A multipass optics (MPO) system is used to increase the optical path length in a limited volume. Well-known concepts such as the White-type cell and the Herriott-type cell are used in many applications. The optical path in these cells leaves a large portion of the cell volume unused. In contrast, MPO systems with astigmatic mirrors have significantly more beam passes per volume, but because of their reduced symmetry along the beam axis they are much more sensitive to misalignment. Our goal is to develop MPO systems that have both: the high beam densities of astigmatic MPO systems and the optical robustness of Herriott-type optics. We show that linearized optical ring resonators, which can be constructed by means of simple 2×2 optical ABCD-matrices, lead to suitable solutions. The concept is demonstrated using a MPO system with a base length of 150 mm and a total beam path length of 19.2 m, optimized for laser beams of 10 µm wavelength. The volume of the cell is 295cm3 with a beam density that is four times higher compared to a standard Herriott-type cell.