Microlensing is a gravitational lensing method that magnifies light from distant objects using intervening masses.Gravitational microlensing is a phenomenon where an unresolved massive object (with mass ranging from a planet to a star) temporarily magnifies a distant source. Light rays are deflected by the lens's gravity, forming two images that merge into one spot. Amplification depends on the alignment and mass of the lens, reaching a maximum at the smallest angular distance. The light curve has a characteristic symmetry, and when a planetary companion is present, it produces sharp spikes—caustics (sharp brightness peaks). The method does not require the lens itself to shine, making it ideal for searching for substellar bodies and dark clumps.
Einstein in 1936 calculated the magnification for a star lens, but considered the event incredibly rare. In the 1960s, Refsdal and others pointed out its observational potential. The first detection came in 1993 by the MACHO project: monitoring millions of stars confirmed dark compact bodies in the Milky Way's halo. Surveys like OGLE and MOA now record thousands of events per year, discovering exoplanets and placing constraints on dark matter.
The lens equation relates the true and observed positions of the source. For a point mass, magnification is maximum at minimum u. The lens's motion relative to the line of sight gives a time-dependent u(t), producing a symmetric light curve of duration t_E. With a second mass (a planet), critical curves and caustics appear in the source plane; when the source crosses a caustic, the brightness changes sharply. Analysis of such anomalies yields the mass ratio and projected separation. Chromatic microlensing uses the absorption difference between the center and edge of the source disk, enabling reconstruction of the brightness profile of a distant star.
Microlensing reveals 'invisibles': lone rogue planets, black holes, dark dwarfs. This is how dark matter is mapped and distant icy worlds are discovered.
In 2017, microlensing revealed a lone planet the size of Jupiter wandering without a parent star through interstellar darkness.
| δθ | variable | centroid shift — angular centroid shift radian |
| u | variable | impact parameter in units of Einstein radius — impact parameter |
| θ_E | variable | Einstein radius — einstein radius radian |
| M_min | variable | Minimum lens mass — mass kilogram |
| sigma_th | variable | Astrometric precision threshold — angular resolution radian |
| D_L | variable | Distance to lens — distance metre |
| D_S | variable | Distance to source — distance metre |
| D_LS | variable | Distance between lens and source — distance metre |
| G | constant | Universal gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \propto | operator | Indicates proportionality — proportionality |
| μ | variable | magnification — magnification |
| ℓ | variable | distance to caustic — distance to caustic metre |
| ∝ | operator | indicates the left side scales as a constant times the right side — proportionality |
| h_L | variable | Lensed gravitational wave strain — gravitational wave strain |
| h_unL | variable | Unlensed gravitational wave strain — gravitational wave strain |
| μ | variable | Magnification factor — magnification |















