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Starshades are a leading technology to enable the detection and spectroscopic characterization of Earth-like exoplanets. In this paper we report on optical experiments of sub-scale starshades that advance critical starlight suppression technologies in preparation for the next generation of space telescopes. These experiments were conducted at the Princeton starshade testbed, an 80 m long enclosure testing 1/1000th scale starshades at a flight-like Fresnel number. We demonstrate 1e-10 contrast at the starshade's geometric inner working angle across 10% of the visible spectrum, with an average contrast at the inner working angle of 2.0e-10 and contrast floor of 2e-11. In addition to these high contrast demonstrations, we validate diffraction models to better than 35% accuracy through tests of intentionally flawed starshades. Overall, this suite of experiments reveals a deviation from scalar diffraction theory due to light propagating through narrow gaps between the starshade petals. We provide a model that accurately captures this effect at contrast levels below 1e-10. The results of these experiments demonstrate that there are no optical impediments to building a starshade that provides sufficient contrast to detect Earth-like exoplanets. This work also sets an upper limit on the effect of unknowns in the diffraction model used to predict starshade performance and set tolerances on the starshade manufacture.