Shape Of Point Spread Function Research Articles

Interactive simulation and visualization of point spread functions in single molecule imaging

The point spread function (PSF) is fundamental to any type of microscopy, most importantly so for single-molecule localization techniques, where the exact PSF shape is crucial for precise molecule localization at the nanoscale. Optical aberrations and fixed fluorophore dipoles often result in non-isotropic and distorted PSFs, impairing and biasing conventional fitting approaches. Further, PSF shapes are deliberately modified in PSF engineering approaches for providing improved sensitivity, e.g., for 3D localization or determination of dipole orientation. As this can lead to highly complex PSF shapes, a tool for visualizing expected PSFs would facilitate the interpretation of obtained data and the design of experimental approaches. To this end, we introduce a comprehensive and accessible computer application that allows for the simulation of realistic PSFs based on the full vectorial PSF model. Our tool incorporates a wide range of microscope and fluorophore parameters, including orientationally constrained fluorophores, as well as custom aberrations, transmission and phase masks, thus enabling an accurate representation of various imaging conditions. An additional feature is the simulation of crowded molecular environments with overlapping PSFs. Further, our app directly provides the Cramér–Rao bound for assessing the best achievable localization precision under given conditions. Finally, our software allows for the fitting of custom aberrations directly from experimental data, as well as the generation of a large dataset with randomized simulation parameters, effectively bridging the gap between simulated and experimental scenarios, and enhancing experimental design and result validation.

HybPSF: Hybrid Point-spread Function Reconstruction for the Observed JWST NIRCam Image

The James Webb Space Telescope (JWST) marks a new era of astronomical observation and discovery, providing unrivaled precision in various measurements, including photometry, morphology, and shear measurement. Accurate point-spread function (PSF) models are essential for many of these measurements. In this paper, we introduce HybPSF, a hybrid PSF construction method for JWST NIRCam imaging data that combines the WebbPSF software, which simulates the PSF for JWST, with observed data to produce more accurate and reliable PSF models. We apply this method to the SMACS J0723 imaging data and construct supplementary structures from residuals obtained by subtracting the WebbPSF PSF model from the data. Our results show that HybPSF significantly reduces discrepancies between the PSF model and the data compared to WebbPSF. Specifically, the PSF shape parameter ellipticity and size comparisons indicate that HybPSF improves precision by approximately 10 times for R 2 and 50% for e. This improvement has important implications for astronomical measurements using JWST NIRCam imaging data.

Enhancing obSTORM imaging performance with cubic spline PSF modeling.

Oblique plane microscopy-based single molecule localization microscopy (obSTORM) has shown great potential for super-resolution imaging of thick biological specimens. Despite its compatibility with tissues and small animals, prior uses of the Gaussian point spread function (PSF) model have resulted in limited imaging resolution and a narrow axial localization range. This is due to the poor fit of the Gaussian PSF model with the actual PSF shapes in obSTORM. To overcome these limitations, we have employed cubic splines for a more accurate modeling of the experimental PSF shapes. This refined PSF model enhances three-dimensional localization precision, leading to significant improvements in obSTORM imaging of mouse retina tissues, such as an approximately 1.2 times increase in imaging resolution, seamless stitching of single molecules between adjacent optical sections, and a doubling of the sectional interval in volumetric obSTORM imaging due to the extended axial range of usable section thickness. The cubic spline PSF model thus offers a path towards more accurate and faster volumetric obSTORM imaging of biological specimens.

Simultaneous single particle tracking, phase retrieval and PSF reconstruction.

3D particle tracking and localization provide direct means to monitor biomolecular processes within nano-scale environments. However, optical aberrations due to inhomogeneous refractive indices are a major shortcoming in probing these processes in situ. In particular, point spread functions (PSF) may be distorted resulting in poor localization and linking across frames. This issue is particularly important when using pre-calibrated PSFs that do not take into account sample induced aberrations. The sample induced aberrations are often removed using experimental techniques such as adaptive optics (AO) by introducing new optical components to microscope setups. Here, we propose a computational method, leveraging a Bayesian framework, as an alternative to the AO techniques. Our Bayesian method is capable of simultaneous particle tracking, phase retrieval and PSF reconstruction directly from a given data set, without adding any new hardware to the optical setup. Moreover, our method is data efficient by rigorously propagating uncertainty from all existing sources in the problem, such as the uncertainty in the shape of PSF, often ignored. We benchmark our method using a wide range of synthetic and experimental data.

SPHERE adaptive optics performance for faint targets

Context. High-contrast imaging is a powerful technique for detecting and characterizing planetary companions at orbital separations ≳100 mas from their parent stars. Aims. We aim to study the limiting magnitude of the VLT/SPHERE adaptive optics (AO) system and the corresponding instrument performance for faint targets (G ≥ 11.0 mag). Methods. We computed the coronagraphic H-band raw contrast and the full width at half maximum (FWHM) of the non-coronagraphic point spread function (PSF), for a total of 111 different stars observed between 2016 and 2022 with IRDIS. For this, we processed a large number of individual frames that were obtained under different atmospheric conditions. We then compared the resulting raw contrast and the PSF shape as a function of the visible wave front sensor (WFS) instant flux, which scales with the G-band stellar magnitude. We repeated this analysis for the top 10% (TCAT10) and top 30% (TCAT38) best turbulence conditions on Cerro Paranal. Results. We found a strong decrease in the coronagraphic contrast for stars fainter than G ∼ 12.5 mag, even under the best atmospheric conditions. In this regime, the AO correction is dominated by the read-out noise of the WFS detector. In particular we found roughly a factor of 10 decrease in the raw contrast ratio between stars with G ∼ 12.5 and G ∼ 14.0 mag. Similarly, we observed a sharp increase in the FWHM of the non-coronagraphic PSF beyond G ∼ 12.5 mag, and a corresponding decrease in the strehl ratio from ∼0.5 to ∼0.2 for the faintest stars. The decrease in the contrast ratio and PSF sharpness is slightly more pronounced for TCAT38 than for TCAT18.

HoloTile: Rapid and speckle-suppressed digital holography by matched sub-hologram tiling and point spread function shaping

In this work, a novel approach to rapid and speckle-reduced hologram generation is presented as HoloTile. HoloTile utilizes an analytic approach for Gaussian beam shaping to modify the Point Spread Function (PSF) of the holographic system into flat-top squares, such as to prevent interference between adjacent random phase values in the reconstruction plane. The PSF shape is determined by the inter-spectral spacing in the reconstruction plane that occurs due to tiling on the spatial light modulator. As such, the final hologram is the product of a once-calculated PSF shaping phase hologram and the tiled object holograms. HoloTile achieves speckle-reduced reconstructions and extremely fast hologram generation, due to the resolution of the object holograms.

Impact of point spread function higher moments error on weak gravitational lensing

ABSTRACT Weak gravitational lensing is one of the most powerful tools for cosmology, while subject to challenges in quantifying subtle systematic biases. The point spread function (PSF) can cause biases in weak lensing shear inference when the PSF model does not match the true PSF that is convolved with the galaxy light profile. Although the effect of PSF size and shape errors – i.e. errors in second moments – is well studied, weak lensing systematics associated with errors in higher moments of the PSF model require further investigation. The goal of our study is to estimate their potential impact for LSST weak lensing analysis. We go beyond second moments of the PSF by using image simulations to relate multiplicative bias in shear to errors in the higher moments of the PSF model. We find that the current level of errors in higher moments of the PSF model in data from the Hyper Suprime-Cam survey can induce a ∼0.05 per cent shear bias, making this effect unimportant for ongoing surveys but relevant at the precision of upcoming surveys such as LSST.

Linearized Field Deblending: Point-spread Function Photometry for Impatient Astronomers

Abstract NASA’s Kepler, K2, and TESS missions employ simple aperture photometry to derive time-series photometry, where an aperture is estimated for each star, and pixels containing each star are summed to create a single light curve. This method is simple, but in crowded fields, the derived time series can be highly contaminated. The alternate method of fitting a point-spread function (PSF) to the data is able to account for crowding but is computationally expensive. In this paper, we present a new approach to extracting photometry from these time-series missions that fits the PSF directly but makes simplifying assumptions in order to greatly reduce the computation expense. Our method fixes the scene of the field in each image, estimates the PSF shape of the instrument with a linear model, and allows only source flux and position to vary. We demonstrate that our method is able to separate the photometry from blended targets in the Kepler data set that are separated by less than a pixel. Our method is fast to compute and fully accounts for uncertainties from degeneracies due to crowded fields. We name the method described in this work linearized field deblending photometry. We demonstrate our method on the false-positive Kepler target KOI-608. We are able to separate the photometry of the two sources in the data and demonstrate that the contaminating transiting signal is consistent with a small, substellar companion with a radius of 2.67 R Jup (0.27 R ☉). Our method is equally applicable to extracting photometry from NASA’s TESS mission.

The point spread function reconstruction – II. The smooth PCA

ABSTRACT Accurate shear measurement is a key topic in weak lensing community. Point spread function (PSF), which smears the observed galaxy image, plays one of the main roles in the systematic errors in shear measurement and must be treated carefully to avoid bias and errors in cosmological parameters. In this paper, we present new PSF measurement methods, Smooth-PCA (SPCA) and Improved-SPCA (iSPCA), which can reconstruct smooth PSFs with high efficiency. Our methods decompose the star images into smooth principal components by using the Expectation-Maximization-PCA (EMPCA) method, and the smooth principal components are composed by Moffatlets basis functions, which are derived from the Moffat function. We demonstrate our approaches based on simulated Moffat PSFs and phosim star images. The constructed smooth principal components show flexible and efficient as the same as EMPCA, and have more stable patterns than EMPCA under noises contamination. We then check the reconstruction accuracy on the shape of PSFs. We find that our methods are able to reconstruct the PSFs at the same precision as the EMPCA method that indicates and iSPCA are promising for weak lensing shear measurement.

Measurement Extraction of Two Targets With Unequal and Unknown Intensities in an FPA

This article extends previous work on location and intensity estimation for measurement extraction of targets in a focal plane array. Prior work has been done to extract single targets and two targets of equal intensity, whereas this work explores the case where two targets have unequal and unknown intensities. Here, we assume a Gaussian point spread function (PSF) with spread $\sigma _{\text{PSF}}$ , but our approach could be applied to other PSF shapes. We present a maximum likelihood (ML) method for target extraction under resolved and unresolved assumptions. In the unresolved case, we estimate the parameters of a single target that represents the centroid of the two unresolved targets. We also present the Cramer–Rao lower bound (CRLB) of the estimation variances for both cases. Our simulation results show that resolved targets have their parameter vectors estimated efficiently (i.e., the variance meets the CRLB) when the targets are separated by $0.9\sigma _{\mathrm{PSF}}$ , or about 1.8 pixel widths. We also find that estimation of the centroid parameters is efficient below a target separation of $0.65\sigma _{{\mathrm{PSF}}}$ . Furthermore, we find that increased difference in the SNR of two targets causes the variances in the resolved scenario to be lower, and in the case of the unresolved scenario, to increase. We also derive and characterize a decision about target cardinality as a hypothesis testing problem, and develop a generalized likelihood ratio test to perform the decision making. The performance of this test is evaluated via Monte Carlo simulations, and matches well to theoretical predictions. Finally, we explore the effect of separation between targets, and individual target SNR on resolvability.

Spatial misregistration in hyperspectral cameras: lab characterization and impact on data quality in real-world images

Hyperspectral cameras capture images where every pixel contains spectral information of the corresponding small area of the depicted scene. Spatial misregistration—differences in spatial sampling between different spectral channels—is one of the key quality parameters of these cameras, because it may have a large impact on the accuracy of the captured spectra. Spatial misregistration unifies various factors, such as differences in the position of the optical point spread function (PSF) in different spectral channels, differences in PSF size, and differences in PSF shape. Ideally, there should be no difference in spatial sampling across the spectral channels, but in any real camera, all these factors are present to some degree. Our work shows the magnitude of the spectral errors caused by these spatial misregistration factors of different magnitudes and in various combinations when acquiring hyperspectral images of real scenes. The spectral errors are calculated in Virtual Camera software where high-resolution airborne images of real-world scenes and several PSFs of different hyperspectral cameras are used as the input. The misregistration factors are simulated. Two different methods for quantifying spatial misregistration in the lab are also tested and compared using the correlation with the errors in the real-world scenes as the criterion. The results are used to suggest the best camera characterization approach that would adequately predict spatial misregistration errors and allow reliable comparison of different hyperspectral cameras to each other.

Reconstruction of the ground-layer adaptive-optics point spread function for MUSE wide field mode observations

Context. Here we describe a simple, efficient, and most importantly fully operational point-spread-function (PSF)-reconstruction approach for laser-assisted ground layer adaptive optics (GLAO) in the frame of the Multi Unit Spectroscopic Explorer (MUSE) wide field mode. Aims. Based on clear astrophysical requirements derived by the MUSE team and using the functionality of the current ESO Adaptive Optics Facility we aim to develop an operational PSF-reconstruction (PSFR) algorithm and test it both in simulations and using on-sky data. Methods. The PSFR approach is based on a Fourier description of the GLAO correction to which the specific instrumental effects of MUSE wide field mode (pixel size, internal aberrations, etc.) have been added. It was first thoroughly validated with full end-to-end simulations. Sensitivity to the main atmospheric and AO system parameters was analysed and the code was re-optimised to account for the sensitivity found. Finally, the optimised algorithm was tested and commissioned using more than one year of on-sky MUSE data. Results. We demonstrate with an on-sky data analysis that our algorithm meets all the requirements imposed by the MUSE scientists, namely an accuracy better than a few percent on the critical PSF parameters including full width at half maximum and global PSF shape through the kurtosis parameter of a Moffat function. Conclusions. The PSFR algorithm is publicly available and is used routinely to assess the MUSE image quality for each observation. It can be included in any post-processing activity which requires knowledge of the PSF.

In Depth 3D Single Molecule Localization Microscopy with Time Modulated Excitation

In Single Molecule Localization Microscopy, the position of the emitters is obtained by fitting the Point Spread Function (PSF). This spatially based localization precision thus strongly relies on the PSF shape, which is degraded by defocusing or aberrations. In particular, this strongly degrades 3D imaging, where axial resolution is always worse than lateral one, and imaging depth limited to few microns. We propose a new localization strategy based on a time signature to retrieve fluorophores’ position over the whole field of view.

Accurate and rapid background estimation in single-molecule localization microscopy using the deep neural network BGnet

Background fluorescence, especially when it exhibits undesired spatial features, is a primary factor for reduced image quality in optical microscopy. Structured background is particularly detrimental when analyzing single-molecule images for 3-dimensional localization microscopy or single-molecule tracking. Here, we introduce BGnet, a deep neural network with a U-net-type architecture, as a general method to rapidly estimate the background underlying the image of a point source with excellent accuracy, even when point-spread function (PSF) engineering is in use to create complex PSF shapes. We trained BGnet to extract the background from images of various PSFs and show that the identification is accurate for a wide range of different interfering background structures constructed from many spatial frequencies. Furthermore, we demonstrate that the obtained background-corrected PSF images, for both simulated and experimental data, lead to a substantial improvement in localization precision. Finally, we verify that structured background estimation with BGnet results in higher quality of superresolution reconstructions of biological structures.

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.

Physics-based model of the adaptive-optics-corrected point spread function

Context.Adaptive optics (AO) systems greatly increase the resolution of large telescopes, but produce complex point spread function (PSF) shapes, varying in time and across the field of view. The PSF must be accurately known since it provides crucial information about optical systems for design, characterization, diagnostics, and image post-processing.Aims.We develop here a model of the AO long-exposure PSF, adapted to various seeing conditions and any AO system. This model is made to match accurately both the core of the PSF and its turbulent halo.Methods.The PSF model we develop is based on a parsimonious parameterization of the phase power spectral density, with only five parameters to describe circularly symmetric PSFs and seven parameters for asymmetrical ones. Moreover, one of the parameters is the Fried parameterr0of the turbulence’s strength. This physical parameter is an asset in the PSF model since it can be correlated with external measurements of ther0, such as phase slopes from the AO real time computer (RTC) or site seeing monitoring.Results.We fit our model against end-to-end simulated PSFs using the OOMAO tool, and against on-sky PSFs from the SPHERE/ZIMPOL imager and the MUSE integral field spectrometer working in AO narrow-field mode. Our model matches the shape of the AO PSF both in the core and the halo, with a relative error smaller than 1% for simulated and experimental data. We also show that we retrieve ther0parameter with sub-centimeter precision on simulated data. For ZIMPOL data, we show a correlation of 97% between ourr0estimation and the RTC estimation. Finally, MUSE allows us to test the spectral dependency of the fittedr0parameter. It follows the theoreticalλ6/5evolution with a standard deviation of 0.3 cm. Evolution of other PSF parameters, such as residual phase variance or aliasing, is also discussed.

Compact snapshot hyperspectral imaging with diffracted rotation

Traditional snapshot hyperspectral imaging systems include various optical elements: a dispersive optical element (prism), a coded aperture, several relay lenses, and an imaging lens, resulting in an impractically large form factor. We seek an alternative, minimal form factor of snapshot spectral imaging based on recent advances in diffractive optical technology. We thereupon present a compact, diffraction-based snapshot hyperspectral imaging method, using only a novel diffractive optical element (DOE) in front of a conventional, bare image sensor. Our diffractive imaging method replaces the common optical elements in hyperspectral imaging with a single optical element. To this end, we tackle two main challenges: First, the traditional diffractive lenses are not suitable for color imaging under incoherent illumination due to severe chromatic aberration because the size of the point spread function (PSF) changes depending on the wavelength. By leveraging this wavelength-dependent property alternatively for hyperspectral imaging, we introduce a novel DOE design that generates an anisotropic shape of the spectrally-varying PSF. The PSF size remains virtually unchanged, but instead the PSF shape rotates as the wavelength of light changes. Second, since there is no dispersive element and no coded aperture mask, the ill-posedness of spectral reconstruction increases significantly. Thus, we propose an end-to-end network solution based on the unrolled architecture of an optimization procedure with a spatial-spectral prior, specifically designed for deconvolution-based spectral reconstruction. Finally, we demonstrate hyperspectral imaging with a fabricated DOE attached to a conventional DSLR sensor. Results show that our method compares well with other state-of-the-art hyperspectral imaging methods in terms of spectral accuracy and spatial resolution, while our compact, diffraction-based spectral imaging method uses only a single optical element on a bare image sensor.

Deformation of Optics for Photon Monte Carlo Simulations

Abstract We develop a comprehensive approach to simulate the deformation of mirrors and lenses due to thermal and mechanical stresses that couples efficiently to photon-based optics simulations. This expands upon previous work where we demonstrated a comprehensive ab initio approach to simulate astronomical images using a photon Monte Carlo method. We apply elasticity theory and estimate thermal effects by adapting a three-dimensional numerical method. We also consider the effect of active optics control systems and active cooling systems in further correcting distortions in the optics. We validate the approach by showing convergence to analytic estimates, and then apply the methodology to the WIYN 3.5 m telescope primary mirror. We demonstrate that changes in the soak temperature result in second-order point-spread function (PSF) defocusing, the gravitational sag and positioning errors result in highly structured PSF distortions, and large-scale thermal gradients result in elliptical PSF distortion patterns. All three aspects of the environment are larger than the intrinsic optical aberrations of the design, and further exploration with a variety of telescopes should lead to detailed PSF size and shape, astrometric distortion, and field variation predictions. The simulation capabilities developed in this work are publicly available with the Photon Simulation package.

Resolution enhancement of confocal scanning microscopy using low-intensity imaging part of point spread function

We introduce a phase mask with a left-handed azimuthal polarization to generate a special shape of point spread function. The proposed point spread function has low-intensity and small size in the central lobe. This central lobe of the point spread function is used to obtain an image on the detector, and therefore the lateral resolution is improved. The proposed method can achieve a remarkable improvement in the lateral resolution and the depth of field compared with conventional confocal scanning microscopy. The image simulation demonstrated that the images obtained by this proposed method have better imaging quality.

Correction of dichroic mirror-induced PSF distortion in STED microscopy

Due to its spectral transmission/reflection properties, dichroic mirror (DM) is widely applied in nearly all microscopes to separate and combine beams with diverse wavelengths. However, its potential distortion effects to the point-spread function (PSF) have been ignored to a large extent. Here, we built a mathematical model to quantify these effects. Specifically, we focus on STED microscopy, whose performance is extremely sensitive to the systematic deficiencies. Both excitation and depletion beams are analysed, and the peak intensity and the shape of the effective PSF are calculated accordingly. More importantly, the strategy to compensate the DM-induced PSF distortion is also given in this paper.