A foreground "lens" star bends the light of a distant background source, splitting its image into two magnified images that straddle the lens. As the lens drifts across the line of sight, the total brightness traces a smooth, symmetric bump — a Paczyński light curve:
u(t) = √( u₀² + ((t − t₀)/tE)² )
A(u) = (u² + 2) / ( u √(u² + 4) )
θE ≈ 1.0 mas × √(M / M☉) (typical Galactic-bulge lens & source distances)
u is the lens–source separation in units of the Einstein radius θE — the angular radius at which a point mass perfectly ring-images a background source directly behind it. u₀ is the minimum separation (impact parameter) and tE is the time to cross one θE, set by the lens mass, distance and transverse velocity.
- u₀ — how close the lens passes to perfect alignment; smaller u₀ gives a sharper, brighter peak.
- tE — sets the real duration of the event (days to weeks for stellar lenses in the Milky Way).
- ρ (source radius) — a source star isn't a point; when u₀ is comparable to ρ the finite disk smears out and caps the peak, rounding the light curve's tip (modelled here with the common effective-separation approximation u_eff = √(u² + ρ²)).
- Lens mass — sets the physical Einstein radius θE shown at right. Mass, distance and velocity are individually degenerate in a single-lens light curve — only their combination tE is directly measured, which is why microlensing alone rarely pins down a lens's mass without extra data (parallax, finite-source effects).
This 2D view looks straight down the line of sight: the yellow source star sits at the centre, the orange lens star drifts past along its trajectory, and two faint cyan images straddle the lens whenever the source is magnified — exactly how surveys like OGLE and the upcoming Roman Space Telescope detect free-floating planets and faint stars that emit no light of their own.