Point Spread Function Calibration Research Articles

The JWST Early Release Science Program for Direct Observations of Exoplanetary Systems. IV. NIRISS Aperture Masking Interferometry Performance and Lessons Learned

We present a performance analysis for the aperture masking interferometry (AMI) mode on board the James Webb Space Telescope Near Infrared Imager and Slitless Spectrograph (JWST/NIRISS). Thanks to self-calibrating observables, AMI accesses inner working angles down to and even within the classical diffraction limit. The scientific potential of this mode has recently been demonstrated by the Early Release Science (ERS) 1386 program with a deep search for close-in companions in the HIP 65426 exoplanetary system. As part of ERS 1386, we use the same data set to explore the random, static, and calibration errors of NIRISS AMI observables. We compare the observed noise properties and achievable contrast to theoretical predictions. We explore possible sources of calibration errors and show that differences in charge migration between the observations of HIP 65426 and point-spread function calibration stars can account for the achieved contrast curves. Lastly, we use self-calibration tests to demonstrate that with adequate calibration NIRISS F380M AMI can reach contrast levels of ∼9–10 mag at ≳λ/D. These tests lead us to observation planning recommendations and strongly motivate future studies aimed at producing sophisticated calibration strategies taking these systematic effects into account. This will unlock the unprecedented capabilities of JWST/NIRISS AMI, with sensitivity to significantly colder, lower-mass exoplanets than lower-contrast ground-based AMI setups, at orbital separations inaccessible to JWST coronagraphy.

Lensless imaging through thin scattering layers under broadband illumination

Lensless scattering imaging is a prospective approach to microscopy in which a high-resolution image of an object is reconstructed from one or more measured speckle patterns, thus providing a solution in situations where the use of imaging optics is not possible. However, current lensless scattering imaging methods are typically limited by the need for a light source with a narrowband spectrum. Here, we propose two general approaches that enable single-shot lensless scattering imaging under broadband illumination in both noninvasive [without point spread function (PSF) calibration] and invasive (with PSF calibration) modes. The first noninvasive approach is based on a numerical refinement of the broadband pattern in the cepstrum incorporated with a modified phase retrieval strategy. The latter invasive approach is correlation inspired and generalized within a computational optimization framework. Both approaches are experimentally verified using visible radiation with a full-width-at-half-maximum bandwidth as wide as 280 nm ( Δ λ / λ = 44.8 % ) and a speckle contrast ratio as low as 0.0823. Because of its generality and ease of implementation, we expect this method to find widespread applications in ultrafast science, passive sensing, and biomedical applications.

Compressive spectral image fusion via a single aperture high throughput imaging system

Spectral image fusion techniques combine the detailed spatial information of a multispectral (MS) image and the rich spectral information of a hyperspectral (HS) image into a high-spatial and high-spectral resolution image. Due to the data deluge entailed by such images, new imaging modalities have exploited their intrinsic correlations in such a way that, a computational algorithm can fuse them from few multiplexed linear projections. The latter has been coined compressive spectral image fusion. State-of-the-art research work have focused mainly on the algorithmic part, simulating instrumentation characteristics and assuming independently registered sensors to conduct compressed MS and HS imaging. In this manuscript, we report on the construction of a unified computational imaging framework that includes a proof-of-concept optical testbed to simultaneously acquire MS and HS compressed projections, and an alternating direction method of multipliers algorithm to reconstruct high-spatial and high-spectral resolution images from the fused compressed measurements. The testbed employs a digital micro-mirror device (DMD) to encode and split the input light towards two compressive imaging arms, which collect MS and HS measurements, respectively. This strategy entails full light throughput sensing since no light is thrown away by the coding process. Further, different resolutions can be dynamically tested by binning the DMD and sensors pixels. Real spectral responses and optical characteristics of the employed equipment are obtained through a per-pixel point spread function calibration approach to enable accurate compressed image fusion performance. The proposed framework is demonstrated through real experiments within the visible spectral range using as few as 5% of the data.

Gaia Early Data Release 3

Context. The unprecedented astrometric precision of the Gaia mission relies on accurate estimates of the locations of sources in the Gaia data stream. This is ultimately performed by point spread function (PSF) fitting, which in turn requires an accurate reconstruction of the PSF, including calibrations of all the major dependences. These include a strong colour dependence due to Gaia’s broad G band and a strong time dependence due to the evolving contamination levels and instrument focus. Accurate PSF reconstruction is also important for photometry. Gaia Early Data Release 3 (EDR3) will, for the first time, use a PSF calibration that models several of the strongest dependences, leading to signficantly reduced systematic errors. Aims. We describe the PSF model and calibration pipeline implemented for Gaia EDR3, including an analysis of the calibration results over the 34 months of data. We include a discussion of the limitations of the current pipeline and directions for future releases. This will be of use both to users of Gaia data and as a reference for other precision astrometry missions. Methods. We develop models of the 1D line spread function (LSF) and 2D PSF profiles based on a linear combination of basis components. These are designed for flexibility and performance, as well as to meet several mathematical criteria such as normalisation. We fit the models to selected primary sources in independent time ranges, using simple parameterisations for the colour and other dependences. Variation in time is smoothed by merging the independent calibrations in a square root information filter, with resets at certain mission events that induce a discontinuous change in the PSF. Results. The PSF calibration shows strong time and colour dependences that accurately reproduce the varying state of the Gaia astrometric instrument. Analysis of the residuals reveals both the performance and the limitations of the current models and calibration pipeline, and indicates the directions for future development. Conclusions. The PSF modelling and calibration carried out for Gaia EDR3 represents a major step forwards in the data processing and will lead to reduced systematic errors in the core mission data products. Further significant improvements are expected in the future data releases.

High-fidelity structured illumination microscopy by point-spread-function engineering

Structured illumination microscopy (SIM) has become a widely used tool for insight into biomedical challenges due to its rapid, long-term, and super-resolution (SR) imaging. However, artifacts that often appear in SIM images have long brought into question its fidelity, and might cause misinterpretation of biological structures. We present HiFi-SIM, a high-fidelity SIM reconstruction algorithm, by engineering the effective point spread function (PSF) into an ideal form. HiFi-SIM can effectively reduce commonly seen artifacts without loss of fine structures and improve the axial sectioning for samples with strong background. In particular, HiFi-SIM is not sensitive to the commonly used PSF and reconstruction parameters; hence, it lowers the requirements for dedicated PSF calibration and complicated parameter adjustment, thus promoting SIM as a daily imaging tool.

Depth-dependent PSF calibration and aberration correction for 3D single-molecule localization.

Three-dimensional single molecule localization microscopy relies on the fitting of the individual molecules with a point spread function (PSF) model. The reconstructed images often show local squeezing or expansion in z. A common cause is depth-induced aberrations in conjunction with an imperfect PSF model calibrated from beads on a coverslip, resulting in a mismatch between measured PSF and real PSF. Here, we developed a strategy for accurate z-localization in which we use the imperfect PSF model for fitting, determine the fitting errors and correct for them in a post-processing step. We present an open-source software tool and a simple experimental calibration procedure that allow retrieving accurate z-positions in any PSF engineering approach or fitting modality, even at large imaging depths.

Modeling Point Spread Function in Fluorescence Microscopy With a Sparse Gaussian Mixture: Tradeoff Between Accuracy and Efficiency.

Deblurring is a fundamental inverse problem in bioimaging. It requires modeling the point spread function (PSF), which captures the optical distortions entailed by the image formation process. The PSF limits the spatial resolution attainable for a given microscope. However, recent applications require a higher resolution and have prompted the development of super-resolution techniques to achieve sub-pixel accuracy. This requirement restricts the class of suitable PSF models to analog ones. In addition, deblurring is computationally intensive, hence further requiring computationally efficient models. A custom candidate fitting both the requirements is the Gaussian model. However, this model cannot capture the rich tail structures found in both the theoretical and empirical PSFs. In this paper, we aim at improving the reconstruction accuracy beyond the Gaussian model, while preserving its computational efficiency. We introduce a new class of analog PSF models based on the Gaussian mixtures. The number of Gaussian kernels controls both the modeling accuracy and the computational efficiency of the model: the lower the number of kernels, the lower the accuracy and the higher the efficiency. To explore the accuracy-efficiency tradeoff, we propose a variational formulation of the PSF calibration problem, where a convex sparsity-inducing penalty on the number of Gaussian kernels allows trading accuracy for efficiency. We derive an efficient algorithm based on a fully split formulation of alternating split Bregman. We assess our framework on synthetic and real data, and demonstrate a better reconstruction accuracy in both geometry and photometry in point source localization-a fundamental inverse problem in fluorescence microscopy.

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.

Bilevel Optimization for Calibrating Point Spread Functions in Blind Deconvolution

Blind deconvolution problems arise in many imaging modalities, where both the underlying point spread function, which parameterizes the convolution operator, and the source image need to be identified. In this work, a novel bilevel optimization approach to blind deconvolution is proposed. The lower-level problem refers to the minimization of a total-variation model, as is typically done in non-blind image deconvolution. The upper-level objective takes into account additional statistical information depending on the particular imaging modality. Bilevel problems of such type are investigated systematically. Analytical properties of the lower-level solution mapping are established based on Robinson's strong regularity condition. Furthermore, several stationarity conditions are derived from the variational geometry induced by the lower-level problem. Numerically, a projected-gradient-type method is employed to obtain a Clarke-type stationary point and its convergence properties are analyzed. We also implement an efficient version of the proposed algorithm and test it through the experiments on point spread function calibration and multiframe blind deconvolution.

Star/galaxy separation at faint magnitudes: application to a simulated Dark Energy Survey

We address the problem of separating stars from galaxies in future large photometric surveys. We focus our analysis on simulations of the Dark Energy Survey (DES). In the first part of the paper, we derive the science requirements on star/galaxy separation, for measurement of the cosmological parameters with the gravitational weak lensing and large-scale structure probes. These requirements are dictated by the need to control both the statistical and systematic errors on the cosmological parameters, and by point spread function calibration. We formulate the requirements in terms of the completeness and purity provided by a given star/galaxy classifier. In order to achieve these requirements at faint magnitudes, we propose a new method for star/galaxy separation in the second part of the paper. We first use principal component analysis to outline the correlations between the objects parameters and extract from it the most relevant information. We then use the reduced set of parameters as input to an Artificial Neural Network. This multiparameter approach improves upon purely morphometric classifiers (such as the classifier implemented in SExtractor), especially at faint magnitudes: it increases the purity by up to 20 per cent for stars and by up to 12 per cent for galaxies, at i-magnitude fainter than 23.

A Fast PSF Calibration Method for Single Lens Imaging

Modern cameras typically consist up to dozens of individual optical elements to compensate for geometric and chromatic aberrations. In recent year, high-quality single lens imaging has been proved possible by eliminating aberrations with computationally. Point spread function (PSF) calibration is key technique for single lens imaging. However, the existing PSF calibration method is time-consuming and has to be completely repeated for every new lens. This paper proposes a fast PSF calibration to accelerate the process. A PSF model is firstly estimated from a group of single lenses, which is close to the ideal PSF for specific tested single lenses. Then the PSF model is used as the iterative starting point in the calibration optimization. Experimental results show that this method can significantly improve the efficiency of PSF calibration process, and deconvolution performance is competitive with existing methods.

Resolving directional ambiguity in dynamic light scattering-based transverse motion velocimetry in optical coherence tomography

Dynamic light scattering-based optical coherence tomography approaches have been successfully implemented to measure total transverse (xy) flow speed, but are unable to resolve directionality. We propose a method to extract directional velocity in the transverse plane by introducing a variable scan bias to our system. Our velocity estimation, which yields the directional velocity component along the scan axis, is also independent of any point-spread function calibration. By combining our approach with Doppler velocimetry, we show three-component velocimetry that is appropriately dependent on latitudinal and longitudinal angle.

Calibration and Limits of Camera‐Based Fluorescence Correlation Spectroscopy: A Supported Lipid Bilayer Study

Camera-based fluorescence correlation spectroscopy (FCS) approaches allow the measurement of thousands of contiguous points yielding excellent statistics and details of sample structure. Imaging total internal reflection FCS (ITIR-FCS) provides these measurements on lipid membranes. Herein, we determine the influence of the point spread function (PSF) of the optical system, the laser power used, and the time resolution of the camera on the accuracy of diffusion coefficient and concentration measurements. We demonstrate that the PSF can be accurately determined by ITIR-FCS and that the laser power and time resolution can be varied over a wide range with limited influence on the measurement of the diffusion coefficient whereas the concentration measurements are sensitive to changes in the measurement parameters. One advantage of ITIR-FCS is that the measurement of the PSF has to be performed only once for a given optical setup, in contrast to confocal FCS in which calibrations have to be performed at least once per measurement day. Using optimized experimental conditions we provide diffusion coefficients for over ten different lipid membranes consisting of one, two and three constituents, measured in over 200,000 individual correlation functions. Using software binning and thus the inherent advantage of ITIR-FCS of providing multiple observation areas in a single measurement we test the FCS diffusion law and show how they can be complemented by the local information provided by the difference in cross-correlation functions (ΔCCF). With the determination of the PSF by ITIR-FCS and the optimization of measurement conditions ITIR-FCS becomes a calibration-free method. This allows us to provide measurements of absolute diffusion coefficients for bilayers with different compositions, which were stable over many different bilayer preparations over a time of at least one year, using a single PSF calibration.

New parametric point spread function calibration methodology for improving the accuracy of patterning prediction in electron-beam lithography

Electron-beam-direct-write lithography has been considered a candidate next-generation technique for achieving high resolution. An accurate point spread function (PSF) is essential for reliable patterning prediction and proximity-effects correction. It can be derived via an effective parametric PSF calibration methodology, typically involving the fitting of the absorbed energy distribution (AED) from an electron-scattering simulation. However, the existing parametric PSF calibration methodology does not employ a systematic approach to obtain a new PSF form that is both compact and accurate when conventional PSF forms are not satisfactory. Only the AED fitting quality (rather than its patterning-prediction quality) is considered during the conventional calibration methodology. It also lacks a process to consider whether the predicted deviation (as simulated using the chosen PSF form) is satisfactory. This paper proposes a new parametric PSF calibration methodology to systematically obtain a PSF form consisting of the smallest number of terms, with a better combination of basis functions and that optimizes pattern accuracy. The effectiveness of using the new methodology is demonstrated in terms of fitting accuracy, patterning-prediction accuracy, and patterning sensitivity.

APPLICATION OF A DAMPED LOCALLY OPTIMIZED COMBINATION OF IMAGES METHOD TO THE SPECTRAL CHARACTERIZATION OF FAINT COMPANIONS USING AN INTEGRAL FIELD SPECTROGRAPH

High-contrast imaging instruments are now being equipped with integral field spectrographs (IFS) to facilitate the detection and characterization of faint substellar companions. Algorithms currently envisioned to handle IFS data, such as the Locally Optimized Combination of Images (LOCI) algorithm, rely upon aggressive point-spread-function (PSF) subtraction, which is ideal for initially identifying companions but results in significantly biased photometry and spectroscopy due to unwanted mixing with residual starlight. This spectro-photometric issue is further complicated by the fact that algorithmic color response is a function of the companion's spectrum, making it difficult to calibrate the effects of the reduction without using iterations involving a series of injected synthetic companions. In this paper, we introduce a new PSF calibration method, which we call "damped LOCI", that seeks to alleviate these concerns. By modifying the cost function that determines the weighting coefficients used to construct PSF reference images, and also forcing those coefficients to be positive, it is possible to extract companion spectra with a precision that is set by calibration of the instrument response and transmission of the atmosphere, and not by post-processing. We demonstrate the utility of this approach using on-sky data obtained with the Project 1640 IFS at Palomar. Damped-LOCI does not require any iterations on the underlying spectral type of the companion, nor does it rely upon priors involving the chromatic and statistical properties of speckles. It is a general technique that can readily be applied to other current and planned instruments that employ IFS's.

Improving PSF calibration in confocal microscopic imaging—estimating and exploiting bilateral symmetry

A method for estimating the axis of reflectional symmetry of an image f(x, y) on the unit disc D={(x, y) : x2+y2≤1} is proposed, given that noisy data of f(x, y) are observed on a discrete grid of edge width Δ. Our estimation procedure is based on minimizing over β∈[0, π) the L2 distance between empirical versions of f and τβf, the image of f after reflection at the axis along (cos β, sin β). Here, f and τβf are estimated using truncated radial series of the Zernike type. The inherent symmetry properties of the Zernike functions result in a particularly simple estimation procedure for β. It is shown that the estimate β̂ converges at the parametric rate Δ−1 for images f of bounded variation. Further, we establish asymptotic normality of β̂ if f is Lipschitz continuous. The method is applied to calibrating the point spread function (PSF) for the deconvolution of images from confocal microscopy. For various reasons the PSF characterizing the problem may not be rotationally invariant but rather only reflection symmetric with respect to two orthogonal axes. For an image of a bead acquired by a confocal laser scanning microscope (Leica TCS), these axes are estimated and corresponding confidence intervals are constructed. They turn out to be close to the coordinate axes of the imaging device. As cause for deviation from rotational invariance, this indicates some slight misalignment of the optical system or anisotropy of the immersion medium rather than some irregular shape of the bead. In an extensive simulation study, we show that using a symmetrized version of the observed PSF significantly improves the subsequent reconstruction process of the target image.

Point spread function calibration requirements for dark energy from cosmic shear

Context. The control of systematic effects when measuring background galaxy shapes is one of the main challenges for cosmic shear analyses. Aims. Study the fundamental limitations on shear accuracy due to the measurement of the point spread function (PSF) from the finite number of stars that are available. We translate the accuracy required for cosmological parameter estimation to the minimum number of stars over which the PSF must be calibrated. Methods. We characterise the error made in the shear arising from errors on the PSF. We consider different PSF models, from a simple elliptical Gaussian to various shapelet parametrisations. First we derive our results analytically in the case of infinitely small pixels (i.e. infinitely high resolution), then image simulations are used to validate these results and investigate the effect of finite pixel size in the case of the elliptical Gaussian PSF. Results. Our results are expressed in terms of the minimum number of stars required to calibrate the PSF in order to ensure that systematic errors are smaller than statistical errors when estimating the cosmological parameters. On scales smaller than the area containing this minimum number of stars, there is not enough information to model the PSF. This means that these small scales should not be used to constrain cosmology unless the instrument and the observing strategy are optimised to make this variability extremely small. The minimum number of stars varies with the square of the star Signal-to-Noise Ratio, with the complexity of the PSF and with the pixel size. In the case of an elliptical Gaussian PSF and in the absence of dithering, 2 pixels per PSF full width at half maximum (FWHM) implies a 20% increase of the minimum number of stars compared to the ideal case of infinitely small pixels; 0.9 pixels per PSF FWHM implies a factor 100 increase. Conclusions. In the case of a good resolution and a typical Signal-to-Noise Ratio distribution of stars, we find that current surveys need the PSF to be calibrated over a few stars, which may explain residual systematics on scales smaller than a few arcmins. Future all-sky cosmic shear surveys require the PSF to be calibrated over a region containing about 50 stars. Due to the simplicity of our models these results should be interpreted as optimistic and therefore provide a measure of a systematic “floor’ intrinsic to shape measurements.

Mid-Infrared Imaging of the Post-Asymptotic Giant Branch Star AC Herculis with the Multiple Mirror Telescope Adaptive Optics System

We utilized the unique 6.5 m Multiplie Mirror Telescope deformable secondary adaptive optics (AO) system to produce high-resolution (FWHM = 03), very high Strehl mid-infrared (9.8, 11.7, and 18 μm) images of the post-asymptotic giant branch star AC Her. The very high (98% ± 2%) Strehls achieved with mid-IR AO led naturally to an ultrastable point-spread function (PSF) independent of air mass, seeing, or location on the sky. We find no significant difference between AC Her's morphology and our unresolved PSF calibration stars (μ UMa and α Her) at 9.8, 11.7, and 18 μm. Our current observations do not confirm any extended mid-IR structure around AC Her. These observations are in conflict with previously reported Keck (seeing-limited) 11.7 and 18 μm images that suggested the presence of a resolved ~06 edge-on circumbinary disk. We conclude that AC Her has no extended mid-IR structure on scales greater than 02 (R < 75 AU). These first results of mid-IR AO science are very encouraging for future high-accuracy mid-IR imaging with this technique.

Observations of Quasar Hosts with Adaptive Optics at Lick Observatory

We present near-infrared H-band observations of the hosts of three z ~ 1 quasars from the Sloan Digital Sky Survey made with the adaptive optics system at Lick Observatory. We derive a point-spread function (PSF) for each quasar and model the host plus quasar nucleus to obtain magnitudes and approximate scale sizes for the host galaxies. We find our recovered host galaxies are similar to those found for z ~ 1 quasars observed with the Hubble Space Telescope. They also have, with one interesting exception, black hole mass estimates from their bulge luminosities that are consistent with those from emission-line widths. We thus demonstrate that adaptive optics can be successfully used for the quantitative study of quasar host galaxies, with the caveat that better PSF calibration will be needed for studies of the hosts of significantly brighter or higher redshift quasars with the Lick system.