I will start by decribing two "variants" of the Poisson formula that are due to Guinand and Meyer. I will then show how these two formulas can be interpreted in terms of the orthospectrum (a family of characteristic lengths) of two convex bodies. With that interpretation in mind, Guinand-Meyer's formulas correspond to the case where the convex bodies are reduced to two points in dimension 3. I will explain how this formula can be extended to two general (strictly) convex bodies and how it encodes certain geometric quantities (mixed volumes). This was obtained in a joint work with Nguyen Viet Dang and Matthieu Léautaud.