The extra color bands on the inner edge of a rainbow come from an inflection point in the crest of a wave of light. To understand how this works, George Airy wrote down what's now called the Airy integral—a basic example of an integral over a rapid decay homology class, and a gateway to the study of asymptotic series and Borel-Laplace summation. By thinking about how integrals like this arise in wave optics, we'll see that each one encodes the geometry of a translation surface. In fact, integrating over a rapid decay homology class is equivalent to taking the Laplace transform of a holomorphic function on a translation surface. This perspective might clarify the role of translation geometry in the theory of Borel-Laplace summation.