the Nancy Grace Roman Space Telescope and the Vera C. Rubin Observatory. Mathematics The mathematics of microlensing, along with modern notation, are described by Gould and we use his notation in this section, though other authors have used other notation. The Einstein radius, also called the Einstein angle, is the angular radius of the Einstein ring in the event of perfect alignment. It depends on the lens mass M, the distance of the lens dL, and the distance of the source dS: (in radians). For M equal to 60 Jupiter masses, dL = 4000 parsecs, and dS = 8000 parsecs (typical for a Bulge microlensing event), the Einstein radius is 0.00024 arcseconds (angle subtended by 1 au at 4000 parsecs). By comparison, ideal Earth-based observations have angular resolution around 0.4 arcseconds, 1660 times greater. Since is so small, it is not generally observed for a typical microlensing event, but it can be observed in some extreme events as described below. Although there is no clear beginning or end of a microlensing event, by convention the event is said to last while the angular separation between the source and lens is less than . Thus the event duration is determined by the time it takes the apparent motion of the lens in the sky to cover an angular distance . The Einstein radius is also the same order of magnitude as the angular separation between the two lensed images, and the astrometric shift of the image positions throughout the course of the microlensing event. During a microlensing event, the brightness of the source is amplified by an amplification factor A. This factor depends only on the closeness of the alignment between observer, lens, and source. The unitless number u is defined as the angular separation of the lens and the source, divided by . The amplification factor is given in terms of this value: This function has several important properties. A(u) is always greater than 1, so microlensing can only increase the brightness of the source star, not decrease it. A(u) always decreases as u increases, so the closer the alignment, the brighter the source becomes. As u approaches infinity, A(u) approaches 1, so that at wide separations, microlensing has no effect. Finally, as u approaches 0, for a point source A(u) approaches infinity as the images approach an Einstein ring. For perfect alignment (u = 0), A(u) is theoretically infinite.