Using the bending of light by massive objects to detect faint or dark celestial bodies.Gravitational microlensing is an astronomical technique that uses the gravitational field of a massive object to bend and magnify light from a background star, acting as a natural lens. Unlike strong lensing, which produces dramatic arcs and multiple images, microlensing causes a temporary brightening of the background source as the lens passes in front of it. This effect is sensitive to dark, faint, or isolated objects that emit little or no light, making it a powerful tool for detecting exoplanets, black holes, and dark matter candidates.
The concept was proposed by Einstein in 1936 and by Soviet astronomer Todorov in 1937, but the first microlensing event was observed in 1993 by the MACHO and EROS collaborations.
When a foreground object (the lens) passes near the line of sight to a distant star, its gravity warps spacetime, focusing more light toward the observer. The observed brightness of the background star rises and falls smoothly over days to weeks, following a characteristic curve. The peak magnification and duration depend on the lens mass, distance, and relative motion. By analyzing these light curves, astronomers can infer the lens properties, even if it is invisible.
Microlensing surveys like OGLE and MOA have discovered thousands of exoplanets, including free-floating planets, and are used to search for primordial black holes as dark matter candidates.
Microlensing can detect planets as small as Earth orbiting stars thousands of light-years away, even though the planet itself never emits or reflects enough light to be seen directly.
| kappa | variable | weak lensing convergence — convergence |
| theta | variable | angular position on the sky — angular position radian |
| chi | variable | comoving distance to the source — comoving distance metre |
| chi' | variable | comoving distance along the line of sight — comoving distance metre |
| q | variable | lensing efficiency function — lensing efficiency |
| a | variable | scale factor — scale factor |
| f_K | variable | comoving angular diameter distance — comoving angular diameter distance metre |
| delta | variable | matter density contrast — density contrast |
| H_0 | constant | current expansion rate of the universe — hubble constant = 2.2e-18 per second |
| Omega_m | constant | ratio of matter density to critical density today — matter density parameter = 0.315 |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| ∫ | operator | summation over infinitesimal elements — integral |
| 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 |















