Shape Of Point Spread Function Research Articles

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.

Detecting unresolved binary stars inEuclidVIS images

Measuring a weak gravitational lensing signal to the level required by the next generation of space-based surveys demands exquisite reconstruction of the point-spread function (PSF). However, unresolved binary stars can significantly distort the PSF shape. In an effort to mitigate this bias, we aim at detecting unresolved binaries in realistic Euclid stellar populations. We tested methods in numerical experiments where (i) the PSF shape is known to Euclid requirements across the field of view, and (ii) the PSF shape is unknown. We drew simulated catalogues of PSF shapes for this proof-of-concept paper. Following the Euclid survey plan, the objects were observed four times. We propose three methods to detect unresolved binary stars. The detection is based on the systematic and correlated biases between exposures of the same object. One method is a simple correlation analysis, while the two others use supervised machine-learning algorithms (random forest and artificial neural network). In both experiments, we demonstrate the ability of our methods to detect unresolved binary stars in simulated catalogues. The performance depends on the level of prior knowledge of the PSF shape and the shape measurement errors. Good detection performances are observed in both experiments. Full complexity, in terms of the images and the survey design, is not included, but key aspects of a more mature pipeline are discussed. Finding unresolved binaries in objects used for PSF reconstruction increases the quality of the PSF determination at arbitrary positions. We show, using different approaches, that we are able to detect at least binary stars that are most damaging for the PSF reconstruction process.

A novel method for determining the optical component of the paper substrate point spread function

Knowledge of the actual shape of the point spread function (PSF) is of the utmost importance for paper and print quality assessment, since the PSF represents the degree of lateral scattering of light which is closely associated with the size of the optical dot gain. Importance of the correct shape of the PSF prompted us to propose a new experimental method for determining optical component of PSF of a paper substrate by studying the interaction of collimated light and paper and at the same time demonstrate superiority of the Lorentzian shaped PSF compared to the Gaussian, which is commonly used in the description of the PSF. Additionally, measured profile of the scattered light was compared with the profile obtained from Monte Carlo simulation for identical wavelength of incident light. Once the shape of the optical PSF was determined, FTIR spectra of samples were recorded and analysed, aiming to determine how the ratio of chemical and mechanical pulp influences the shape of the optical PSF. All results indicate better approximation of Lorentzian PSF compared to Gaussian, and imply correlation between the share of mechanical and chemical pulp in paper and characteristics of PSF.

Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines

The resolution of super-resolution microscopy based on single molecule localization is in part determined by the accuracy of the localization algorithm. In most published approaches to date this localization is done by fitting an analytical function that approximates the point spread function (PSF) of the microscope. However, particularly for localization in 3D, analytical functions such as a Gaussian, which are computationally inexpensive, may not accurately capture the PSF shape leading to reduced fitting accuracy. On the other hand, analytical functions that can accurately capture the PSF shape, such as those based on pupil functions, can be computationally expensive. Here we investigate the use of cubic splines as an alternative fitting approach. We demonstrate that cubic splines can capture the shape of any PSF with high accuracy and that they can be used for fitting the PSF with only a 2–3x increase in computation time as compared to Gaussian fitting. We provide an open-source software package that measures the PSF of any microscope and uses the measured PSF to perform 3D single molecule localization microscopy analysis with reasonable accuracy and speed.

Constraint matrix factorization for space variant PSFs field restoration

In large-scale spatial surveys, the point spread function (PSF) varies across the instrument field of view (FOV). Local measurements of the PSFs are given by the isolated star images. Yet, these estimates may not be directly usable for post-processing because of the observational noise and potentially the aliasing. Given a set of aliased and noisy star images from a telescope, we aim to estimate well-resolved and noise-free PSFs at the observed star positions. In particular, exploiting the spatial correlation of the PSFs across the FOV. We introduce RCA (resolved components analysis) which is a noise-robust dimension reduction and super-resolution method based on matrix-factorization. We propose an original way of using the PSFs spatial correlation in the restoration process through sparsity. The introduced formalism can be applied to correlated data sets with respect to any euclidean parametric space. We tested our method on simulated monochromatic PSFs of Euclid telescope (launch planned for 2020). The proposed method outperforms existing PSFs restoration and dimension reduction methods. We show that a coupled sparsity constraint on individual PSFs and their spatial distribution yields a significant improvement on both the restored PSFs shapes and the PSFs subspace identification, in presence of aliasing. RCA can be naturally extended to account for the wavelength dependency of the PSFs.

The Impact of Interpixel Capacitance in CMOS Detectors on PSF Shapes and Implications for WFIRST

Unlike optical CCDs, near-infrared detectors, which are based on CMOS hybrid readout technology, typically suffer from electrical crosstalk between the pixels. The interpixel capacitance (IPC) responsible for the crosstalk affects the point-spread function (PSF) of the telescope, increasing the size and modifying the shape of all objects in the images while correlating the Poisson noise. Upcoming weak lensing surveys that use these detectors, such as WFIRST, place stringent requirements on the PSF size and shape (and the level at which these are known), which in turn must be translated into requirements on IPC. To facilitate this process, we present a first study of the effect of IPC on WFIRST PSF sizes and shapes. Realistic PSFs are forward-simulated from physical principles for each WFIRST bandpass. We explore how the PSF size and shape depends on the range of IPC coupling with pixels that are connected along an edge or corner; for the expected level of IPC in WFIRST, IPC increases the PSF sizes by ∼5%. We present a linear fitting formula that describes the uncertainty in the PSF size or shape due to uncertainty in the IPC, which could arise for example due to unknown time evolution of IPC as the detectors age or due to spatial variation of IPC across the detector. We also study of the effect of a small anisotropy in the IPC, which further modifies the PSF shapes. Our results are a first, critical step in determining the hardware and characterization requirements for the detectors used in the WFIRST survey.

Evaluating the effect of stellar multiplicity on the point spread function of space-based weak lensing surveys

The next generation of space-based telescopes used for weak lensing surveys will require exquisite point spread function (PSF) determination. Previously negligible effects may become important in the reconstruction of the PSF, in part because of the improved spatial resolution. In this paper, we show that unresolved multiple star systems can affect the ellipticity and size of the PSF and that this effect is not cancelled even when using many stars in the reconstruction process. We estimate the error in the reconstruction of the PSF due to the binaries in the star sample both analytically and with image simulations for different PSFs and stellar populations. The simulations support our analytical finding that the error on the size of the PSF is a function of the multiple stars distribution and of the intrinsic value of the size of the PSF, i.e. if all stars were single. Similarly, the modification of each of the complex ellipticity components (e1,e2) depends on the distribution of multiple stars and on the intrinsic complex ellipticity. Using image simulations, we also show that the predicted error in the PSF shape is a theoretical limit that can be reached only if large number of stars (up to thousands) are used together to build the PSF at any desired spatial position. For a lower number of stars, the PSF reconstruction is worse. Finally, we compute the effect of binarity for different stellar magnitudes and show that bright stars alter the PSF size and ellipticity more than faint stars. This may affect the design of PSF calibration strategies and the choice of the related calibration fields.

Accurate PSF-matched photometry and photometric redshifts for the extreme deep field with the Chebyshev–Fourier functions

Photometric redshifts, which have become the cornerstone of several of the largest astronomical surveys like PanStarrs, DES, J-PAS or the LSST, require precise measurements of galaxy photometry in different bands using a consistent physical aperture. This is not trivial, due to the variation in the shape and width of the Point Spread Function (PSF) introduced by wavelength differences, instrument positions and atmospheric conditions. Current methods to correct for this effect rely on a detailed knowledge of the PSF characteristics as a function of the survey coordinates, which can be difficult due to the relative paucity of stars tracking the PSF behaviour. Here we show that it is possible to measure accurate, consistent multicolour photometry without knowing the shape of PSF. The Chebyshev-Fourier Functions (CHEFs) can fit the observed profile of each object and produce high signal-to-noise integrated flux measurements unaffected by the PSF. These total fluxes, which encompass all the galaxy populations, are much more useful for Galaxy Evolution studies than aperture photometry. We compare the total magnitudes and colours obtained using our software to traditional photometry with SExtractor, using real data from the COSMOS survey and the Hubble Ultra Deep Field. We also apply the CHEFs technique to the recently published Extreme Deep Field and compare the results to those from ColorPro on the HUDF. We produce a photometric catalogue with 35732 sources (10823 with S/N>5), reaching a photometric redshift precision of 2% due to the extraordinary depth and wavelength coverage of the XDF images.

Effect of rotational diffusion in an orientational potential well on the point spread function of electric dipole emitters.

A study is presented of the point spread function (PSF) of electric dipole emitters that go through a series of absorption-emission cycles while the dipole orientation is changing due to rotational diffusion within the constraint of an orientational potential well. An analytical expression for the PSF is derived valid for arbitrary orientational potential wells in the limit of image acquisition times much larger than the rotational relaxation time. This framework is used to study the effects of the direction of incidence, polarization, and degree of coherence of the illumination. In the limit of fast rotational diffusion on the scale of the fluorescence lifetime the illumination influences only the PSF height, not its shape. In the limit of slow rotational diffusion on the scale of the fluorescence lifetime there is a significant effect on the PSF shape as well, provided the illumination is (partially) coherent. For oblique incidence, illumination asymmetries can arise in the PSF that give rise to position offsets in localization based on Gaussian spot fitting. These asymmetries persist in the limit of free diffusion in a zero orientational potential well.

Determination of the point spread function of layered metamaterials assisted with the blind deconvolution algorithm

We propose to use the blind deconvolution and its modification to extract the point spread function (PSF) of layered metamaterials from a SNOM measurement. The measurement results are processed using the blind deconvolution algorithm to reconstruct the real-valued non-coherent PSF, or using the modified blind deconvolution introduced in this paper to reconstruct the complex-valued coherent PSF. The two algorithms are tested in simulations with a layered metamaterial deposited on a thin metallic mask with test apertures. We show that the modified algorithm is capable of recovering the approximate shape of complex PSF with a sub-wavelength full width at half maximum from a measurement in which the apertures are larger than the wavelength.

Variations in optical coherence tomography resolution and uniformity: a multi-system performance comparison.

Point spread function (PSF) phantoms based on unstructured distributions of sub-resolution particles in a transparent matrix have been demonstrated as a useful tool for evaluating resolution and its spatial variation across image volumes in optical coherence tomography (OCT) systems. Measurements based on PSF phantoms have the potential to become a standard test method for consistent, objective and quantitative inter-comparison of OCT system performance. Towards this end, we have evaluated three PSF phantoms and investigated their ability to compare the performance of four OCT systems. The phantoms are based on 260-nm-diameter gold nanoshells, 400-nm-diameter iron oxide particles and 1.5-micron-diameter silica particles. The OCT systems included spectral-domain and swept source systems in free-beam geometries as well as a time-domain system in both free-beam and fiberoptic probe geometries. Results indicated that iron oxide particles and gold nanoshells were most effective for measuring spatial variations in the magnitude and shape of PSFs across the image volume. The intensity of individual particles was also used to evaluate spatial variations in signal intensity uniformity. Significant system-to-system differences in resolution and signal intensity and their spatial variation were readily quantified. The phantoms proved useful for identification and characterization of irregularities such as astigmatism. Our multi-system results provide evidence of the practical utility of PSF-phantom-based test methods for quantitative inter-comparison of OCT system resolution and signal uniformity.

Error analysis of moment-based modal wavefront sensing

The shape of a focus-modulated point spread function (PSF) is used as a quick visual assessment tool of aberration modes in the PSF. Further analysis in terms of shape moments can permit quantifying the modal coefficients with an accuracy comparable to that of typical wavefront sensors. In this Letter, the error of the moment-based wavefront sensing is analytically described in terms of the pixelation and photon/readout noise. All components highly depend on the (unknown) PSF shape but can be estimated from the measured PSF sampled at a reasonable spatial resolution and photon count. Numerical simulations verified that the models consistently predicted the behavior of the modal estimation error of the moment-based wavefront sensing.

Photon Counting Histogram Using Numerical Data of Point Spread Function

Photon counting histogram (PCH) is a fluorescence fluctuation method that can quantify the brightness and concentration of different fluorescent molecules in solution at a single molecule level using confocal optics. The current method assumes that the point spread function (PSF) of confocal optics is Gaussian function. However, this could be problematic when the actual PSF profile is not Gaussian. Here, we propose an improved PCH analysis method using numerical PSF data. This method does not require any analytical equation for the PSF profile, and can handle any arbitrary shape of PSF. We report a proof-of-concept estimation of this method using a model PSF.

Determination of one‐dimensional spherically aberrated point spread function in depth profiling by confocal Raman microscopy

We present a simple experiment that allows the complete and direct characterization of the point spread function (PSF) in refraction‐aberrated depth profiling experiments with confocal Raman microscopy. We used a wedge‐shaped solid polymer film to induce refraction aberrations on the response of an infinitesimally thin Raman scatterer, represented by a polished silicon wafer. The system, with the film pasted on top of the Si wafer, was probed by a depth slicing technique under a dry‐optics configuration. Post‐acquisition processing of the Si and polymer intensity maps allowed the reconstruction of the axial PSF spatially resolved each 1 µm or less in the z‐axis and for virtually continuous values of focusing depth. In agreement with theory, we found that PSF broadens asymmetrically with focusing depth, with a marked shift in the focus point. From the shape of PSF, we obtained values of depth resolution within the film that confirm that axial discrimination is not drastically deteriorated, as suggested by previous works, and that confocal aperture effectively reduces the collection volume even under severe refraction interference. Copyright © 2013 John Wiley & Sons, Ltd.

Interpolating point spread function anisotropy

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 effect 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). 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 $\sigma_{sys}^2$ better than the $1\times10^{-7}$ upper bound expected by future space-based surveys, with the local interpolators performing better than the global ones.

Atmospheric point spread function interpolation for weak lensing in short exposure imaging data

A main science goal for the Large Synoptic Survey Telescope (LSST) is to measure the cosmic shear signal from weak lensing to extreme accuracy. One difficulty, however, is that with the short exposure time ($\simeq$15 seconds) proposed, the spatial variation of the Point Spread Function (PSF) shapes may be dominated by the atmosphere, in addition to optics errors. While optics errors mainly cause the PSF to vary on angular scales similar or larger than a single CCD sensor, the atmosphere generates stochastic structures on a wide range of angular scales. It thus becomes a challenge to infer the multi-scale, complex atmospheric PSF patterns by interpolating the sparsely sampled stars in the field. In this paper we present a new method, PSFent, for interpolating the PSF shape parameters, based on reconstructing underlying shape parameter maps with a multi-scale maximum entropy algorithm. We demonstrate, using images from the LSST Photon Simulator, the performance of our approach relative to a 5th-order polynomial fit (representing the current standard) and a simple boxcar smoothing technique. Quantitatively, PSFent predicts more accurate PSF models in all scenarios and the residual PSF errors are spatially less correlated. This improvement in PSF interpolation leads to a factor of 3.5 lower systematic errors in the shear power spectrum on scales smaller than $\sim13'$, compared to polynomial fitting. We estimate that with PSFent and for stellar densities greater than $\simeq1/{\rm arcmin}^{2}$, the spurious shear correlation from PSF interpolation, after combining a complete 10-year dataset from LSST, is lower than the corresponding statistical uncertainties on the cosmic shear power spectrum, even under a conservative scenario.

An upper-bound metric for characterizing spectral and spatial coregistration errors in spectral imaging

Coregistration errors in multi- and hyperspectral imaging sensors arise when the spatial sensitivity pattern differs between bands or when the spectral response varies across the field of view, potentially leading to large errors in the recorded image data. In imaging spectrometers, spectral and spatial offset errors are customarily specified as "smile" and "keystone" distortions. However these characteristics do not account for errors resulting from variations in point spread function shape or spectral bandwidth. This paper proposes improved metrics for coregistration error both in the spatial and spectral dimensions. The metrics are essentially the integrated difference between point spread functions. It is shown that these metrics correspond to an upper bound on the error in image data. The metrics enable estimation of actual data errors for a given image, and can be used as part of the merit function in optical design optimization, as well as for benchmarking of spectral image sensors.

Characterization of Cytoplasmic / Membrane-Bound Protein Mixtures by Z-Scan Fluorescence Fluctuation Spectroscopy

Fluorescence fluctuation spectroscopy (FFS) has been employed to quantify the stoichiometry of soluble proteins in cells. However, some proteins have both soluble (cytoplasmic) and membrane-bound fractions. In such conditions, coexcitation of the membrane-bound and cytoplasmic proteins makes standard FFS unsuitable. In this work, we apply z-scan FFS to characterize the intensity profile of proteins with both a cytoplasmic and membrane-bound population. Analysis of the intensity profile determines unequivocally the intensity contributions from each membrane layer and the cytoplasm, as well as, the length of cytoplasm layer. Experimentally, we choose Matrix-EGFP (the MA domain of HTLV-1 Gag) as our model system and apply a dual color z-scan technique. Cells are cotransfected with Matrix-EGFP and mCherry and their emitted signal is split into two different detection channels based on color. Simultaneous fitting of both channels with separate model geometries aids in correct determination of parameters. The use of the dual color technique is possible because we demonstrate a co-localization of the observation volume and agreement in the point spread function shape factors for both the red and green channels. We extend our work by applying z-scan FFS to determine the brightness (stoichiometry) of the cytoplasmic protein fraction. Yet determining the brightness of the membrane-bound protein is significantly more challenging because of slower diffusion times, inhomogeneity in protein distribution, and possible brightness bias due to geometry and orientation effects. Here, we investigate the potential of z-scan FFS to address these factors and measure the unbiased brightness of membrane proteins. This study provides insight into the fundamental considerations for correct application of FFS in the study of proteins with both cytoplasmic and membrane-bound fractions. This work is supported by NIH grant GM064589 and NIH grant GM075401.

Poster — Thur Eve — 54: Discrete Point Spread Functions for Electronic Portal Imaging Devices

EPID images are related to the fluence by a (possibly position‐dependent) Point Spread Function (PSF), or kernel. So far, work concerning finding the PSF for a certain EPID has relied on continuous representations. Since the EPID image itself corresponds to a discrete pixel grid, an interesting problem is to find a discrete PSF and do so based only on measurements, without resorting to Monte Carlo simulations. The present work concerns a method for finding such a discrete kernel for the simple case when the kernel is translation‐ and rotation‐invariant. The method relies on minimizing the difference, in a least‐squares sense, between the true acquired image and the image obtained with the calculated kernel. The method was tested using a simulated fluence and EPID image corresponding to a uniform rectangular field. The EPID image was generated by convolving the fluence with a known PSF. The developed algorithm was then tested by comparing the PSF shape produced by the algorithm (based on the image and fluence) with the actual PSF shape used to construct the EPID image. The two were found to match perfectly. A second test was performed by introducing a random error, uniformly distributed in the (−10%, +10%) interval, into the fluence used as input for the algorithm and then reconstructing the EPID image using the calculated PSF. The difference between the “true” EPID image and the reconstructed one was found to be smaller than 0.1% for the simulated field that was studied.

Proper Analytic Point Spread Function for Lateral Modulation

For ultrasonic lateral modulation for the imaging and measurement of tissue motion, better envelope shapes of the point spread function (PSF) than of a parabolic function are searched for within analytic functions or windows on the basis of the knowledge of the ideal shape of PSF previously obtained, i.e., having a large full width at half maximum and short feet. Through simulation of displacement vector measurement, better shapes are determined. As a better shape, a new window is obtained from a Turkey window by changing Hanning windows by power functions with an order larger than the second order. The order of measurement accuracies obtained is as follows, the new window > rectangular window > power function with a higher order > parabolic function > Akaike window.