Among all photosynthetic organisms, green bacteria have evolved one of the most efficient light-harvesting antenna, the chlorosome, that contains hundreds of thousands of bacteriochlorophyll molecules, allowing these bacteria to grow photosynthetically by absorbing only a few photons per bacteriochlorophyll molecule per day. In contrast to other photosynthetic light harvesting antenna systems, for which A protein scaffold imposes the proper positioning of the chromophores with respect to each other, in chlorosomes, this is accomplished solely by self-assembly. This has aroused enormous interest in the structure function relations of these assemblies, as they can serve as blueprints for artificial light harvesting systems. In spite of these efforts, conclusive structural information is not available yet, reflecting the sample heterogeneity inherent to the natural system. Here we combine mutagenesis, polarization-resolved single-particle fluorescence excitation spectroscopy, cryo-electron microscopy, and theoretical modeling to study the chlorosomes of the green sulfur bacterium Chlorobaculum tepidum. We demonstrate that only the combination of these techniques yields unambiguous information on the structure of the bacteriochlorophyll aggregates within the chlorosomes. Moreover, we provide a quantitative estimate of the curvature variation of these aggregates that explains ongoing debates concerning the chlorosome structure.