Maximizing precision in saturation-limited absorption measurements

Quantum fluctuations in the intensity of an optical probe is noise which limits measurement precision in absorption spectroscopy. Increased probe power can offer greater precision; however, this strategy is often constrained by sample saturation. Here, we analyze measurement precision for a generalized absorption model in which we account for saturation and explore its effect on both classical and quantum probe performance. We present a classical probe-sample optimization strategy to maximize precision and find that optimal probe powers always fall within the saturation regime. We apply our optimization strategy to two examples, high-precision Doppler broadened thermometry and an absorption spectroscopy measurement of chlorophyll a. We derive a limit on the maximum precision gained from using a nonclassical probe and find a strategy capable of saturating this bound. We evaluate amplitude-squeezed light as a viable experimental probe state and find it capable of providing precision that reaches to within >85% of the ultimate quantum limit with currently available technology.