arXiv subjects

S. Patil

Publications and source records attributed to S. Patil.

At least 19 recordsLinked to original sources

arXiv2026

The South Pole Telescope AGN Monitoring Campaign: First Release of SPTpol Bright AGN Light Curves

The South Pole Telescope (SPT) collaboration has recently embarked upon a campaign to monitor the brightness of a sample of active galactic nuclei (AGN), both in real time and in archival SPT data. The original design of the SPT was optimized for observations of the cosmic microwave background (CMB) at arc-minute and larger angular scales, and it has been used for this purpose for nearly twenty years, using three generations of CMB cameras. Recently it has been recognized that data from CMB experiments have the potential to be used for AGN monitoring. In this paper, we present the first public release of data from a full sample of SPT-monitored AGN, comprising 158 AGN light curves and associated data from the SPTpol camera, which was operational from 2012-2016. These light curves were created using observations from the SPTpol 500 deg$^{2}$ survey, in which the instrument was used to scan a 500 deg$^2$ patch of the sky several times per day with detectors sensitive to radiation in bands centered at 90 and 150 GHz. We provide a comprehensive description of the observations, the data processing methods, and the resulting light curve catalog. As an example of analyses that these data enable, we searched for a correlation between variability and spectral index, and we looked for ``bluer-when-brighter'' trends in the sample. Our analysis finds $> 10 \sigma$ correlation between fractional intrinsic variance and mean spectral index in the sample, but no significant evidence for bluer-when-brighter trends. The datasets from this study can be accessed through the SPT Treasury Record of AGN With Historical Activity and Time-Series or STRAWHAT catalog. This initial data release includes SPTpol light curves at 90 and 150 GHz, focusing on total intensity. In later updates, SPTpol polarization data and new observations from the SPT-3G instrument at 90, 150, and 220 GHz will be included.

astro-ph.GA↗

arXiv2026

Microscopic origin of hard-plane antiferromagnetism in the Kondo lattice Ce2Rh3Ge5

Hard plane antiferromagnetic order where ordered moments lie perpendicular to the single-ion crystal electric field easy axis is rare in Ce-based Kondo lattices and is a subject of active interest. Here we show that Ce$_2$Rh$_3$Ge$_5$ realizes a hard-plane antiferromagnetic state in which partial delocalization of the local moment gives rise to an RKKY exchange that overturns the single-ion easy-axis preference. Neutron diffraction reveals moments in the $ab$ plane, while inelastic neutron scattering and susceptibility establish a magnetic easy axis along $c$ in the paramagnetic regime, highlighting a clear inversion between single-ion and ordered-state anisotropies. In this work, we establish a unified microscopic framework to consistently account for partial $4f$-moment delocalization, enhanced in-plane RKKY exchange, and the resulting hard-plane antiferromagnetic order. Ce$_2$Rh$_3$Ge$_5$ thus provides a benchmark system in which single-ion anisotropy, Kondo screening, and RKKY exchange compete on comparable energy scales, revealing a cooperative route to hard-axis ordering in strongly hybridized Kondo lattices.

cond-mat.str-el↗

arXiv2025

Assembly, testing, and installation of mPMT photosensor for the Water Cherenkov Test Experiment

The multi-Photomultiplier Tube (mPMT) photosensors will be used in the Water Cherenkov Test Experiment (WCTE) to efficiently detect the photons produced in the whole detector. One of the aims behind the development of WCTE is to test the technology and implement it in future water Cherenkov experiments such as the Hyper-Kamiokande experiment and its Intermediate Water Cherenkov Detector. Each mPMT is built using nineteen 3-inch PMTs arranged on a semi-spherical support matrix. In this paper, we describe the design and manufacture of the mechanical components, the procedures for casting an optical gel between PMTs and acrylic cover, and the overall assembly procedure of the mPMTs. Details of the electronics used in the mPMT modules are not included in this paper and will be presented in a separate publication. We also report on the R&D performed on the selection of the optical gel ratio along with transmittance measurements and the reflectance measurements performed on the aluminium reflector. We also present the optical tests performed on the mPMT module using a 405 nm LED and the resulting increase in the effective photosensitive area by surrounding the PMTs with a reflector. A summary of the production and installation of the mPMTs for the WCTE is also presented in this paper.

physics.ins-det↗

arXiv2025

Measurements of the Temperature and E-mode Polarization of the Cosmic Microwave Background from the Full 500-square-degree SPTpol Dataset

Using the full four-year SPTpol 500 deg$^2$ dataset in both the 95 GHz and 150 GHz frequency bands, we present measurements of the temperature and $E$-mode polarization of the cosmic microwave background (CMB), as well as the $E$-mode polarization auto-power spectrum ($EE$) and temperature-$E$-mode cross-power spectrum ($TE$) in the angular multipole range $50<\ell<8000$. We find the SPTpol dataset to be self-consistent, passing several internal consistency tests based on maps, frequency bands, bandpowers, and cosmological parameters. The full SPTpol dataset is well-fit by the $\Lambda CDM$ model, for which we find $H_0=70.48\pm2.16$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega_m=0.271\pm0.026$, when using only the SPTpol data and a Planck-based prior on the optical depth to reionization. The $\Lambda CDM$ parameter constraints are consistent across the 95 GHz-only, 150 GHz-only, $TE$-only, and $EE$-only data splits. Between the $\ell<1000$ and $\ell>1000$ data splits, the $\Lambda CDM$ parameter constraints are borderline consistent at the $\sim2\sigma$ level. This consistency improves when including a parameter $A_L$, the degree of lensing of the CMB inferred from the smearing of acoustic peaks. When marginalized over $A_L$, the $\Lambda CDM$ parameter constraints from SPTpol are consistent with those from Planck. The power spectra presented here are the most sensitive measurements of the lensed CMB damping tail to date for roughly $\ell > 1700$ in $TE$ and $\ell > 2000$ in $EE$.

astro-ph.CO↗

arXiv2024

First Constraints on the Epoch of Reionization Using the non-Gaussianity of the Kinematic Sunyaev-Zel{'}dovich Effect from the South Pole Telescope and {\it Herschel}-SPIRE Observations

We report results from an analysis aimed at detecting the trispectrum of the kinematic Sunyaev-Zel{'}dovich (kSZ) effect by combining data from the South Pole Telescope (SPT) and {\it Herschel}-SPIRE experiments over a 100 ${\rm deg}^{2}$ field. The SPT observations combine data from the previous and current surveys, namely SPTpol and SPT-3G, to achieve depths of 4.5, 3, and 16 $\mu {\rm K-arcmin}$ in bands centered at 95, 150, and 220 GHz. For SPIRE, we include data from the 600 and 857 GHz bands. We reconstruct the velocity-induced large-scale correlation of the small-scale kSZ signal with a quadratic estimator that uses two cosmic microwave background (CMB) temperature maps, constructed by optimally combining data from all the frequency bands. We reject the null hypothesis of a zero trispectrum at $10.3\sigma$ level. However, the measured trispectrum contains contributions from both the kSZ and other undesired components, such as CMB lensing and astrophysical foregrounds, with kSZ being sub-dominant. We use the \textsc{Agora} simulations to estimate the expected signal from CMB lensing and astrophysical foregrounds. After accounting for the contributions from CMB lensing and foreground signals, we do not detect an excess kSZ-only trispectrum and use this non-detection to set constraints on reionization. By applying a prior based on observations of the Gunn-Peterson trough, we obtain an upper limit on the duration of reionization of $\Delta z_{\rm re, 50} < 4.5$ (95\% C.L). We find these constraints are fairly robust to foregrounds assumptions. This trispectrum measurement is independent of, but consistent with, {\it Planck}'s optical depth measurement. This result is the first constraint on the epoch of reionization using the non-Gaussian nature of the kSZ signal.

astro-ph.CO↗

arXiv2023

Galaxy Clusters Discovered via the Thermal Sunyaev-Zel'dovich Effect in the 500-square-degree SPTpol Survey

We present a catalog of 689 galaxy cluster candidates detected at significance $\xi>4$ via their thermal Sunyaev-Zel'dovich (SZ) effect signature in 95 and 150 GHz data from the 500-square-degree SPTpol survey. We use optical and infrared data from the Dark Energy Camera and the Wide-field Infrared Survey Explorer (WISE) and \spitzer \ satellites, to confirm 544 of these candidates as clusters with $\sim94\%$ purity. The sample has an approximately redshift-independent mass threshold at redshift $z>0.25$ and spans $1.5 \times 10^{14} < M_{500c} < 9.1 \times 10^{14}$ $M_\odot/h_{70}$ \ and $0.03 1$. We use external radio data from the Sydney University Molonglo Sky Survey (SUMSS) to estimate contamination to the SZ signal from synchrotron sources. The contamination reduces the recovered $\xi$ by a median value of 0.032, or $\sim0.8\%$ of the $\xi=4$ threshold value, and $\sim7\%$ of candidates have a predicted contamination greater than $\Delta \xi = 1$. With the exception of a small number of systems $(<1\%)$, an analysis of clusters detected in single-frequency 95 and 150 GHz data shows no significant contamination of the SZ signal by emission from dusty or synchrotron sources. This cluster sample will be a key component in upcoming astrophysical and cosmological analyses of clusters. The SPTpol millimeter-wave maps and associated data products used to produce this sample are available at https://pole.uchicago.edu/public/data/sptpol_500d_clusters/index.html, and the NASA LAMBDA website. An interactive sky server with the SPTpol maps and Dark Energy Survey data release 2 images is also available at NCSA https://skyviewer.ncsa.illinois.edu.

astro-ph.CO↗

arXiv2023

Robotic Barrier Construction through Weaved, Inflatable Tubes

In this article, we present a mechanism and related path planning algorithm to construct light-duty barriers out of extruded, inflated tubes weaved around existing environmental features. Our extruded tubes are based on everted vine-robots and in this context, we present a new method to steer their growth. We characterize the mechanism in terms of accuracy resilience, and, towards their use as barriers, the ability of the tubes to withstand distributed loads. We further explore an algorithm which, given a feature map and the size and direction of the external load, can determine where and how to extrude the barrier. Finally, we showcase the potential of this method in an autonomously extruded two-layer wall weaved around three pipes. While preliminary, our work indicates that this method has the potential for barrier construction in cluttered environments, e.g. shelters against wind or snow. Future work may show how to achieve tighter weaves, how to leverage weave friction for improved strength, how to assess barrier performance for feedback control, and how to operate the extrusion mechanism off of a mobile robot.

cs.RO↗

arXiv2023

Simultaneous Millimeter-wave, Gamma-ray, and Optical Monitoring of the Blazar PKS 2326-502 During a Flaring State

Including millimeter-wave (mm-wave) data in multi-wavelength studies of the variability of active galactic nuclei (AGN) can provide insights into AGN physics that are not easily accessible at other wavelengths. We demonstrate in this work the potential of cosmic microwave background (CMB) telescopes to provide long-term, high-cadence mm-wave AGN monitoring over large fractions of sky. We report on a pilot study using data from the SPTpol instrument on the South Pole Telescope (SPT), which was designed to observe the CMB at arcminute and larger angular scales. Between 2013 and 2016, SPTpol was used primarily to observe a single 500 deg^2 field, covering the entire field several times per day with detectors sensitive to radiation in bands centered at 95 and 150 GHz. We use SPT 150 GHz observations to create AGN light curves, and we compare these mm-wave light curves to those at other wavelengths, in particular gamma-ray and optical. In this Letter, we focus on a single source, PKS 2326-502, which has extensive, day-timescale monitoring data in gamma-ray, optical, and now mm-wave between 2013 and 2016. We find PKS 2326-502 to be in a flaring state in the first two years of this monitoring, and we present a search for evidence of correlated variability between mm-wave, optical R band, and gamma-ray observations. This pilot study is paving the way for AGN monitoring with current and upcoming CMB experiments such as SPT-3G, Simons Observatory, and CMB-S4, including multi-wavelength studies with facilities such as VRO-LSST.

astro-ph.HE↗

arXiv2020

Optimal CMB Lensing Reconstruction and Parameter Estimation with SPTpol Data

We perform the first simultaneous Bayesian parameter inference and optimal reconstruction of the gravitational lensing of the cosmic microwave background (CMB), using 100 deg$^2$ of polarization observations from the SPTpol receiver on the South Pole Telescope. These data reach noise levels as low as 5.8 $\mu$K-arcmin in polarization, which are low enough that the typically used quadratic estimator (QE) technique for analyzing CMB lensing is significantly sub-optimal. Conversely, the Bayesian procedure extracts all lensing information from the data and is optimal at any noise level. We infer the amplitude of the gravitational lensing potential to be $A_\phi\,{=}\,0.949\,{\pm}\,0.122$ using the Bayesian pipeline, consistent with our QE pipeline result, but with 17\% smaller error bars. The Bayesian analysis also provides a simple way to account for systematic uncertainties, performing a similar job as frequentist "bias hardening," and reducing the systematic uncertainty on $A_\phi$ due to polarization calibration from almost half of the statistical error to effectively zero. Finally, we jointly constrain $A_\phi$ along with $A_{\rm L}$, the amplitude of lensing-like effects on the CMB power spectra, demonstrating that the Bayesian method can be used to easily infer parameters both from an optimal lensing reconstruction and from the delensed CMB, while exactly accounting for the correlation between the two. These results demonstrate the feasibility of the Bayesian approach on real data, and pave the way for future analysis of deep CMB polarization measurements with SPT-3G, Simons Observatory, and CMB-S4, where improvements relative to the QE can reach 1.5 times tighter constraints on $A_\phi$ and 7 times lower effective lensing reconstruction noise.

astro-ph.CO↗

arXiv2020

A Demonstration of Improved Constraints on Primordial Gravitational Waves with Delensing

We present a constraint on the tensor-to-scalar ratio, $r$, derived from measurements of cosmic microwave background (CMB) polarization $B$-modes with "delensing," whereby the uncertainty on $r$ contributed by the sample variance of the gravitational lensing $B$-modes is reduced by cross-correlating against a lensing $B$-mode template. This template is constructed by combining an estimate of the polarized CMB with a tracer of the projected large-scale structure. The large-scale-structure tracer used is a map of the cosmic infrared background derived from Planck satellite data, while the polarized CMB map comes from a combination of South Pole Telescope, BICEP/Keck, and Planck data. We expand the BICEP/Keck likelihood analysis framework to accept a lensing template and apply it to the BICEP/Keck data set collected through 2014 using the same parametric foreground modelling as in the previous analysis. From simulations, we find that the uncertainty on $r$ is reduced by $\sim10\%$, from $\sigma(r)$= 0.024 to 0.022, which can be compared with a $\sim26\%$ reduction obtained when using a perfect lensing template. Applying the technique to the real data, the constraint on $r$ is improved from $r_{0.05} < 0.090$ to $r_{0.05} < 0.082$ (95\% C.L.). This is the first demonstration of improvement in an $r$ constraint through delensing.

astro-ph.CO↗

arXiv2020

Searching for Anisotropic Cosmic Birefringence with Polarization Data from SPTpol

We present a search for anisotropic cosmic birefringence in 500 deg$^2$ of southern sky observed at 150 GHz with the SPTpol camera on the South Pole Telescope. We reconstruct a map of cosmic polarization rotation anisotropies using higher-order correlations between the observed cosmic microwave background (CMB) $E$ and $B$ fields. We then measure the angular power spectrum of this map, which is found to be consistent with zero. The non-detection is translated into an upper limit on the amplitude of the scale-invariant cosmic rotation power spectrum, $L(L+1)C_L^{\alpha\alpha}/2\pi < 0.10 \times 10^{-4}$ rad$^2$ (0.033 deg$^2$, 95% C.L.). This upper limit can be used to place constraints on the strength of primordial magnetic fields, $B_{1 \rm Mpc} < 17 {\rm nG} $ (95% C.L.), and on the coupling constant of the Chern-Simons electromagnetic term $g_{a\gamma} < 4.0 \times 10^{-2}/H_I $ (95% C.L.), where $H_I$ is the inflationary Hubble scale. For the first time, we also cross-correlate the CMB temperature fluctuations with the reconstructed rotation angle map, a signal expected to be non-vanishing in certain theoretical scenarios, and find no detectable signal. We perform a suite of systematics and consistency checks and find no evidence for contamination.

astro-ph.CO↗

arXiv2020

Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way

In two dimensions, topological phases of free Majorana fermions coupled to a $\mathbb{Z}_2$ gauge field are known to be classified according to the Chern number $\nu \in \mathbb{Z}$. Its value mod 16 specifies the type of anyonic excitations. In this paper, we investigate triangular vortex configurations (and their dual) in the Kitaev honeycomb model and show that fourteen of these sixteen phases can be obtained by adding a time-reversal symmetry-breaking term. Missing phases are $\nu=\pm 7$. More generally, we prove that any periodic vortex configuration with an odd number of vortices per geometric unit cell can only host even Chern numbers whereas odd Chern numbers can be found in other cases.

cond-mat.str-el↗

arXiv2020

An Improved Measurement of the Secondary Cosmic Microwave Background Anisotropies from the SPT-SZ + SPTpol Surveys

We report new measurements of millimeter-wave power spectra in the angular multipole range $2000 \le \ell \le 11,000$ (angular scales $5^\prime \gtrsim \theta \gtrsim 1^\prime$). By adding 95 and 150\,GHz data from the low-noise 500 deg$^2$ SPTpol survey to the SPT-SZ three-frequency 2540 deg$^2$ survey, we substantially reduce the uncertainties in these bands. These power spectra include contributions from the primary cosmic microwave background, cosmic infrared background, radio galaxies, and thermal and kinematic Sunyaev-Zel'dovich (SZ) effects. The data favor a thermal SZ (tSZ) power at 143\,GHz of $D^{\rm tSZ}_{3000} = 3.42 \pm 0.54~ \mu {\rm K}^2$ and a kinematic SZ (kSZ) power of $D^{\rm kSZ}_{3000} = 3.0 \pm 1.0~ \mu {\rm K}^2$. This is the first measurement of kSZ power at $\ge 3\,\sigma$. We study the implications of the measured kSZ power for the epoch of reionization, finding the duration of reionization to be $\Delta z_{re} = 1.0^{+1.6}_{-0.7}$ ($\Delta z_{re}< 4.1$ at 95% confidence), when combined with our previously published tSZ bispectrum measurement.

astro-ph.CO↗

arXiv2019

Constraints on Cosmological Parameters from the 500 deg$^2$ SPTpol Lensing Power Spectrum

We present cosmological constraints based on the cosmic microwave background (CMB) lensing potential power spectrum measurement from the recent 500 deg$^2$ SPTpol survey, the most precise CMB lensing measurement from the ground to date. We fit a flat $\Lambda$CDM model to the reconstructed lensing power spectrum alone and in addition with other data sets: baryon acoustic oscillations (BAO) as well as primary CMB spectra from Planck and SPTpol. The cosmological constraints based on SPTpol and Planck lensing band powers are in good agreement when analysed alone and in combination with Planck full-sky primary CMB data. With weak priors on the baryon density and other parameters, the CMB lensing data alone provide a 4\% constraint on $\sigma_8\Omega_m^{0.25} = 0.0593 \pm 0.025$.. Jointly fitting with BAO data, we find $\sigma_8=0.779 \pm 0.023$, $\Omega_m = 0.368^{+0.032}_{-0.037}$, and $H_0 = 72.0^{+2.1}_{-2.5}\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1} $, up to $2\,\sigma$ away from the central values preferred by Planck lensing + BAO. However, we recover good agreement between SPTpol and Planck when restricting the analysis to similar scales. We also consider single-parameter extensions to the flat $\Lambda$CDM model. The SPTpol lensing spectrum constrains the spatial curvature to be $\Omega_K = -0.0007 \pm 0.0025$ and the sum of the neutrino masses to be $\sum m_{\nu} < 0.23$ eV at 95\% C.L. (with Planck primary CMB and BAO data), in good agreement with the Planck lensing results. With the differences in the $S/N$ of the lensing modes and the angular scales covered in the lensing spectra, this analysis represents an important independent check on the full-sky Planck lensing measurement.

astro-ph.CO↗

arXiv2019

Measurements of B-mode Polarization of the Cosmic Microwave Background from 500 Square Degrees of SPTpol Data

We report a B-mode power spectrum measurement from the cosmic microwave background (CMB) polarization anisotropy observations made using the SPTpol instrument on the South Pole Telescope. This work uses 500 deg$^2$ of SPTpol data, a five-fold increase over the last SPTpol B-mode release. As a result, the bandpower uncertainties have been reduced by more than a factor of two, and the measurement extends to lower multipoles: $52 < \ell < 2301$. Data from both 95 and 150 GHz are used, allowing for three cross-spectra: 95 GHz x 95 GHz, 95 GHz x 150 GHz, and 150 GHz x 150 GHz. B-mode power is detected at very high significance; we find $P(BB < 0) = 5.8 \times 10^{-71}$, corresponding to a $18.1 \sigma$ detection of power. An upper limit is set on the tensor-to-scalar ratio, $r < 0.44$ at 95% confidence (the expected $1 \sigma$ constraint on $r$ given the measurement uncertainties is 0.22). We find the measured B-mode power is consistent with the Planck best-fit $\Lambda$CDM model predictions. Scaling the predicted lensing B-mode power in this model by a factor Alens, the data prefer Alens = $1.17 \pm 0.13$. These data are currently the most precise measurements of B-mode power at $\ell > 320$.

astro-ph.CO↗

arXiv2019

Optical-vortex diagnostics via Fraunhofer slit diffraction with controllable wavefront curvature

Far-field slit-diffraction of circular optical-vortex (OV) beams is efficient for measurement of the topological charge (TC) magnitude but does not reveal its sign. We show that this is because in the common diffraction schemes the diffraction plane coincides with the incident OV waist plane. With explicit involvement of the incident beam spherical wavefront and based on the examples of Laguerre-Gaussian modes we show that the far-field profile possesses an asymmetry depending on the wavefront curvature and the TC sign. These features enable simple and efficient ways for the simultaneous diagnostics of the TC magnitude and sign, which can be useful in many OV applications, including the OV-assisted metrology and information processing.

physics.optics↗

arXiv2019

Galaxy Clusters Selected via the Sunyaev-Zel'dovich Effect in the SPTpol 100-Square-Degree Survey

We present a catalog of galaxy cluster candidates detected in 100 square degrees surveyed with the SPTpol receiver on the South Pole Telescope. The catalog contains 89 candidates detected with a signal-to-noise ratio greater than 4.6. The candidates are selected using the Sunyaev-Zel'dovich effect at 95 and 150 GHz. Using both space- and ground-based optical and infrared telescopes, we have confirmed 81 candidates as galaxy clusters. We use these follow-up images and archival images to estimate photometric redshifts for 66 galaxy clusters and spectroscopic observations to obtain redshifts for 13 systems. An additional 2 galaxy clusters are confirmed using the overdensity of near-infrared galaxies only, and are presented without redshifts. We find that 15 candidates (18% of the total sample) are at redshift of $z \geq 1.0$, with a maximum confirmed redshift of $z_{\rm{max}} = 1.38 \pm 0.10$. We expect this catalog to contain every galaxy cluster with $M_{500c} > 2.6 \times 10^{14} M_\odot h^{-1}_{70}$ and $z > 0.25$ in the survey area. The mass threshold is approximately constant above $z = 0.25$, and the complete catalog has a median mass of approximately $ M_{500c} = 2.7 \times 10^{14} M_\odot h^{-1}_{70}$. Compared to previous SPT works, the increased depth of the millimeter-wave data (11.2 and 6.5 $\mu$K-arcmin at 95 and 150 GHz, respectively) makes it possible to find more galaxy clusters at high redshift and lower mass.

astro-ph.CO↗

arXiv2019

A Detection of CMB-Cluster Lensing using Polarization Data from SPTpol

We report the first detection of gravitational lensing due to galaxy clusters using only the polarization of the cosmic microwave background (CMB). The lensing signal is obtained using a new estimator that extracts the lensing dipole signature from stacked images formed by rotating the cluster-centered Stokes $Q/U$ map cutouts along the direction of the locally measured background CMB polarization gradient. Using data from the SPTpol 500 deg$^{2}$ survey at the locations of roughly 18,000 clusters with richness $\lambda \ge 10$ from the Dark Energy Survey (DES) Year-3 full galaxy cluster catalog, we detect lensing at $4.8\sigma$. The mean stacked mass of the selected sample is found to be $(1.43 \pm 0.4)\ \times 10^{14}\ {\rm M_{\odot}}$ which is in good agreement with optical weak lensing based estimates using DES data and CMB-lensing based estimates using SPTpol temperature data. This measurement is a key first step for cluster cosmology with future low-noise CMB surveys, like CMB-S4, for which CMB polarization will be the primary channel for cluster lensing measurements.

astro-ph.CO↗