquaternion generalization of Maxwell's equations. These equations describe the electromagnetic fields of emitters of electromagnetic (EM) waves and electro-gravimagnetic waves (EGM), moving in a fixed direction with a constant speed, which is less than the speed of propagation of waves in an electromagnetic medium (the speed of light). Fundamental and generalized transport solutions have constructed that describe the EM fields of moving objects in the entire range of speeds, from light to superluminal.The electromagnetic field generated by a moving point emitter on the Z-axis described by the biquaternion Green's function (bifunction) in a moving coordinate system constructed using the Fourier transform of generalized functions. The energy density and Poynting vector of this field were determined. Influence of movement speed researched on field characteristics

Систематические ошибки установки углового положения в матричных имитаторах радиоэлектронной обстановки

Estimates of the error in setting the angular position of the apparent center of radiation by a matrix simulator, which are, in fact, its systematic error, are considered. It is shown that the cause of the error is the replacement of the simulated point emitter by several points. Analytical relations have been obtained that allow calculating the magnitude of the systematic direction fin-ding error based on the characteristics of the matrix simulator and the radiation pattern of the receiving antenna operating with the matrix simulator of the radio engineering system. It is shown that the considered error is completely determined by the nonlinearity of the direction finding characteristic of the antenna. It is established that the error is most significant when simulating the apparent center of radiation outside the matrix. For the area inside the matrix, the dependences of the maximum error values and their angular positions on the shape of the antenna pattern and the specified position of the radiation point are obtained. The relations allowing to estimate errors depending on the ratio of the angular dimensions of the matrix, the width of the antenna radiation pattern and the coefficients of approximation of its radiation pattern are obtained. The reliability of the obtained results is confirmed by comparison with the results obtained by numerical simulation. The results of the work can be used to solve applied problems related to the development of matrix simulators and simulation complexes based on them, as well as to predict their accuracy characteristics.

High-throughput single-molecule localization microscopy: Potential clinical applications.

High-throughput single-molecule localization microscopy: Potential clinical applications.

Quantum-Inspired Multi-Parameter Adaptive Bayesian Estimation for Sensing and Imaging

It is well known in Bayesian estimation theory that the conditional estimator attains the minimum mean squared error (MMSE) for estimating a scalar parameter of interest. In quantum, e.g., optical and atomic, imaging and sensing tasks the user has access to the quantum state that encodes the parameter. The choice of a measurement operator, i.e. a positive-operator valued measure (POVM), leads to a measurement outcome on which the aforesaid classical MMSE estimator is employed. Personick found the optimum POVM that attains the MMSE= over all possible physically allowable measurements and the resulting MMSE [1]. This result from 1971 is less-widely known than the quantum Fisher information (QFI), which lower bounds the variance of an unbiased estimator over all measurements without considering any prior probability. For multi-parameter estimation, in quantum Fisher estimation theory the inverse of the QFI matrix provides an operator lower bound on the covariance of an unbiased estimator, and this bound is understood in the positive semidefinite sense. However, there has been little work on quantifying the quantum limits and measurement designs, for multi-parameter quantum estimation in a Bayesian setting. In this work, we build upon Personick's result to construct a Bayesian adaptive (greedy) measurement scheme for multiparameter estimation. We illustrate our proposed measurement scheme with the application of localizing a cluster of point emitters in a highly sub-Rayleigh angular field-of-view, an important problem in fluorescence microscopy and astronomy. Our algorithm translates to a multi-spatial-mode transformation prior to a photon-detection array, with electro-optic feedback to adapt the mode sorter. We show that this receiver performs superior to quantum-noise-limited focal-plane direct imaging.

Field-dependent deep learning enables high-throughput whole-cell 3D super-resolution imaging.

Single-molecule localization microscopy in a typical wide-field setup has been widely used for investigating subcellular structures with super resolution; however, field-dependent aberrations restrict the field of view (FOV) to only tens of micrometers. Here, we present a deep-learning method for precise localization of spatially variant point emitters (FD-DeepLoc) over a large FOV covering the full chip of a modern sCMOS camera. Using a graphic processing unit-based vectorial point spread function (PSF) fitter, we can fast and accurately model the spatially variant PSF of a high numerical aperture objective in the entire FOV. Combined with deformable mirror-based optimal PSF engineering, we demonstrate high-accuracy three-dimensional single-molecule localization microscopy over a volume of ~180 × 180 × 5 μm3, allowing us to image mitochondria and nuclear pore complexes in entire cells in a single imaging cycle without hardware scanning; a 100-fold increase in throughput compared to the state of the art.

Three-dimensional wide-field fluorescence microscopy for transcranial mapping of cortical microcirculation

Wide-field fluorescence imaging is an indispensable tool for studying large-scale biodynamics. Limited space-bandwidth product and strong light diffusion make conventional implementations incapable of high-resolution mapping of fluorescence biodistribution in three dimensions. We introduce a volumetric wide-field fluorescence microscopy based on optical astigmatism combined with fluorescence source localization, covering 5.6×5.6×0.6 mm3 imaging volume. Two alternative configurations are proposed exploiting multifocal illumination or sparse localization of point emitters, which are herein seamlessly integrated in one system. We demonstrate real-time volumetric mapping of the murine cortical microcirculation at capillary resolution without employing cranial windows, thus simultaneously delivering quantitative perfusion information across both brain hemispheres. Morphological and functional changes of cerebral vascular networks are further investigated after an acute ischemic stroke, enabling cortex-wide observation of concurrent collateral recruitment events occurring on a sub-second scale. The reported technique thus offers a wealth of unmatched possibilities for non- or minimally invasive imaging of biodynamics across scales.

Super‐Resolution Near‐Infrared Fluorescence Microscopy of Single‐Walled Carbon Nanotubes Using Deep Learning

Single‐walled carbon nanotubes (SWCNTs) have unique optical and physical properties, with numerous biomedical imaging and sensing applications, owing to their near‐infrared (nIR) fluorescence which overlaps with the biological transparency window. However, their longer emission wavelengths compared to emitters in the visible range result in a lower resolution due to the diffraction limit. Moreover, the elongated high‐aspect‐ratio structure of SWCNTs poses an additional challenge on super‐resolution techniques that assume point emitters. Utilizing the advantages of deep learning and convolutional neural networks, along with the super‐resolution radial fluctuation (SRRF) algorithm for network training, a fast, parameter‐free, computational method is offered for enhancing the spatial resolution of nIR fluorescence images of SWCNTs. An average improvement of 22% in the resolution and 47% in signal‐to‐noise ratio (SNR) compared to the original images is shown, whereas SRRF leads to only 24% SNR improvement. The approach is demonstrated for a variety of SWCNT densities and length distributions, and a wide range of imaging conditions with challenging SNRs, including real‐time videos, without compromising the temporal resolution. The results open the path for accelerated and accessible super‐resolution of nIR fluorescent SWCNTs images, further advancing their applicability as nanoscale optical probes.

Gas-Discharge Point Source of UV Radiation Based on a Gas-Vapor Mixture of Argon and Copper

The characteristics of a pulse periodic source of a long-range UV radiation with overvoltage pumping by a bipolar discharge of nanosecond duration between copper electrodes in argon at atmospheric pressure are investigated. Copper vapors were introduced into the discharge due to the ectonic mechanism, in which a sufficient amount of the electrode material vapors is introduced into the discharge gap due to microexplosions of inhomogeneities of the surface of metal electrodes in a strong electric field of an overvoltage high-current nanosecond discharge. The characteristics of an overvoltage nanosecond discharge at a distance between the electrodes of 2 mm are studied. The emission spectra of the discharge were analysed, and the intensity of the UV radiation of a point emitter was optimized depending on the supply voltage of the high-voltage modulator and the repeti-tion rate of discharge pulses. The identification of the emission spectra of plasma made it possible to establish the main excited plasma products that form the spectrum of the UV radiation of the plas-ma. The study of the spectral characteristics of plasma based on gas-vapor mixtures "copper – ar-gon" showed that the most intense were the spectral resonance spectral lines of the copper atom and ion. It was found that a space-uniform overvoltage nanosecond discharge was ignited between copper electrodes at an inter-electrode distance of 2 mm. It was found that the maximum value of the average UV power at p(Ar) = 101 kPa was observed for the UV-A range.

Quantum limits to resolution and discrimination of spontaneous emission lifetimes

In this work we investigate the quantum information theoretical limits to several tasks related to lifetime estimation and discrimination of a two-level spontaneous optical emitter. We focus in particular on the model problem of resolving two mutually incoherent exponential decays with highly overlapping temporal probability profiles. Mirroring recent work on quantum-inspired super-resolution of point emitters, we find that direct lifetime measurement suffers from an analogue of "Rayleigh's Curse" when the time constants of the two decay channels approach one another. We propose alternative measurement schemes that circumvent this limit, and also demonstrate superiority to direct measurement for a related binary hypothesis test. Our findings add to a growing list of examples in which a quantum analysis uncovers significant information gains for certain tasks in opto-molecular metrology that do not rely on multiphoton interference, but evidently do benefit from a more thorough exploitation of the coherence properties of single photons.

Effect of Approximate Planar Wavefront on Far-Field Direction Finding

Existing sensor array direction-finding algorithms in the open literature simplify the far-field source wavefront as exactly planar in order to facilitate the algorithmic development. In fact, since the wavefront of a point emitter is necessarily spherical, this planar wavefront assumption should actually be approximate, especially for large-scale arrays. Mismatch between the actual and approximate propagation models would introduce a non-random bias on the performance of the direction-finding algorithms. This non-random bias is inevitable due to the mismatch between the algorithm’s presumptions and the data it actually processes. This work derives the mathematical expression of this non-random bias, along with several qualitative analyses. The analysis is carried out using the Taylor-series expansion. Also, the effect of the model mismatch on direction-finding algorithms is evaluated numerically.

Light sheet based volume flow cytometry (VFC) for rapid volume reconstruction and parameter estimation on the go

Optical imaging is paramount for disease diagnosis and to access its progression over time. The proposed optical flow imaging (VFC/iLIFE) is a powerful technique that adds new capabilities (3D volume visualization, organelle-level resolution, and multi-organelle screening) to the existing system. Unlike state-of-the-art point-illumination-based biomedical imaging techniques, the sheet-based VFC technique is capable of single-shot sectional visualization, high throughput interrogation, real-time parameter estimation, and instant volume reconstruction with organelle-level resolution of live specimens. The specimen flow system was realized on a multichannel (Y-type) microfluidic chip that enables visualization of organelle distribution in several cells in-parallel at a relatively high flow-rate (2000 nl/min). The calibration of VFC system requires the study of point emitters (fluorescent beads) at physiologically relevant flow-rates (500–2000 nl/min) for determining flow-induced optical aberration in the system point spread function (PSF). Subsequently, the recorded raw images and volumes were computationally deconvolved with flow-variant PSF to reconstruct the cell volume. High throughput investigation of the mitochondrial network in HeLa cancer cell was carried out at sub-cellular resolution in real-time and critical parameters (mitochondria count and size distribution, morphology, entropy, and cell strain statistics) were determined on-the-go. These parameters determine the physiological state of cells, and the changes over-time, revealing the metastatic progression of diseases. Overall, the developed VFC system enables real-time monitoring of sub-cellular organelle organization at a high-throughput with high-content capacity.

Exploring the hidden depth by confocal Raman experiments with variable objective aperture and magnification

The article analyzes experimentally and theoretically the influence of microscope parameters on the pinhole-assisted Raman depth profiles in uniform and composite refractive media. The main objective is the reliable mapping of deep sample regions. The easiest to interpret results are found with low magnification, low aperture, and small pinholes. Here, the intensities and shapes of the Raman signals are independent of the location of the emitter relative to the sample surface. Theoretically, the results can be well described with a simple analytical equation containing the axial depth resolution of the microscope and the position of the emitter. The lower determinable object size is limited to 2–4 μm. If sub-micrometer resolution is desired, high magnification, mostly combined with high aperture, becomes necessary. The signal intensities and shapes depend now in refractive media on the position relative to the sample surface. This aspect is investigated on a number of uniform and stacked polymer layers, 2–160 μm thick, with the best available transparency. The experimental depth profiles are numerically fitted with excellent accuracy by inserting a Gaussian excitation beam of variable waist and fill fraction through the focusing lens area, and by treating the Raman emission with geometric optics as spontaneous isotropic process through the lens and the variable pinhole, respectively. The intersectional area of these two solid angles yields the leading factor in understanding confocal (pinhole-assisted) Raman depth profiles.Graphical abstractSpearfishing is a well-known example of the effects of refraction at the boundary between two index-mismatched media. The object Greal is seen, due to refraction, as Gvir from the angle β (without knowing the depth position). The real position is obtained under the angle α. In a microscope (see inset), index mismatch deforms the image point of Greal into an image line. The pinhole substantially reduces deformations and allows the determination of the position of the point emitter G. (Cartoon designed by Sofia Anker)

Localization precision in chromatic multifocal imaging

Multifocal microscopy affords fast acquisition of microscopic 3D images. This is made possible using a multifocal grating optic; however, this induces chromatic dispersion effects in the point spread function, impacting image quality and single-molecule localization precision. To minimize this effect, researchers use narrow-band emission filters. However, the choice of optimal emission filter bandwidth in such systems is, thus far, unclear. This work presents a theoretical framework to investigate how the localization precision of a point emitter is affected by the emission filter bandwidth. We calculate the Cramér–Rao lower bound for the 3D position of a single emitter imaged using a chromatic multifocal microscope. Simulation results for a range of emission bandwidth systems show that in the absence of background photons and detector noise localization improves for broader emission filter bandwidth due to increased photon throughput despite a larger chromatic dispersion. When realistic background and measurement noise sources are considered in the imaging process being simulated, there is an optimal bandwidth (not the broadest emission filter bandwidth) which provides the highest localization precision. This study provides a framework for optimally designing chromatic multifocal optics and serves as a theoretical foundation for interpretting results.

Localization of Nonblinking Point Sources Using Higher-Order-Mode Detection and Optical Heterodyning: Developing a Strategy for Extending the Scope of Molecular, Super-resolution Imaging.

While the stochastic, "blinking" nature of fluorescent systems has enabled the super-resolution of their localization by the fitting of their point-spread functions (PSFs), this strategy cannot be exploited for similar resolution of "nonblinking" systems, such as those that might be encountered in a coherent Raman experiment. An alternative method for subdiffraction-limited imaging lies in the exploitation of optical heterodyning. For example, if a Gaussian PSF (a TEM00 mode) of a point emitter is displaced with respect to the origin of the optical system, photons in the higher-order TEM modes carry information about that displacement. Information concerning the displacement can be extracted from photons in these higher-order modes. These photons can be collected by optical heterodyning, which exploits the large gain in a detector's response to an optical signal from an emitter coupled to a local oscillator, which is prepared in the TEM of interest, e.g., TEM10. We have generalized and developed the heterodyning technique to localize point emitters via the detection of higher-order spatial modes. We have developed a theoretical approach to find a practical estimation limit of the localization parameters using a realistic model that accounts for shot noise, background noise, and Gaussian noise. To demonstrate the applicability of the method, we designed experiments in which a laser is a surrogate for one and two point emitters. Using the Fisher information and its accompanying Cramér-Rao lower bound, we demonstrate super-resolution localization in these cases: we show that objects can be localized to roughly 2-3 orders of magnitude of their point-spread function's size for a given optical system. Finally and most importantly, it is suggested that the results will ultimately be generalizable to multiple emitters and, most importantly, to "nonblinking" molecular systems, which will be essential for broadening the scope of super-resolution measurements beyond the limits of fluorescence-based techniques.

Elementary Emitter at the Boundary of a Flat-Layered Structure

A rigorous theory of emission of an elementary dipole located at the boundary of or within a flat-layered structure has been considered. A method of analytic simplification of the solution has been demonstrated for a particular case of emission of a dipole located on the free boundary of a single film. The proposed method has made it possible to reduce expressions for emitted fields to 1D integrals, which has considerably simplified analysis of the problem and reduced the computation time. As a concrete technical application of the theory, the radiation patterns have been obtained for point emitters (molecules, nanostructures) located on the free surface of a metal film in the Kretschmann configuration, possessing the induced dipole moment directed along the normal to the film surface. The effect of a surface wave on the directional properties of surface emitters has been considered.

Декомпозиционная оптико-механическая модель светодиодного излучающего элемента

Light-emitting diodes are ahead of traditional light sources in terms of luminous efficacy (luminous flux per unit of electrical power consumption), which arouses an increased interest in the developers of LED lamps in the standard size of incandescent lamps. When designing LED lamps for direct replacement of incandescent lamps, it is necessary to ensure a spherical light distribution in these lighting devices. The design of the lamp with filamentary LED emitting elements is recognized as the best in terms of uniformity of the spatial distribution of light. In this work, a decomposition model of an LED emitting element has been developed, which is created on the basis of the parameters of an optical-mechanical model of LED emitting crystals, and includes the following sequentially performed actions: – construction of a geometric model of the LED emitting element; – determination of the properties of the surface source of the LED emitting element and the angular distribution of radiation of the LED emitting element model as a point emitter; – development of a primary model of an LED crystal with subsequent adjustment of its parameters; – verification of the decomposition model by comparison with the experimentally measured parameters of the LED emitting element. An assessment of the quality of the LED emitting element model as a point emitter was carried out; for this, the averaged measured and modeled LIDCs were superimposed at the same azimuthal angles on top of each other. The discrepancies between the calculated and experimental data do not exceed 10%, which confirms a high accuracy of the LED emitting element model as a point emitter. The resulting file is the properties of the surface source and the value of the luminous flux of the LED emitting element, equal to FW = 254 mW. The model is characterized by increased versatility and can be used for LED emitting elements with an arbitrary configuration of LED crystals and LED lamps based on them.

Efficient Integration of Single-Photon Emitters in Thin InSe Films into Resonance Silicon Waveguides

A concept of the optimal design of a silicon waveguide based on optically coupled Mie-resonant nanoantennas for efficient inputting of light from point emitters associated with excitons localized at defects in a thin InSe film is proposed. Numerical calculations demonstrate that the efficiency of coupling between a dipole emitter and a resonant silicon waveguide is four orders of magnitude greater than that for a conventional ridge waveguide.

An Elementary Dipole Emitter Located Either on the Boundary of a Layered Structure or Inside It

A rigorous theory of radiation of an elementary dipole that is located either on the boundary of a plane-layered structure or inside it is considered. For a particular case of radiation from a dipole located on a free boundary of one film, a method of analytical simplification of the solution is demonstrated. This method has made it possible to reduce the formulas for emitted fields to one-dimensional integrals, which greatly simplified the analysis of the problem and speeded up numerical calculations. As a specific technical application of the theory, directional patterns of point emitters (molecules, nanostructures) located on the free surface of a metal film in the Kretschmann scheme and having an induced dipole moment along the film surface have been obtained. The influence of the surface wave on the directional properties of emitters has been determined.