Impact of point spread function higher moments error on weak gravitational lensing – II. A comprehensive study

Context. Weak gravitational lensing requires precise measurements of galaxy shapes and therefore accurate knowledge of the point spread function (PSF) model. The latter can be a source of systematics that affect the shear two-point correlation function. A key aspect of weak-lensing analysis is the forecasting of the systematics due to the PSF. Aims. Correlation functions of galaxies and the PSF, the so-called ρ and τ statistics, are used to evaluate the level of systematics coming from the PSF model and PSF corrections and contributing to the two-point correlation function used to perform cosmological inference. Our goal is to introduce a fast and simple method to estimate this level of systematics and to assess its agreement with state-of-the-art approaches. Methods. We introduce a new way to estimate the covariance matrix of τ statistics using analytical expressions. The covariance allows us to estimate parameters directly related to the level of systematics associated with the PSF and provides us with a tool to validate the PSF model used in a weak-lensing analysis. We applied these methods to data from the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS). Results. We show that semi-analytical covariance yields results comparable to those obtained by using covariances obtained from simulations or jackknife resampling. The approach requires less computation time and is therefore well suited to rapid comparison of the systematic level obtained from different catalogues. We also show how one can break degeneracies between parameters with a redefinition of the τ statistics. Conclusions. The methods developed in this work will be useful tools in the analysis of current weak-lensing data but also of Stage IV surveys such as Euclid, LSST, and Roman. They provide fast and accurate diagnostics on PSF systematics that are crucial in the context of cosmic shear studies.

Aims. Calibrating the point spread function (PSF) is a fundamental part of weak gravitational lensing analyses. Even with corrected galaxy images, imperfect calibrations can introduce biases. We propose an analytical framework for quantifying PSF-induced systematics as diagnostics for cross-correlation measurements of weak lensing with density tracers; for example, galaxy-galaxy lensing. We show how those systematics propagate to physical parameters of the density tracers. Those diagnostics only require a shape catalog of PSF stars and foreground galaxy positions. Methods. We considered the PSF-induced multiplicative bias, and introduced three second-order statistics as additive biases. We computed both biases for the weak-lensing derived halo mass of spectroscopic foreground galaxy samples; in particular, their effect on the tangential shear and fit halo mass as a function of stellar mass. In addition, we assessed their impact on the recently published black-hole – halo-mass relation for type I active galactic nuclei (AGNs). Results. Using weak-lensing catalogs from the Ultraviolet Near Infrared Optical Northern Survey (UNIONS) and the Dark Energy Survey (DES), we find the multiplicative biases in the tangential shear to be less than 0.5%. No correlations between additive bias and galaxy properties of the foreground sample are detected. The combined PSF systematics affect low-mass galaxies and small angular scales; halo mass estimates can be biased by up to 18% for a sample of central galaxies in the stellar mass range of 9.0 ≤ log M*/M⊙ < 9.5. Conclusions. The PSF-induced multiplicative bias is a subdominant contribution to current studies of weak-lensing – density cross-correlations, but might become significant for upcoming stage IV surveys. For samples with a low tangential shear, additive PSF systematics can induce a significant bias on derived properties such as the halo mass.

We investigate the impact of point spread function (PSF) fitting errors on cosmic shear measurements using the concepts of complexity and sparsity. Complexity, introduced in a previous paper, characterizes the number of degrees of freedom of the PSF. For instance, fitting an underlying PSF with a model with low complexity will lead to small statistical errors on the model parameters, however these parameters could suffer from large biases. Alternatively, fitting with a large number of parameters will tend to reduce biases at the expense of statistical errors. We perform an optimisation of scatters and biases by studying the mean squared error of a PSF model. We also characterize a model sparsity, which describes how efficiently the model is able to represent the underlying PSF using a limited number of free parameters. We present the general case and illustrate it for a realistic example of PSF fitted with shapelet basis sets. We derive the relation between complexity and sparsity of the PSF model, signal-to-noise ratio of stars and systematic errors on cosmological parameters. With the constraint of maintaining the systematics below the statistical uncertainties, this lead to a relation between the required number of stars to calibrate the PSF and the sparsity. We discuss the impact of our results for current and future cosmic shear surveys. In the typical case where the biases can be represented as a power law of the complexity, we show that current weak lensing surveys can calibrate the PSF with few stars, while future surveys will require hard constraints on the sparsity in order to calibrate the PSF with 50 stars.

As recently shown by Viola et al., the common (KSB) method for measuring weak gravitational shear creates a non-linear relation between the measured and the true shear of objects. We investigate here what effect such a non-linear calibration relation may have on cosmological parameter estimates from weak lensing if a simpler, linear calibration relation is assumed. We show that the non-linear relation introduces a bias in the shear-correlation amplitude and thus a bias in the cosmological parameters Omega_matter and sigma_8. Its direction and magnitude depends on whether the point-spread function is narrow or wide compared to the galaxy images from which the shear is measured. Substantial over- or underestimates of the cosmological parameters are equally possible, depending also on the variant of the KSB method. Our results show that for trustable cosmological-parameter estimates from measurements of weak lensing, one must verify that the method employed is free from ellipticity-dependent biases or monitor that the calibration relation inferred from simulations is applicable to the survey at hand.

A joint analysis of the clustering of galaxies and their weak gravitational lensing signal is well-suited to simultaneously constrain the galaxy-halo connection as well as the cosmological parameters by breaking the degeneracy between galaxy bias and the amplitude of clustering signal. In a series of two papers, we perform such an analysis at the highest redshift ($z\sim0.53$) in the literature using CMASS galaxies in the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey Eleventh Data Release (SDSS-III/BOSS DR11) catalog spanning 8300~deg$^2$. In this paper, we present details of the clustering and weak lensing measurements of these galaxies. We define a subsample of 400,916 CMASS galaxies based on their redshifts and stellar mass estimates so that the galaxies constitute an approximately volume-limited and similar population over the redshift range $0.47\le z\le 0.59$. We obtain a signal-to-noise ratio $S/N\simeq 56$ for the galaxy clustering measurement. We also explore the redshift and stellar mass dependence of the clustering signal. For the weak lensing measurement, we use existing deeper imaging data from the CFHTLS with publicly available shape and photometric redshift catalogs from CFHTLenS, but only in a 105~deg$^2$ area which overlaps with BOSS. This restricts the lensing measurement to only 5,084 CMASS galaxies. After careful systematic tests, we find a highly significant detection of the CMASS weak lensing signal, with total $S/N\simeq 26$. These measurements form the basis of the halo occupation distribution and cosmology analysis presented in More et al. (Paper II).

We present and characterize the catalog of galaxy shape measurements that will be used for cosmological weak lensing measurements in the Wide layer of the first year of the Hyper Suprime-Cam (HSC) survey. The catalog covers an area of 136.9 deg2 split into six fields, with a mean i-band seeing of 0${^{\prime\prime}_{.}}$58 and 5σ point-source depth of i ∼ 26. Given conservative galaxy selection criteria for first-year science, the depth and excellent image quality results in unweighted and weighted source number densities of 24.6 and 21.8 arcmin−2, respectively. We define the requirements for cosmological weak lensing science with this catalog, then focus on characterizing potential systematics in the catalog using a series of internal null tests for problems with point-spread function (PSF) modeling, shear estimation, and other aspects of the image processing. We find that the PSF models narrowly meet requirements for weak lensing science with this catalog, with fractional PSF model size residuals of approximately 0.003 (requirement: 0.004) and the PSF model shape correlation function ρ1 < 3 × 10−7 (requirement: 4 × 10−7) at 0${^{\circ}_{.}}$5 scales. A variety of galaxy shape-related null tests are statistically consistent with zero, but star–galaxy shape correlations reveal additive systematics on >1° scales that are sufficiently large as to require mitigation in cosmic shear measurements. Finally, we discuss the dominant systematics and the planned algorithmic changes to reduce them in future data reductions.

Lesion-detection performance in oncologic PET depends in part upon count statistics, with shorter scans having higher noise and reduced lesion detectability. However, advanced techniques such as time-of-flight (TOF) and point spread function (PSF) modeling can improve lesion detectability. This work investigates the relationship between reducing count levels (as a surrogate for scan time) and reconstructing with PSF model and TOF. A series of 24 whole-body phantom scans was acquired on a Biograph mCT TOF PET/CT scanner using the experimental methodology prescribed for the Utah PET Lesion Detection Database. Six scans were acquired each day over 4 days, with up to 23 68Ge shell-less lesions (diam. 6, 8, 10, 12, 16mm) distributed throughout the phantom thorax and pelvis. Each scan acquired 6 bed positions at 240s/bed in listmode format. The listmode files were then statistically pruned, preserving Poisson statistics, to equivalent count levels for scan times of 180s, 120s, 90s, 60s, 45s, 30s, and 15s per bed field-of-view. Each dataset was reconstructed using ordinary Poisson line-of-response (LOR) OSEM, with PSF model, with TOF, and with PSF+TOF. Localization receiver operating characteristics (LROC) analysis was then performed using the channelized non-prewhitened (CNPW) observer. The results were analyzed to delineate the relationship between scan time, reconstruction method, and strength of post-reconstruction filter. Lesion-detection performance degraded as scan time was reduced, and progressively stronger filters were required to maximize performance for the shorter scans. PSF modeling and TOF were found to improve detection performance, offsetting in part the reduced detectability for shorter scans. Notably, PSF+TOF at 120s per bed position preserved essentially the same detection performance as the baseline reconstruction at 240s/bed — effectively cutting whole-body scan time in half without degrading lesion-detection performance in these data.

<i>Aims. <i/>We combine measurements of weak gravitational lensing from the CFHTLS-Wide survey, supernovae Ia from CFHT SNLS and CMB anisotropies from WMAP5 to obtain joint constraints on cosmological parameters, in particular, the dark-energy equation-of-state parameter <i>w<i/>. We assess the influence of systematics in the data on the results and look for possible correlations with cosmological parameters.<i>Methods. <i/>We implemented an MCMC algorithm to sample the parameter space of a flat CDM model with a dark-energy component of constant <i>w<i/>. Systematics in the data are parametrised and included in the analysis. We determine the influence of photometric calibration of SNIa data on cosmological results by calculating the response of the distance modulus to photometric zero-point variations. The weak lensing data set is tested for anomalous field-to-field variations and a systematic shape measurement bias for high-redshift galaxies.<i>Results. <i/>Ignoring photometric uncertainties for SNLS biases cosmological parameters by at most 20% of the statistical errors, using supernovae alone; the parameter uncertainties are underestimated by 10%. The weak-lensing field-to-field variance between 1 deg<sup>2<sup/>-MegaCam pointings is 5-15% higher than predicted from <i>N<i/>-body simulations. We find no bias in the lensing signal at high redshift, within the framework of a simple model, and marginalising over cosmological parameters. Assuming a systematic underestimation of the lensing signal, the normalisation increases by up to 8%. Combining all three probes we obtain at 68% confidence ( at 95%), including systematic errors. Our results are therefore consistent with the cosmological constant <i>Λ<i/>. Systematics in the data increase the error bars by up to 35%; the best-fit values change by less than 0.15<i>σ<i/>.

Weak gravitational lensing convergence peaks, the local maxima in weak lensing convergence maps, have been shown to contain valuable cosmological information complementary to commonly used two-point statistics. To exploit the full power of weak lensing for cosmology, we must model baryonic feedback processes because these reshape the matter distribution on non-linear and mildly non-linear scales. We study the impact of baryonic physics on the number density of weak lensing peaks using the FLAMINGO cosmological hydrodynamical simulation suite. We generate ray-traced full-sky convergence maps mimicking the characteristics of a Stage IV weak lensing survey. We compare the number densities of peaks in simulations that have been calibrated to reproduce the observed galaxy mass function and cluster gas fraction or to match a shifted version of these, and that use either thermally driven or jet active galactic nucleus feedback. We show that the differences induced by realistic baryonic feedback prescriptions (typically 5–30 per cent for κ = 0.1–0.4) are smaller than those induced by reasonable variations in cosmological parameters (20–60 per cent for κ = 0.1–0.4) but must be modelled carefully to obtain unbiased results. The reasons behind these differences can be understood by considering the impact of feedback on halo masses, or by considering the impact of different cosmological parameters on the halo mass function. Our analysis demonstrates that, for the range of models we investigated, the baryonic suppression is insensitive to changes in cosmology up to κ ≈ 0.4 and that the higher κ regime is dominated by Poisson noise and cosmic variance.

BackgroundThe maximum standardized uptake value (SUVmax) is a common clinical parameter for quantification in F18-fluorodeoxyglucose positron emission tomography/computed tomography (FDG-PET/CT), but it is influenced by image reconstruction. The aim of this study was to analyze the association of SUVmax deviations related to point spread function (PSF) and time-of-flight (TOF) reconstruction with tumor-to-background ratios (TBR) in colorectal liver metastases (CRLM).MethodsFifteen patients (f, 6; m, 9; median age, 59 years; range, 32 to 72 years) with 28 liver metastases were included retrospectively. FDG-PET/CT imaging (median activity, 237 MBq; range, 231 to 252 MBq; median uptake, 61 min; range, 55 to 67 min) was performed on a Siemens Biograph mCT 64 followed by image reconstruction using 3D-ordered subset expectation maximization (3D-OSEM) or 3D-OSEM with PSF modeling - both with and without TOF information. Differences in SUVmax were analyzed using the Friedman test and Wilcoxon test for paired non-parametric data. The correlation of inter-method differences with the lesions’ TBR was studied using Spearman’s rank correlation coefficient (rho). Differences between lesions with low (<4.8) and high (>4.8) TBR were analyzed using the Mann-Whitney U test (TBR measured with 3D-OSEM; binarized by its median).ResultsThere was a significant correlation of the lesions’ TBR with relative SUVmax differences related to PSF (PSF + TOF vs. 3D-OSEM + TOF, rho = 0.61; PSF vs. 3D-OSEM, rho = 0.52) or TOF (PSF + TOF vs. PSF, rho = −0.58; 3D-OSEM + TOF vs. 3D-OSEM, rho = −0.61). Accordingly, PSF algorithms only showed higher SUVmax than non-PSF algorithms in lesions with a high TBR (median differences at low/high TBR, +2.6%/+9.1% [PSF + TOF vs. 3D-OSEM + TOF]; +0.7%/+6.4% [PSF vs. 3D-OSEM]). TOF integration also led to higher SUVmax but mainly at low TBR (low/high TBR, +10.4%/+1.8% [PSF + TOF vs. PSF]; +8.6%/−0.1% [3D-OSEM + TOF vs. 3D-OSEM]).ConclusionsBoth PSF and TOF reconstruction resulted in a substantial alteration of SUVmax in CRLM. TOF provided the highest SUVmax increase in low-contrast lesions while - vice versa - PSF showed the most relevant increase in high-contrast lesions. Thus, one should be aware that quantitative analyses of lesions with varying TBR, e.g., in radiotherapy or follow-up studies, may be mainly affected by either PSF or TOF reconstruction, respectively.

Current measurements of the weak lensing signal induced by large-scale structure provide useful constraints on a range of cosmological parameters. However, the ultimate success of this technique depends on the accuracy with which one corrects for the effect of the point spread function (PSF), in particular the correction for the PSF anisotropy. With upcoming large weak lensing surveys, a proper understanding of residual systematics is necessary. In this paper, we examine the importance of the adopted model for the spacial variation of the PSF anisotropy using images of fields with a large number of stars. A wrong parametrization of the PSF anisotropy leads to a residual signal in the data, affecting the cosmic shear measurements. We use data taken with the Canada‐France‐Hawaii 12k (CFH12k) camera, and note that some of the results might not be valid for other instruments. We select a random subset of stars which are used to characterize the PSF and to correct the shapes of the remaining stars. The ellipticity correlation function of the residuals is studied to quantify the effect of residual PSF anisotropy on cosmic shear studies. In order to single out the effect of the parametrization, we assume a perfect method for the actual correction of galaxy shapes. The PSF anisotropy is typically modelled for each individual chip of a mosaic; consequently, the residuals are coherent on small scales. As a result, the systematic signal decreases rapidly with increasing angular scale. Separation of the signal into ‘E’ (curl-free) and ‘B’ (curl) components can help to identify the presence of residual systematics, but in general, the amplitude of the ‘B’ mode is different from that of the ‘E’ mode. The study of fields with many stars can be beneficial in finding a proper description of the variation of PSF anisotropy, and consequently can help to improve the accuracy with which the cosmic shear signal can be measured significantly. We show that such an approach can lead to an appreciable reduction in systematics. The results suggest that the prospects for accurate measurements of the cosmic shear signal on scales larger than ∼10 arcmin are excellent.

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.

We present a joint weak lensing and X-ray analysis of 4 deg$^2$ from the\nCFHTLS and XMM-LSS surveys. Our weak lensing analysis is the first analysis of\na real survey using shapelets, a new generation weak lensing analysis method.\nWe create projected mass maps of the images, and extract 6\nweak-lensing-detected clusters of galaxies. We show that their counts can be\nused to constrain the power spectrum normalisation $\\sigma_8\n=0.92_{-0.30}^{+0.26}$ for $\\Omega_m=0.24$. We show that despite the large\nscatter generally observed in the M-T relation derived from lensing masses,\ntight constraints on both its slope and normalisation $M_*$ can be obtained\nwith a moderate number of sources provided that the covered mass range is large\nenough. Adding clusters from Bardeau et al. (2007) to our sample, we measure\n$M_* = 2.71_{-0.61}^{+0.79} 10^{14} h^{-1} M_\\odot$. Although they are\ndominated by shot noise and sample variance, our measurements are consistent\nwith currently favoured values, and set the stage for future surveys. We thus\ninvestigate the dependence of those estimates on survey size, depth, and\nintegration time, for joint weak lensing and X-ray surveys. We show that deep\nsurveys should be dedicated to the study of the physics of clusters and groups\nof galaxies. For a given exposure time, wide surveys provide a larger number of\ndetected clusters and are therefore preferred for the measurement of\ncosmological parameters such as $\\sigma_8$ and $M_*$. We show that a wide\nsurvey of a few hundred square degrees is needed to improve upon current\nmeasurements of these parameters. More ambitious surveys covering 7000 deg$^2$\nwill provide the 1% accuracy in the estimation of the power spectrum and the\nM-T relation normalisations.\n

Lesion-detection performance in oncologic PET depends in part upon count statistics, with shorter scans having higher noise and reduced lesion detectability. However, advanced techniques such as time-of-flight (TOF) and point spread function (PSF) modeling can improve lesion detection. This work investigates the relationship between reducing count levels (as a surrogate for scan time) and reconstructing with PSF model and TOF. A series of twenty-four whole-body phantom scans was acquired on a Biograph mCT TOF PET/CT scanner using the experimental methodology prescribed for the Utah PET Lesion Detection Database. Six scans were acquired each day over four days, with up to 23 (68)Ge shell-less lesions (diam. 6, 8, 10, 12, 16 mm) distributed throughout the phantom thorax and pelvis. Each scan acquired 6 bed positions at 240 s/bed in listmode format. The listmode files were then statistically pruned, preserving Poisson statistics, to equivalent count levels for scan times of 180 s, 120 s, 90 s, 60 s, 45 s, 30 s, and 15 s per bed field-of-view, corresponding to whole-body scan times of 1.5-24 min. Each dataset was reconstructed using ordinary Poisson line-of-response (LOR) OSEM, with PSF model, with TOF, and with PSF+TOF. Localization receiver operating characteristics (LROC) analysis was then performed using the channelized non-prewhitened (CNPW) observer. The results were analyzed to delineate the relationship between scan time, reconstruction method, and strength of post-reconstruction filter. Lesion-detection performance degraded as scan time was reduced, and progressively stronger filters were required to maximize performance for the shorter scans. PSF modeling and TOF were found to improve detection performance, but the degree of improvement for TOF was much larger than for PSF for the large phantom used in this study. Notably, the images using TOF provided equivalent lesion-detection performance to the images without TOF for scan durations 40% shorter, suggesting that TOF may offset, at least in part, the need for longer scan times in larger patients.

The Siemens Biograph TruePoint TrueV (B-TPTV) positron emission tomography (PET) scanner performs 3D PET reconstruction using a system matrix with point spread function (PSF) modeling (called the True X reconstruction). PET resolution was dramatically improved with the True X method. In this study, we assessed the spatial resolution and image quality on a B-TPTV PET scanner. In addition, we assessed the feasibility of animal imaging with a B-TPTV PET and compared it with a microPET R4 scanner. Spatial resolution was measured at center and at 8 cm offset from the center in transverse plane with warm background activity. True X, ordered subset expectation maximization (OSEM) without PSF modeling, and filtered back-projection (FBP) reconstruction methods were used. Percent contrast (% contrast) and percent background variability (% BV) were assessed according to NEMA NU2-2007. The recovery coefficient (RC), non-uniformity, spill-over ratio (SOR), and PET imaging of the Micro Deluxe Phantom were assessed to compare image quality of B-TPTV PET with that of the microPET R4. When True X reconstruction was used, spatial resolution was <3.65 mm with warm background activity. % contrast and % BV with True X reconstruction were higher than those with the OSEM reconstruction algorithm without PSF modeling. In addition, the RC with True X reconstruction was higher than that with the FBP method and the OSEM without PSF modeling method on the microPET R4. The non-uniformity with True X reconstruction was higher than that with FBP and OSEM without PSF modeling on microPET R4. SOR with True X reconstruction was better than that with FBP or OSEM without PSF modeling on the microPET R4. This study assessed the performance of the True X reconstruction. Spatial resolution with True X reconstruction was improved by 45 % and its % contrast was significantly improved compared to those with the conventional OSEM without PSF modeling reconstruction algorithm. The noise level was higher than that with the other reconstruction algorithm. Therefore, True X reconstruction should be used with caution when quantifying PET data.