Showing papers on "Point spread function published in 2013"

Measuring image resolution in optical nanoscopy.

Abstract: Resolution in optical nanoscopy (or super-resolution microscopy) depends on the localization uncertainty and density of single fluorescent labels and on the sample's spatial structure. Currently there is no integral, practical resolution measure that accounts for all factors. We introduce a measure based on Fourier ring correlation (FRC) that can be computed directly from an image. We demonstrate its validity and benefits on two-dimensional (2D) and 3D localization microscopy images of tubulin and actin filaments. Our FRC resolution method makes it possible to compare achieved resolutions in images taken with different nanoscopy methods, to optimize and rank different emitter localization and labeling strategies, to define a stopping criterion for data acquisition, to describe image anisotropy and heterogeneity, and even to estimate the average number of localizations per emitter. Our findings challenge the current focus on obtaining the best localization precision, showing instead how the best image resolution can be achieved as fast as possible.

Superresolution Multidimensional Imaging with Structured Illumination Microscopy

Abstract: The resolution of an optical microscope is fundamentally limited by diffraction. In a conventional wide-field fluorescence microscope, the resolution limit is at best 200 nm. However, modern superresolution methods can bypass this limit. Pointillistic imaging techniques like PALM (photoactivated localization microscopy) and STORM (stochastic optical reconstruction microscopy) do so by precisely localizing each individual molecule in a sample. In contrast, STED uses the stimulated emission process driven to saturation to dramatically reduce the size of the region in the sample that is capable of spontaneously emitting fluorescence. Structured illumination microscopy (SIM) illuminates the sample with a pattern, typically the image of a grating. This computationally removes the out-of-focus blur, a method known as optical sectioning SIM. Furthermore, frequency mixing of the illumination pattern with the sample caused by the moire effect results in a downmodulation of fine sample detail into the frequency-sup...

Nonparametric Blind Super-resolution

Abstract: Super resolution (SR) algorithms typically assume that the blur kernel is known (either the Point Spread Function 'PSF' of the camera, or some default low-pass filter, e.g. a Gaussian). However, the performance of SR methods significantly deteriorates when the assumed blur kernel deviates from the true one. We propose a general framework for "blind" super resolution. In particular, we show that: (i) Unlike the common belief, the PSF of the camera is the wrong blur kernel to use in SR algorithms. (ii) We show how the correct SR blur kernel can be recovered directly from the low-resolution image. This is done by exploiting the inherent recurrence property of small natural image patches (either internally within the same image, or externally in a collection of other natural images). In particular, we show that recurrence of small patches across scales of the low-res image (which forms the basis for single-image SR), can also be used for estimating the optimal blur kernel. This leads to significant improvement in SR results.

3‐D PSF fitting for fluorescence microscopy: implementation and localization application

Abstract: Localization microscopy relies on computationally efficient Gaussian approximations of the point spread function for the calculation of fluorophore positions. Theoretical predictions show that under specific experimental conditions, localization accuracy is significantly improved when the localization is performed using a more realistic model. Here, we show how this can be achieved by considering three-dimensional (3-D) point spread function models for the wide field microscope. We introduce a least-squares point spread function fitting framework that utilizes the Gibson and Lanni model and propose a computationally efficient way for evaluating its derivative functions. We demonstrate the usefulness of the proposed approach with algorithms for particle localization and defocus estimation, both implemented as plugins for ImageJ.

Acoustic super-resolution with ultrasound and microbubbles.

Abstract: Ultrasound (US) is a widely used clinical imaging modality that offers penetration depths in tissue of >10 cm. However, the spatial resolution in US imaging is fundamentally limited by diffraction to approximately half the wavelength of the sound wave employed. The spatial resolution of optical microscopy is limited by the same fundamental physics, but in recent years super-resolution imaging techniques have been developed that overcome the diffraction limit through the localization of many spatially separated photo-switchable or photo-activatable fluorophores. In this paper, we apply a related approach to demonstrate super-resolution imaging with US. We imaged dilute suspensions of microbubble contrast agents flowing through narrow tube-based phantoms. By spatially localizing multiple spatially isolated microbubbles, we constructed super-resolved microbubble location density maps that clearly resolve features 5.1–2.2 times smaller than the US system point spread function full width half maximum in the lateral and axial directions respectively. Our initial characterization experiment using a fixed 100 µm diameter brass wire and a US frequency of 2 MHz suggests that for an ideal stationary point scatterer the ultimate resolution of the unmodified clinical US system used could be in the range of 2–4 µm.

Superresolution by image scanning microscopy using pixel reassignment

Abstract: The effect of detector array size on resolution and signal collection efficiency of image scanning microscopy based on pixel reassignment is studied. It is shown how the method can also be employed if there is a Stokes shift in fluorescence emission wavelength. With no Stokes shift, the width of the point spread function can be sharpened by a factor of 1.53, and its peak intensity increased by a factor of 1.84.

Resolution limits for imaging through multi-mode fiber

Abstract: We experimentally demonstrate endoscopic imaging through a multi-mode fiber (MMF) in which the number of resolvable image features approaches four times the number of spatial modes per polarization propagating in the fiber. In our method, a sequence of random field patterns is input to the fiber, generating a sequence of random intensity patterns at the output, which are used to sample an object. Reflected power values are returned through the fiber and linear optimization is used to reconstruct an image. The factor-of-four resolution enhancement is due to mixing of modes by the squaring inherent in field-to-intensity conversion. The incoherent point-spread function (PSF) at the center of the fiber output plane is an Airy disk equivalent to the coherent PSF of a conventional diffraction-limited imaging system having a numerical aperture twice that of the fiber. All previous methods for imaging through MMF can only resolve a number of features equal to the number of modes. Most of these methods use localized intensity patterns for sampling the object and use local image reconstruction.

A Robust Directional Saliency-Based Method for Infrared Small-Target Detection Under Various Complex Backgrounds

Abstract: Infrared small-target detection plays an important role in image processing for infrared remote sensing. In this letter, different from traditional algorithms, we formulate this problem as salient region detection, which is inspired by the fact that a small target can often attract attention of human eyes in infrared images. This visual effect arises from the discrepancy that a small target resembles isotropic Gaussian-like shape due to the optics point spread function of the thermal imaging system at a long distance, whereas background clutters are generally local orientational. Based on this observation, a new robust directional saliency-based method is proposed incorporating with visual attention theory for infrared small-target detection. Experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art methods for real infrared images with various typical complex backgrounds.

Resolving stellar populations with crowded field 3D spectroscopy

Abstract: We describe a new method of extracting the spectra of stars from observations of crowded stellar fields with integral field spectroscopy (IFS). Our approach extends the well-established concept of crowded field photometry in images into the domain of 3-dimensional spectroscopic datacubes. The main features of our algorithm follow. (1) We assume that a high-fidelity input source catalogue already exists, e.g. from HST data, and that it is not needed to perform sophisticated source detection in the IFS data. (2) Source positions and properties of the point spread function (PSF) vary smoothly between spectral layers of the datacube, and these variations can be described by simple fitting functions. (3) The shape of the PSF can be adequately described by an analytical function. Even without isolated PSF calibrator stars we can therefore estimate the PSF by a model fit to the full ensemble of stars visible within the field of view. (4) By using sparse matrices to describe the sources, the problem of extracting the spectra of many stars simultaneously becomes computationally tractable. We present extensive performance and validation tests of our algorithm using realistic simulated datacubes that closely reproduce actual IFS observations of the central regions of Galactic globular clusters. We investigate the quality of the extracted spectra under the effects of crowding with respect to the resulting signal-to-noise ratios (S/N) and any possible changes in the continuum level, as well as with respect to absorption line spectral parameters, radial velocities, and equivalent widths. The main effect of blending between two nearby stars is a decrease in the S/N in their spectra. The effect increases with the crowding in the field in a way that the maximum number of stars with useful spectra is always ~0.2 per spatial resolution element. This balance breaks down when exceeding a total source density of one significantly detected star per resolution element. We also explore the effects of PSF mismatch and other systematics. We close with an outlook by applying our method to a simulated globular cluster observation with the upcoming MUSE instrument at the ESO-VLT.

High-Definition Infrared Spectroscopic Imaging

Abstract: The quality of images from an infrared (IR) microscope has traditionally been limited by considerations of throughput and signal-to-noise ratio (SNR). An understanding of the achievable quality as a function of instrument parameters, from first principals is needed for improved instrument design. Here, we first present a model for light propagation through an IR spectroscopic imaging system based on scalar wave theory. The model analytically describes the propagation of light along the entire beam path from the source to the detector. The effect of various optical elements and the sample in the microscope is understood in terms of the accessible spatial frequencies by using a Fourier optics approach and simulations are conducted to gain insights into spectroscopic image formation. The optimal pixel size at the sample plane is calculated and shown much smaller than that in current mid-IR microscopy systems. A commercial imaging system is modified, and experimental data are presented to demonstrate the validity of the developed model. Building on this validated theoretical foundation, an optimal sampling configuration is set up. Acquired data were of high spatial quality but, as expected, of poorer SNR. Signal processing approaches were implemented to improve the spectral SNR. The resulting data demonstrated the ability to perform high-definition IR imaging in the laboratory by using minimally-modified commercial instruments.

An optical super-microscope for far-field, real-time imaging beyond the diffraction limit.

Abstract: Optical microscopy suffers from a fundamental resolution limitation arising from the diffractive nature of light. While current solutions to sub-diffraction optical microscopy involve combinations of near-field, non-linear and fine scanning operations, we hereby propose and demonstrate the optical super-microscope (OSM) - a superoscillation-based linear imaging system with far-field working and observation distances - which can image an object in real-time and with sub-diffraction resolution. With our proof-of-principle prototype we report a point spread function with a spot size clearly reduced from the diffraction limit, and demonstrate corresponding improvements in two-point resolution experiments. Harnessing a new understanding of superoscillations, based on antenna array theory, our OSM achieves far-field, sub-diffraction optical imaging of an object without the need for fine scanning, data post-processing or object pre-treatment. Hence the OSM can be used in a wide variety of imaging applications beyond the diffraction limit, including real-time imaging of moving objects.

Single snapshot imaging of optical properties.

Abstract: A novel acquisition and processing method that enables single snapshot wide field imaging of optical properties in the Spatial Frequency Domain (SFD) is described. This method makes use of a Fourier transform performed on a single image and processing in the frequency space to extract two spatial frequency images at once. The performance of the method is compared to the standard six image SFD acquisition method, assessed on tissue mimicking phantoms and in vivo. Overall both methods perform similarly in extracting optical properties.

Determination of the Point-spread Function for the Fermi Large Area Telescope from On-orbit Data and Limits on Pair Halos of Active Galactic Nuclei

Abstract: The Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope is a pair-conversion telescope designed to detect photons with energies from ≈20 MeV to >300 GeV. The pre-launch response functions of the LAT were determined through extensive Monte Carlo simulations and beam tests. The point-spread function (PSF) characterizing the angular distribution of reconstructed photons as a function of energy and geometry in the detector is determined here from two years of on-orbit data by examining the distributions of γ rays from pulsars and active galactic nuclei (AGNs). Above 3 GeV, the PSF is found to be broader than the pre-launch PSF. We checked for dependence of the PSF on the class of γ-ray source and observation epoch and found none. We also investigated several possible spatial models for pair-halo emission around BL Lac AGNs. We found no evidence for a component with spatial extension larger than the PSF and set upper limits on the amplitude of halo emission in stacked images of low- and high-redshift BL Lac AGNs and the TeV blazars 1ES0229+200 and 1ES0347-121.

Classical imaging theory of a microlens with super-resolution

Abstract: Super-resolution in imaging through a transparent spherical microlens has attracted lots of attention because of recent promising experimental results with remarkable resolution improvement. To provide physical insight for this super-resolution phenomenon, previous studies adopted a phenomenological explanation mainly based on the super-focusing effect of a photonic nanojet, while a direct imaging calculation with classical imaging theory has rarely been studied. Here we theoretically model the imaging process through a microlens with vectorial electromagnetic analysis, and then exclude the previously plausible explanation of super-resolution based on the super-focusing effect. The results showed that, in the context of classical imaging theory subject to the two-point resolution criterion, a microlens with a perfect spherical shape cannot achieve the experimentally verified sub-100 nm resolution. Therefore, there must be some other physical mechanisms that contribute to the reported ultrahigh resolution but have not been revealed in theory.

Projection Reconstruction Magnetic Particle Imaging

Abstract: We acquire the first experimental 3-D tomographic images with magnetic particle imaging (MPI) using projection reconstruction methodology, which is similar to algorithms employed in X-ray computed tomography. The primary advantage of projection reconstruction methods is an order of magnitude increase in signal-to-noise ratio (SNR) due to averaging. We first derive the point spread function, resolution, number of projections required, and the SNR gain in projection reconstruction MPI. We then design and construct the first scanner capable of gathering the necessary data for nonaliased projection reconstruction and experimentally verify our mathematical predictions. We demonstrate that filtered backprojection in MPI is experimentally feasible and illustrate the SNR and resolution improvements with projection reconstruction. Finally, we show that MPI is capable of producing three dimensional imaging volumes in both phantoms and postmortem mice.

Image quality improvement in optical coherence tomography using Lucy–Richardson deconvolution algorithm

Abstract: Optical coherence tomography (OCT) has the potential for skin tissue characterization due to its high axial and transverse resolution and its acceptable depth penetration. In practice, OCT cannot reach the theoretical resolutions due to imperfections of some of the components used. One way to improve the quality of the images is to estimate the point spread function (PSF) of the OCT system and deconvolve it from the output images. In this paper, we investigate the use of solid phantoms to estimate the PSF of the imaging system. We then utilize iterative Lucy-Richardson deconvolution algorithm to improve the quality of the images. The performance of the proposed algorithm is demonstrated on OCT images acquired from a variety of samples, such as epoxy-resin phantoms, fingertip skin and basaloid larynx and eyelid tissues.

Improvement of axial resolution and contrast in temporally focused widefield two-photon microscopy with structured light illumination

Abstract: Although temporally focused wide-field two-photon microscopy (TFM) can perform depth resolved wide field imaging, it cannot avoid the image degradation due to scattering of excitation and emission photons when imaging in a turbid medium. Further, its axial resolution is inferior to standard point-scanning two-photon microscopy. We implemented a structured light illumination for TFM and have shown that it can effectively reject the out-of-focus scattered emission photons improving image contrast. Further, the depth resolution of the improved system is dictated by the spatial frequency of the structure light with the potential of attaining depth resolution better than point-scanning two-photon microscopy.

Three dimensional single molecule localization using a phase retrieved pupil function

Abstract: 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.

Nonlinear Camera Response Functions and Image Deblurring: Theoretical Analysis and Practice

Abstract: This paper investigates the role that nonlinear camera response functions (CRFs) have on image deblurring. We present a comprehensive study to analyze the effects of CRFs on motion deblurring. In particular, we show how nonlinear CRFs can cause a spatially invariant blur to behave as a spatially varying blur. We prove that such nonlinearity can cause large errors around edges when directly applying deconvolution to a motion blurred image without CRF correction. These errors are inevitable even with a known point spread function (PSF) and with state-of-the-art regularization-based deconvolution algorithms. In addition, we show how CRFs can adversely affect PSF estimation algorithms in the case of blind deconvolution. To help counter these effects, we introduce two methods to estimate the CRF directly from one or more blurred images when the PSF is known or unknown. Our experimental results on synthetic and real images validate our analysis and demonstrate the robustness and accuracy of our approaches.

Clinical Impact of Time-of-Flight and Point Response Modeling in PET Reconstructions: A Lesion Detection Study

Abstract: Time-of-flight (TOF) and point spread function (PSF) modeling have been shown to improve PET reconstructions, but the impact on physicians in the clinical setting has not been thoroughly investigated. A lesion detection and localization study was performed using simulated lesions in real patient images. Four reconstruction schemes were considered: ordinary Poisson OSEM (OP) alone and combined with TOF, PSF, and TOF + PSF. The images were presented to physicians experienced in reading PET images, and the performance of each was quantified using localization receiver operating characteristic. Numerical observers (non-prewhitening and Hotelling) were used to identify optimal reconstruction parameters, and observer SNR was compared to the performance of the physicians. The numerical models showed good agreement with human performance, and best performance was achieved by both when using TOF + PSF. These findings suggest a large potential benefit of TOF + PSF for oncology PET studies, especially in the detection of small, low-intensity, focal disease in larger patients.

Interpolating point spread function anisotropy

Abstract: Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling e ect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). In all our methods we model the PSF using a single Mo at profile and we interpolate the fitted parameters at a set of required positions. This allowed us to win the Star-challenge of GREAT10, with the B-splines method. However, we also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics 2 sys better than the 1 10 7 upper bound expected by future space-based surveys, with the local interpolators performing better than

Rotating point spread function via pupil-phase engineering.

Abstract: A simple approach based on the use of a properly designed pupil-phase profile can yield a 3D point-spread function (PSF) that rotates with changing defocus, while keeping its transverse shape approximately invariant over ±3-4 waves of defocus. Unlike Gauss-Laguerre mode-based approaches, it generalizes readily for encoding spherical aberration too via PSF rotation.

Reconstruction of surface potential from Kelvin probe force microscopy images.

Abstract: We present an algorithm for reconstructing a sample surface potential from its Kelvin probe force microscopy (KPFM) image. The measured KPFM image is a weighted average of the surface potential underneath the tip apex due to the long-range electrostatic forces. We model the KPFM measurement by a linear shift-invariant system where the impulse response is the point spread function (PSF). By calculating the PSF of the KPFM probe (tip+cantilever) and using the measured noise statistics, we deconvolve the measured KPFM image to obtain the surface potential of the sample.The reconstruction algorithm is applied to measurements of CdS-PbS nanorods measured in amplitude modulation KPFM (AM-KPFM) and to graphene layers measured in frequency modulation KPFM (FM-KPFM). We show that in the AM-KPFM measurements the averaging effect is substantial, whereas in the FM-KPFM measurements the averaging effect is negligible.

Coherence scanning interferometry: linear theory of surface measurement

Abstract: The characterization of imaging methods as three-dimensional (3D) linear filtering operations provides a useful way to compare the 3D performance of optical surface topography measuring instruments, such as coherence scanning interferometry, confocal and structured light microscopy. In this way, the imaging system is defined in terms of the point spread function in the space domain or equivalently by the transfer function in the spatial frequency domain. The derivation of these characteristics usually involves making the Born approximation, which is strictly only applicable to weakly scattering objects; however, for the case of surface scattering, the system is linear if multiple scattering is assumed to be negligible and the Kirchhoff approximation is assumed. A difference between the filter characteristics derived in each case is found. However this paper discusses these differences and explains the equivalence of the two approaches when applied to a weakly scattering object.

Holographic imaging of crowded fields: high angular resolution imaging with excellent quality at very low cost

Abstract: We present a method for speckle holography that is optimised for crowded fields. Its two key features are an iterativ improvement of the instantaneous Point Spread Functions (PSFs) extracted from each speckle frame and the (optional) simultaneous use of multiple reference stars. In this way, high signal-to-noise and accuracy can be achieved on the PSF for each short exposure, which results in sensitive, high-Strehl re- constructed images. We have tested our method with different instruments, on a range of targets, and from the N- to the I-band. In terms of PSF cosmetics, stability and Strehl ratio, holographic imaging can be equal, and even superior, to the capabilities of currently available Adaptive Optics (AO) systems, particularly at short near-infrared to optical wavelengths. It outperforms lucky imaging because it makes use of the entire PSF and reduces the need for frame selection, thus leading to higher Strehl and improved sensitivity. Image reconstruction a posteriori, the possibility to use multiple reference stars and the fact that these reference stars can be rather faint means that holographic imaging offers a simple way to image large, dense stellar fields near the diffraction limit of large telescopes, similar to, but much less technologically demanding than, the capabilities of a multi-conjugate adaptive optics system. The method can be used with a large range of already existing imaging instruments and can also be combined with AO imaging when the corrected PSF is unstable.

CREANUIS: A Non-linear Radiofrequency Ultrasound Image Simulator

Abstract: Nonlinear ultrasound methods are widely used in clinical applications for tissue or contrast harmonic imaging. Accurate non-linear imaging simulation tools are required in research studies for the development of new methods. However, in existing simulators, the possible inhomogeneity of the coefficient of non-linearity, which is generally observed in tissue and in particular when contrast agents are involved, has not yet been implemented. This article describes a new ultrasound simulator, called CREANUIS, devoted to the computation of B-mode images where both linear and non-linear propagation in media is considered, with a possible inhomogeneous coefficient of non-linearity. The resulting fundamental images, based on a spatially variant and non-linear point spread function, are in accordance with those obtained through the reference linear FieldII simulator, with computation time reduced by a factor of at least 1.8. Non-linear images of media exhibiting inhomogeneous coefficients of non-linearity are also provided. The simulation software can be freely downloaded from our website.

Structured illumination quantitative phase microscopy for enhanced resolution amplitude and phase imaging

Abstract: Structured illumination microscopy (SIM) is an established microscopy technique typically used to image samples at resolutions beyond the diffraction limit. Until now, however, achieving sub-diffraction resolution has predominantly been limited to intensity-based imaging modalities. Here, we introduce an analogue to conventional SIM that allows sub-diffraction resolution, quantitative phase-contrast imaging of optically transparent objects. We demonstrate sub-diffraction resolution amplitude and quantitative-phase imaging of phantom targets and enhanced resolution quantitative-phase imaging of cells. We report a phase accuracy to within 5% and phase noise of 0.06 rad.

Tuning donut profile for spatial resolution in stimulated emission depletion microscopy

Abstract: In stimulated emission depletion (STED)-based or up-conversion depletion-based super-resolution optical microscopy, the donut-shaped depletion beam profile is of critical importance to its resolution. In this study, we investigate the transformation of the donut-shaped depletion beam focused by a high numerical aperture (NA) microscope objective, and model STED point spread function (PSF) as a function of donut beam profile. We show experimentally that the intensity profile of the dark kernel of the donut can be approximated as a parabolic function, whose slope is determined by the donut beam size before the objective back aperture, or the effective NA. Based on this, we derive the mathematical expression for continuous wave (CW) STED PSF as a function of focal plane donut and excitation beam profiles, as well as dye properties. We find that the effective NA and the residual intensity at the center are critical factors for STED imaging quality and the resolution. The effective NA is critical for STED resolution in that it not only determines the donut shape but also the area the depletion laser power is dispersed. An improperly expanded depletion beam will have negligible improvement in resolution. The polarization of the depletion beam also plays an important role as it affects the residual intensity in the center of the donut. Finally, we construct a CW STED microscope operating at 488 nm excitation and 592 nm depletion with a resolution of 70 nm. Our study provides detailed insight to the property of donut beam, and parameters that are important for the optimal performance of STED microscopes. This paper will provide a useful guide for the construction and future development of STED microscopes.

Optimized Principal Component Analysis on Coronagraphic Images of the Fomalhaut System

Abstract: We present the results of a study to optimize the principal component analysis (PCA) algorithm for planet detection, a new algorithm complementing angular differential imaging and locally optimized combination of images (LOCI) for increasing the contrast achievable next to a bright star. The stellar point spread function (PSF) is constructed by removing linear combinations of principal components, allowing the flux from an extrasolar planet to shine through. The number of principal components used determines how well the stellar PSF is globally modeled. Using more principal components may decrease the number of speckles in the final image, but also increases the background noise. We apply PCA to Fomalhaut Very Large Telescope NaCo images acquired at 4.05 μm with an apodized phase plate. We do not detect any companions, with a model dependent upper mass limit of 13-18 M Jup from 4-10 AU. PCA achieves greater sensitivity than the LOCI algorithm for the Fomalhaut coronagraphic data by up to 1 mag. We make several adaptations to the PCA code and determine which of these prove the most effective at maximizing the signal-to-noise from a planet very close to its parent star. We demonstrate that optimizing the number of principal components used in PCA proves most effective for pulling out a planet signal.