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gravitational lensing measures the gravitational influence of matter without requiring that matter to shine. In general relativity a point mass produces small-angle deflectionFor a thin lens, with angular-diameter distances $D_d,D_s,D_{ds}$,Image multiplicity, distortion and magnification therefore constrain projected gravitating mass, with source and lens geometry measured separately.

Strong lensing gives multiple images, arcs and Einstein rings. Their positions and, where available, time delays constrain a central mass distribution. Weak lensing measures correlated small image distortions over a larger field. Using the critical surface density for gravitational lensing and reduced gravitational shear, the convergence and shear satisfyBecause intrinsic galaxy shapes are unknown, weak shear is inferred statistically using many sources. Point-spread-function anisotropy, shear calibration, photometric redshifts, intrinsic alignments and foreground contamination must be controlled.

An inferred lensing mass can be compared with the independently estimated stellar and hot-gas mass. The bullet Cluster dark-matter separation provides a particularly informative separation of components: the collisional X-ray-emitting gas is displaced from the galaxies, while lensing mass peaks approximately follow the less-collisional galaxy component. The primary analysis combined wide-field and Hubble imaging rather than inferring lensing mass from X-ray hydrostatic equilibrium.^[ref] This favors a dominant relatively collisionless unseen component. Translating a merger offset into a particle self-interaction cross section also requires a merger model and projection uncertainties; lensing does not directly reveal a WIMP's mass or quantum numbers.

Microlensing tests a different possibility: dark matter in compact objects. A compact foreground lens can create an unresolved, time-dependent magnification of a background star. Event frequency and duration constrain the abundance and mass range of compact lenses only after survey cadence, detection efficiency, blending, source sizes and halo geometry are included. Achromaticity and the expected light-curve shape help distinguish simple lensing from intrinsic variability. A null survey result does not exclude every compact-object mass at every location.

Weak-lensing correlations and small-scale strong-lens structure also test the matter power spectrum and halo substructure, potentially distinguishing cold from warm free-streaming behavior. Baryonic feedback can change the same small-scale mass distribution. There are intrinsic inversion ambiguities: the mass-sheet transformationleaves reduced gravitational shear unchanged. Source-redshift information, absolute magnification or other data can restrict such degeneracies. Lensing establishes where gravitating matter is and tests its distribution and interactions; identification of its particle species requires complementary evidence.