Editing Gravitational lens (section)

==Measuring weak lensing==
[[File:Galaxy cluster MACS J2129-0741 and lensed galaxy MACS2129-1.jpg|thumb|Galaxy cluster MACS J2129-0741 and lensed galaxy MACS2129-1.<ref>{{cite web|title=Galaxy cluster MACS J2129-0741 and lensed galaxy MACS2129-1|url=https://www.spacetelescope.org/images/opo1726a/|website=www.spacetelescope.org|access-date=23 June 2017}}</ref>]]
Kaiser, Squires and Broadhurst (1995),<ref name=KSB-1995>{{cite journal|last1=Kaiser|first1=Nick|last2=Squires|first2=Gordon|last3=Broadhurst|first3=Tom|title=A Method for Weak Lensing Observations|journal=The Astrophysical Journal|date=August 1995|volume=449|pages=460–475|doi=10.1086/176071|arxiv = astro-ph/9411005 |bibcode = 1995ApJ...449..460K |s2cid=119382511}}</ref> Luppino & Kaiser (1997)<ref name=LK-1997>{{cite journal|last1=Luppino|first1=G. A.|last2=Kaiser|first2=Nick|title=Detection of Weak Lensing by a Cluster of Galaxies at z = 0.83|journal=The Astrophysical Journal|date=20 January 1997|volume=475|issue=1|pages=20–28|doi=10.1086/303508|arxiv = astro-ph/9601194 |bibcode = 1997ApJ...475...20L |s2cid=6294167}}</ref> and Hoekstra et al. (1998) prescribed a method to invert the effects of the [[point spread function]] (PSF) smearing and shearing, recovering a shear estimator uncontaminated by the systematic distortion of the PSF. This method (KSB+) is the most widely used method in weak lensing shear measurements.<ref>{{cite book |title=Statistical Challenges in Modern Astronomy IV: Proceedings of a Conference Held at Pennsylvania State University, University Park, Pennsylvania, USA, 12–15 June 2006, Volume 371 |edition=illustrated |first1=Gutti Jogesh |last1=Babu |first2=Eric D. |last2=Feigelson |publisher=Astronomical Society of the Pacific |year=2007 |isbn=978-1-58381-240-2 |page=66 |url=https://books.google.com/books?id=dHPvAAAAMAAJ}}</ref><ref>{{cite book |title=A Pan-Chromatic View of Clusters of Galaxies and the Large-Scale Structure |edition=illustrated |first1=Manolis |last1=Plionis |first2=O. |last2=López-Cruz |first3=D. |last3=Hughes |publisher=Springer Science & Business Media |year=2008 |isbn=978-1-4020-6940-6 |page=233 |url=https://books.google.com/books?id=TnovKp-nJuMC&pg=PA233}}</ref>
 
Galaxies have random rotations and inclinations. As a result, the shear effects in weak lensing need to be determined by statistically preferred orientations. The primary source of error in lensing measurement is due to the convolution of the PSF with the lensed image. The KSB method measures the ellipticity of a galaxy image. The shear is proportional to the ellipticity. The objects in lensed images are parameterized according to their weighted quadrupole moments. For a perfect ellipse, the weighted quadrupole moments are related to the weighted ellipticity. KSB calculate how a weighted ellipticity measure is related to the shear and use the same formalism to remove the effects of the PSF.<ref>{{cite book |title=Gravitational Lensing: An Astrophysical Tool |edition=illustrated |first1=Frederic Courbin, Dante Minniti |last1=Frederic Courbin, Dante Minniti |publisher=Springer |year=2008 |isbn=978-3-540-45857-9 |page=69 |url=https://books.google.com/books?id=TsxrCQAAQBAJ&pg=PA69}}</ref>

KSB's primary advantages are its mathematical ease and relatively simple implementation. However, KSB is based on a key assumption that the PSF is circular with an anisotropic distortion. This is a reasonable assumption for cosmic shear surveys, but the next generation of surveys (e.g. [[Large Synoptic Survey Telescope|LSST]]) may need much better accuracy than KSB can provide.