Erratum: Measurement of Variations in Gas Refractive Index with 10^-9Resolution Using Laser Speckle (ACS Photonics (2022) 9:3 (830-836) DOI: 10.1021/acsphotonics.1c01355)

In the manuscript we incorrectly considered the inflection point of the Lorentzian similarity profile to be at the HWHM (half width at half-maximum) of the profile. More precisely, in the similarity profile given by S = 1/1+(Δn/Δn₀)²(1) (eq 4 in the main paper) where Δn₀is the HWHM, the inflection point is not found at Δn = Δn₀as claimed, but at Δn = Δn₀/√3. The purpose of using the inflection point was to maximize the slope. At Δn = Δn₀, the slope is -1/(2x₀) = -0.5/Δn₀. At Δn = Δn₀, the true inflection point, the slope is -9/(8√3 Δn₀) ≈ -0.65/Δn₀. The slope at the true inflection point is about 1.3 times greater. For a given uncertainty on the measurement of S, the corresponding uncertainty on the refractive index variation decreases when the slope increases. This does not change any conclusion of the manuscript. The point we used is simply not the optimal point. The uncertainty can be further reduced by a factor of 1.3.