Seidel sum

Seidel sums are mathematical expressions used in optics to describe and quantify the five primary aberrations of a lens: spherical aberration, coma, astigmatism, Petzval field curvature, and distortion. These aberrations represent deviations of the light wave emerging from a lens from a perfect spherical shape.1

The Seidel sums, denoted as (S_1) through (S_5), are calculated using paraxial ray tracing. Each sum corresponds to a specific aberration, which can distort the image formed by the lens. For example, the (S_5) aberration, known as distortion, can cause a square object to appear barrel-shaped or cushion-shaped. While these aberrations are typically very small, they are significant enough to require correction in high-quality optical systems.12