Ruze's equation is an equation relating the gain of an antenna to the root mean square (RMS) of the antenna's random surface errors. The equation was originally developed for parabolic reflector antennas, and later extended to phased arrays. The equation is named after John Ruze, who introduced the equation in a paper he wrote in 1952. The equation states that the antenna's gain is inversely proportional to the exponential of the square of the RMS surface errors. Mathematically, the equation for parabolic reflector antennas can be expressed as: