Point Spread Function Of Microscope Research Articles

Three-dimensional point spread function estimation method for mid-wave infrared microscope imaging.

A three-dimensional point spread function experimental estimation method based on the system's focal plane array spatial local impulse response of a mid-wave infrared microscope is presented. The method uses several out-of-focus two-dimensional point spread function planes to achieve a single three-dimensional point spread function of the whole microscope's optical spreading, expanding the limits of infrared optical technology by one dimension. This technique includes stages of image acquisition, nonuniformity correction, filtering, and multi-planar reconstruction steps, and its effectiveness is demonstrated on biological sample image restoration by means of a multi-planar refocusing application.

Computational framework for single-cell spatiotemporal dynamics of optogenetic membrane recruitment

SummaryWe describe a modular computational framework for analyzing cell-wide spatiotemporal signaling dynamics in single-cell microscopy experiments that accounts for the experiment-specific geometric and diffractive complexities that arise from heterogeneous cell morphologies and optical instrumentation. Inputs are unique cell geometries and protein concentrations derived from confocal stacks and spatiotemporally varying environmental stimuli. After simulating the system with a model of choice, the output is convolved with the microscope point-spread function for direct comparison with the observable image. We experimentally validate this approach in single cells with BcLOV4, an optogenetic membrane recruitment system for versatile control over cell signaling, using a three-dimensional non-linear finite element model with all parameters experimentally derived. The simulations recapitulate observed subcellular and cell-to-cell variability in BcLOV4 signaling, allowing for inter-experimental differences of cellular and instrumentation origins to be elucidated and resolved for improved interpretive robustness. This single-cell approach will enhance optogenetics and spatiotemporally resolved signaling studies.

Image Reconstruction in Light-Sheet Microscopy: Spatially Varying Deconvolution and Mixed Noise

We study the problem of deconvolution for light-sheet microscopy, where the data is corrupted by spatially varying blur and a combination of Poisson and Gaussian noise. The spatial variation of the point spread function of a light-sheet microscope is determined by the interaction between the excitation sheet and the detection objective PSF. We introduce a model of the image formation process that incorporates this interaction and we formulate a variational model that accounts for the combination of Poisson and Gaussian noise through a data fidelity term consisting of the infimal convolution of the single noise fidelities, first introduced in L. Calatroni et al. (SIAM J Imaging Sci 10(3):1196–1233, 2017). We establish convergence rates and a discrepancy principle for the infimal convolution fidelity and the inverse problem is solved by applying the primal–dual hybrid gradient (PDHG) algorithm in a novel way. Numerical experiments performed on simulated and real data show superior reconstruction results in comparison with other methods.

Analyses on cytoskeleton structure basing on confocalmicroscope

Actin microfilaments are the main components of cytoskeleton. Some previous studies have shown that the state of cell adhesion regulates the biological behavior of stem cells such as differentiation and apoptosis by affecting the structure of microfilaments. The primary method of observing the structure of microfilaments is using laser confocal microscopy to obtain fluorescence images of microfilament, but usually only the two-dimensional structure of microfilaments was analyzed, and few studies have focused on the three-dimensional structure of microfilaments. In this paper, we proposed a three-dimensional reconstruction method of microfilaments based on laser confocal microscopy. The point spread function of a confocal microscope was fitted by three-dimensional Gaussian function, and then we got the Gaussian distribution of the z -axis light intensity by decoupling the x - y direction with the z direction of the function. Subsequently, the geometric parameters of the major fibers in a cell were obtained through image processing methods, and then the three-dimensional geometric information of the microfilament was extracted by using fitting calculation, density clustering, ellipsoid fitting and other operations to deal with filament images. In addition, we constructed circular and branch-shaped micropatterned substrates with an area of 1256 μm2, and we adopted the three-dimensional reconstruction method established in this study to reconstruct and analyze the microfilaments of bone marrow mesenchymal stem cells, which were cultured on the micropatterned substrates. The results showed that the spatial distribution of geometric parameters such as the orientation of the microfilaments, the number of intersection, the volume, and the aspect ratio for the cells with two shapes were significantly different, indicating that the mechanical state of the cells was influenced by the spreading shape. The purpose of this study is to establish a method for extracting the three-dimensional structural parameters of microfilaments, which can provide a basis for revealing the mechanism of mechanotransduction inside cells.

An Approach to Measuring the Point Spread Function of the Confocal Raman Microscope.

The confocal Raman microscope (CRM) is a powerful tool in analytical science. Image quality is the most important performance indicator of CRM systems. The point spread function (PSF) is one of the most useful tools to evaluate the image quality of microscopic systems. A method based on a point-like object is proposed to measure the PSF of CRM, and the size effect of spherical objects is discussed. A series of phantoms are fabricated by embedding different sizes of polystyrene microspheres into polydimethylsiloxane matrix. The diameters of microspheres are from 0.2 µm to 5 µm. The phantoms are tested by measuring the PSF of a commercial CRM whose nominal lateral resolution is about 1 µm. Results of the PSF are obtained and the accuracy of resolution is used to evaluate the size effect of the microspheres. Experimental results are well consistent with theoretical analysis. The error of the PSF can be decreased by reducing the diameter of the microsphere but meanwhile the signal-to-noise ratio (S/N) will be lowered as well. The proper diameter of microspheres is proposed in consideration of the trade-off between the S/N and the measurement error of the PSF. Results indicate that the method provides a useful approach to measurement of the PSF and the resolution of the CRM.

Multiplanar full-field blur correction method for infrared microscopy imaging.

We propose a 3D full-field focusing method for microscopic mid-wave infrared (MWIR) imagery. The method is based on the experimental estimation of a confined volumetric vision microscope point spread function. The technique employs our well-known constant-range-based nonuniformity correction algorithm as a preprocessing step and then an iteration in the z-axis Fourier-based deconvolution. The technique's ability to compensate for localized blur is demonstrated using two different real MWIR microscopic video sequences, captured from two microscopic living organisms using a Janos-Sofradir MWIR microscopy setup. The performance of the proposed algorithm is assessed on real and simulated noisy infrared data by computing the root-mean-square error and the roughness Laplacian pattern indexes, which are specifically developed for the present work.

Estimation of point spread function of an optical microscope using stochastic minimization of least square errors

In this paper we propose a point spread function (PSF) estimation scheme for an optical microscope. The scheme is based on minimizing the least square error between the image of an arbitrary target and the convolution of a stochastically constructed PSF array with the geometrical-optics predicted image of the target. The proposed scheme is independent of the geometry of the imaging system and will work in any type of optical microscopes. The scheme enables PSF estimation without requiring any modification of the microscope setup. We have demonstrated the proposed scheme both numerically and experimentally.

Restoration of Out-of-Focus Fluorescence Microscopy Images Using Learning-Based Depth-Variant Deconvolution

Image quality is degraded in the out-of-focus region because of the depth-variant (DV) point spread function (DV-PSF) of a fluorescence microscope. Either non-blind or blind deconvolution for restoration results in limited improvement. In this work, we propose a two-step learning-based DV deconvolution (LB-DVD) to restore the out-of-focus image. In the first step, DV-PSF is predicted by a defocus level prediction convolutional neural network (DelpNet). In the second step, the extracted DV-PSF is used for DV deconvolution. To our knowledge, LB-DVD is proposed and demonstrated for the first time. DelpNet achieves an accuracy of 98.2% for predicting defocus levels of image patches ( $84 \times 84$ pixels). The subsequent DV deconvolution gives rise to good performance in peak signal-to-noise ratios and structural similarity index, which are improved by up to 6.6 dB and 11%, respectively, before and after the deconvolution. As for a wide-field image, there exist different DV-PSFs within the two-dimensional fluorescence image due to the surface undulation. An overlapping weighting patch-wise LB-DVD is used in image montage to eliminate patch boundary artifacts. As a result, our LB-DVD shows the feasibility and promise to be applied to typical fluorescence microscopy in practical applications.

DeconvTest: Simulation framework for quantifying errors and selecting optimal parameters of image deconvolution.

Deconvolution is an essential step of image processing that aims to compensate for the image blur caused by the microscope's point spread function. With many existing deconvolution methods, it is challenging to choose the method and its parameters most appropriate for particular image data at hand. To facilitate this task, we developed DeconvTest: an open-source Python-based framework for generating synthetic microscopy images, deconvolving them with different algorithms, and quantifying reconstruction errors. In contrast to existing software, DeconvTest combines all components required to analyze deconvolution performance in a systematic, high-throughput and quantitative manner. We demonstrate the power of the framework by using it to identify the optimal deconvolution settings for synthetic and real image data. Based on this, we provide a guideline for (a) choosing optimal values of deconvolution parameters for image data at hand and (b) optimizing imaging conditions for best results in combination with subsequent image deconvolution.

Exploring the Parameter Space of Point Spread Function Determination for the Scanning Electron Microscope—Part I: Effect on the Point Spread Function

The point spread function (PSF) of the scanning electron microscope (SEM) can be determined using a recently developed nanoparticle calibration method. Many parameters are involved in PSF determination and introduce a previously unstudied amount of uncertainty into the PSF size and shape. Signal type, support material thickness, reference particle size, PSF smoothing (K), and background correction were investigated regarding their effect on the PSF. Experimental data were complemented by CASINO simulations. Differences in detector position between the observed particles and the method's simulated reference particles caused shifting between secondary electron PSFs and backscattered electron PSFs. Support material thickness did not have a practical effect on the PSF at the tested voltages. Uncertainty in reference particle size varied the PSF full width at half maximum (FWHM) within ±0.7 nm at 2σ, with virtually no uncertainty in some cases. K and background correction within a reasonable range of values resulted in PSF FWHM differences within ±0.9 nm, except at 2 kV for K with an upper bound of ±1.9 nm due to increased noise. Tailoring K and background correction case-by-case would result in smaller differences. The interconnection of these parameters may help in future efforts to calculate their best selection.

Design and simulation of a snapshot multi-focal interferometric microscope.

Realizing both high temporal and spatial resolution across a large volume is a key challenge for 3D fluorescent imaging. Towards achieving this objective, we introduce an interferometric multifocus microscopy (iMFM) system, a combination of multifocus microscopy (MFM) with two opposing objective lenses. We show that the proposed iMFM is capable of simultaneously producing multiple focal plane interferometry that provides axial super-resolution and hence isotropic 3D resolution with a single exposure. We design and simulate the iMFM microscope by employing two special diffractive optical elements. The point spread function of this new iMFM microscope is simulated and the image formation model is given. For reconstruction, we use the Richardson-Lucy deconvolution algorithm with total variation regularization for 3D extended object recovery, and a maximum likelihood estimator (MLE) for single molecule tracking. A method for determining an initial axial position of the molecule is also proposed to improve the convergence of the MLE. We demonstrate both theoretically and numerically that isotropic 3D nanoscopic localization accuracy is achievable with an axial imaging range of 2um when tracking a fluorescent molecule in three dimensions and that the diffraction limited axial resolution can be improved by 3-4 times in the single shot wide-field 3D extended object recovery. We believe that iMFM will be a useful tool in 3D dynamic event imaging that requires both high temporal and spatial resolution.

Self-interference 3D super-resolution microscopy for deep tissue investigations.

Fluorescence localization microscopy has achieved near-molecular resolution capable of revealing ultra-structures, with a broad range of applications, especially in cellular biology. However, it remains challenging to attain such resolution in three dimensions and inside biological tissues beyond the first cell layer. Here we introduce SELFI, a framework for 3D single-molecule localization within multicellular specimens and tissues. The approach relies on self-interference generated within the microscope's point spread function (PSF) to simultaneously encode equiphase and intensity fluorescence signals, which together provide the 3D position of an emitter. We combined SELFI with conventional localization microscopy to visualize F-actin 3D filament networks and reveal the spatial distribution of the transcription factor OCT4 in human induced pluripotent stem cells at depths up to 50 µm inside uncleared tissue spheroids. SELFI paves the way to nanoscale investigations of native cellular processes in intact tissues.

Bayesian deconvolution of scanning electron microscopy images using point-spread function estimation and non-local regularization.

Microscopy is one of the most essential imaging techniques in life sciences. High-quality images are required in order to solve (potentially life-saving) biomedical research problems. Many microscopy techniques do not achieve sufficient resolution for these purposes, being limited by physical diffraction and hardware deficiencies. Electron microscopy addresses optical diffraction by measuring emitted or transmitted electrons instead of photons, yielding nanometer resolution. Despite pushing back the diffraction limit, blur should still be taken into account because of practical hardware imperfections and remaining electron diffraction. Deconvolution algorithms can remove some of the blur in post-processing but they depend on knowledge of the point-spread function (PSF) and should accurately regularize noise. Any errors in the estimated PSF or noise model will reduce their effectiveness. This paper proposes a new procedure to estimate the lateral component of the point spread function of a 3D scanning electron microscope more accurately. We also propose a Bayesian maximum a posteriori deconvolution algorithm with a non-local image prior which employs this PSF estimate and previously developed noise statistics. We demonstrate visual quality improvements and show that applying our method improves the quality of subsequent segmentation steps.

3D Single-Molecule Super-Resolution Fluorescence Microscopy with the Corkscrew Point Spread Function

The Moerner Laboratory has been engineering the point spread function (PSF) of a wide-field fluorescence microscope in order to obtain simultaneous X, Y, and Z spatial information from single molecules over a large Z-range. The new PSFs (e.g., the double-helix, tetrapod, and corkscrew PSFs) change their shapes or positions as the single-molecule emitter moves along the optical (Z) axis—thus conveying rich information about the Z position of the molecule. These approaches are relevant both for tracking individual biomolecules at low concentration as well as reconstructing super-resolution images by single-molecule localization microscopy. The corkscrew PSF is special because it behaves like a single Gaussian spot of light that moves along a U-shaped path as the emitter moves along the optical axis. Hence, the corkscrew PSF occupies less space on the camera as compared to our other 3D PSFs and allows us to image a sample more quickly at a higher density of localizations per camera frame.In this work, we use the corkscrew PSF to image a rectilinear array of nanoholes filled with fluorescent molecules to calibrate the three-dimensional response of our microscope. This involves mapping the 3D object space of molecules within a sample to the 2D image space on our camera. By sampling the microscope's response throughout the field of view, we account for field-dependent aberrations that would otherwise cause errors in the position measurements of single molecules. Recent progress in imaging biomolecules with the corkscrew PSF will be summarized.

Rapid Measurement of Molecular Transport and Interaction Inside Living Cells with Single Plane Illumination Microscopy

Fundamental physiological processes within cells and tissues including cell adhesion, signaling, movement, division or metabolism are based on the transport and interaction of biomolecules. Biomolecular dynamics is usually measured by applying single particle tracking (SPT) analysis to camera images or by using fluorescence fluctuation spectroscopy (FFS) methods based on single point detection. We show that image mean square displacement (iMSD) analysis, applied to single plane illumination microscopy (SPIM) data, is a faster and more efficient way of unravelling rapid, three-dimensional molecular transport and interaction within solutions and in living cells. From a stack of camera images recorded in a few seconds only, the type of dynamics such as free diffusion, flow or binding can be identified and quantified without suffering from the limitation of current camera frame rates. Also, the SPIM-iMSD method does not require calibration of the microscope point spread function (PSF) and light exposure levels are very low. We quantified the dynamics of several different proteins in the cyto- and nucleoplasm of living cells to demonstrate the advantages of our approach. As an example, from a single measurement, we were able to determine the diffusion coefficient of free clathrin molecules as well as the transport velocity of clathrin-coated vesicles involved in endocytosis. Used in conjunction with dual view detection, we further show how protein-protein interactions can be quantified. Work supported in part by NIH grants P50 GM076516 and P41 GM103540.

Rapid measurement of molecular transport and interaction inside living cells using single plane illumination.

The ability to measure biomolecular dynamics within cells and tissues is very important to understand fundamental physiological processes including cell adhesion, signalling, movement, division or metabolism. Usually, such information is obtained using particle tracking methods or single point fluctuation spectroscopy. We show that image mean square displacement analysis, applied to single plane illumination microscopy data, is a faster and more efficient way of unravelling rapid, three-dimensional molecular transport and interaction within living cells. From a stack of camera images recorded in seconds, the type of dynamics such as free diffusion, flow or binding can be identified and quantified without being limited by current camera frame rates. Also, light exposure levels are very low and the image mean square displacement method does not require calibration of the microscope point spread function. To demonstrate the advantages of our approach, we quantified the dynamics of several different proteins in the cyto- and nucleoplasm of living cells. For example, from a single measurement, we were able to determine the diffusion coefficient of free clathrin molecules as well as the transport velocity of clathrin-coated vesicles involved in endocytosis. Used in conjunction with dual view detection, we further show how protein-protein interactions can be quantified.

Microscope point spread function, focus and calculation of optimal microscope set-up

If we are observing very small objects in the microscope the information appears somehow distorted. This distortion is called point spread function (PSF) and it can be measured and simulated as we show in this article. Many experiments and simulations were done in the field of confocal or deconvolution microscopy, but we want to present 3D reconstruction and measurement of PSF in the bright field (or phase contrast) microscopy. Our goal is to use this knowledge about PSF to estimate objective focus. We want to use this method for automatic focusing of the microscope. We measured the PSF on our microscope in bright field using a 100×objective. We used 15 nm gold and 200 nm latex particles as point sources. We used two different simulations; first one was Airy disc simulation; the second one was Extended Nijboer–Zernike theory. Both approaches were used for description of PSF and finding the position of the focus.

Correcting spherical aberrations in confocal light sheet microscopy: A theoretical study

In the last years, fluorescence light sheet microscopy has attracted an increasing interest among the microscopy community. One of the most promising applications of this technique is the reconstruction of macroscopic biological specimens with microscopic resolution, without physical sectioning. To this aim, light sheet microscopy is combined with clearing protocols based on refractive index matching, which render the tissue transparent. However, these protocols lead to a huge drop in the fluorescence signal, limiting their practical applicability. The reduction of signal to background ratio is commonly ascribed to chemical degradation of the fluorophores by the organic solvents used for clearing. This view however completely neglects another important factor of contrast loss, i.e., optical aberrations. In fact, commercially available objectives suitable for light sheet microscopy are not designed for the refractive index of the clearing solutions, and this mismatch introduces severe spherical aberration. Here we simulated the aberrated point spread function (PSF) of a light sheet microscope with confocal slit detection. We investigated the variation of the PSF as a function of objective numerical aperture (NA) and of imaging depth inside the clearing solution. We also explored the possibility of correcting such spherical aberration by introducing extra optical devices in the detection path. By correcting up to the second order spherical aberration, a quasi-diffraction-limited regime can be recovered, and image quality is restored.

Three dimensional single molecule localization using a phase retrieved pupil function

Localization-based superresolution imaging is dependent on finding the positions of individual fluorophores in a sample by fitting the observed single-molecule intensity pattern to the microscope point spread function (PSF). For three-dimensional imaging, system-specific aberrations of the optical system can lead to inaccurate localizations when the PSF model does not account for these aberrations. Here we describe the use of phase-retrieved pupil functions to generate a more accurate PSF and therefore more accurate 3D localizations. The complex-valued pupil function contains information about the system-specific aberrations and can thus be used to generate the PSF for arbitrary defocus. Further, it can be modified to include depth dependent aberrations. We describe the phase retrieval process, the method for including depth dependent aberrations, and a fast fitting algorithm using graphics processing units. The superior localization accuracy of the pupil function generated PSF is demonstrated with dual focal plane 3D superresolution imaging of biological structures.

Extraction of Sub-microscopic Ca Fluxes from Blurred and Noisy Fluorescent Indicator Images with a Detailed Model Fitting Approach

The release of Ca from intracellular stores is key to cardiac muscle function; however, the molecular control of intracellular Ca release remains unclear. Depletion of the intracellular Ca store (sarcoplasmic reticulum, SR) may play an important role, but the ability to measure local SR Ca with fluorescent Ca indicators is limited by the microscope optical resolution and properties of the indicator. This leads to an uncertain degree of spatio-temporal blurring, which is not easily corrected (by deconvolution methods) due to the low signal-to-noise ratio of the recorded signals. In this study, a 3D computer model was constructed to calculate local Ca fluxes and consequent dye signals, which were then blurred by a measured microscope point spread function. Parameter fitting was employed to adjust a release basis function until the model output fitted recorded (2D) Ca spark data. This ‘forward method’ allowed us to obtain estimates of the time-course of Ca release flux and depletion within the sub-microscopic local SR associated with a number of Ca sparks. While variability in focal position relative to Ca spark sites causes more out-of-focus events to have smaller calculated fluxes (and less SR depletion), the average SR depletion was to 20±10% (s.d.) of the resting level. This focus problem implies that the actual SR depletion is likely to be larger and the five largest depletions analyzed were to 8±6% of the resting level. This profound depletion limits SR release flux during a Ca spark, which peaked at 8±3 pA and declined with a half time of 7±2 ms. By comparison, RyR open probability declined more slowly, suggesting release termination is dominated by neither SR Ca depletion nor intrinsic RyR gating, but results from an interaction of these processes.