Highly resolved determination of refractive index is vital in fields ranging from biosensing through to laser range finding. Laser speckle is known to be a sensitive probe of the properties of the light and the environment, but to date speckle-based refractive index measurements have been restricted to 10-6 resolution. In this work we identify a strategy to optimize the sensitivity of speckle to refractive index changes, namely, by maximizing the width of the distribution of optical path lengths in the medium. We show that this can be realized experimentally by encapsulating the medium of interest within an integrating sphere. While mitigating against laser-induced heating effects, we demonstrate that variations of the refractive index of air as small as 4.5 × 10-9 can be resolved with an uncertainty of 7 × 10-10. This is an improvement of 3 orders of magnitude when compared to previous speckle-based methods.
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