# Re-Visiting Acoustic Sounding to Advance the Measurement of Optical Turbulence
## 3 Results and Discussion
The profiles of \(C_{n}^{2}\) at both 24.5 and 10.2 m for July 14 are overlaid in Figure 8. As is the case in Figures 6 and 7 above, each profile at the height of interest is obtained by combining the wind velocity and calculated small scale fluctuations of the index of refraction gradients with the velocity structure constant, \(C_{v}\), using the primary sonic anemometer's (whether at 24.5 or 10.2 m) point measurements. There is no discernible difference in the magnitude of the \(C_{n}^{2}\) at each level in Figure 8, as is evident in the top image of Figure 4; this is likely due to the turbulent refractive index gradient in the 10.2 to 24.5 m layer being the primary calculation component for the \(C_{n}^{2}\) at both levels. In Figure 9, the DELTA \(C_{n}^{2}\) profile overlays those of the sonic anemometers quite well through the day, even at the sunset/sunrise quiescent periods, though there is a notable separation at approximately 1700 UTC to 2400 UTC. The DELTA's lower afternoon \(C_{n}^{2}\) values brought its mean \(C_{n}^{2}\) value for the day to less than half the mean value found using both sonic anemometer methods. Examining the DELTA camera images shown in Figure 10 below seems to suggest this separation occurred as the target board's feature points became more difficult to discern and track, specifically from approximately 1700 UTC through 2100 UTC, when the target board became more backlit as the sun transited to the western portion of the sky. Additionally, the 14/0006 UTC image in Figure 10 shows that the target board illumination that was used during the field test appears to overwhelm the near sunset lighting conditions causing such a high contrast that only large feature separation distances are discernible. This could have had the effect of limiting the number of weighting functions such that the DELTA would provide more of an integrated path \(C_{n}^{2}\) value weighted slightly toward the camera end of the path--which was 30 m high on a 60-meter tower. This increases the likelihood that the DELTA and 30-meter mast sonic anemometer instruments were sampling significantly different volumes of air. The 14/1200 UTC image in Figure 10 shows the target board clearly displayed many different feature separations such that the full number of weighting functions--including one peaking near the 600-meter distance from the DELTA receiver to the 30-meter mast--should have been available for a true profiling capability. Additionally, it is evident in Figure 10 that the target board position shifted significantly in the images throughout the day, this had little consequence on the system's ability to quantify and profile turbulence along the path since multiple feature separation distances were always visible within the camera's processing \"mask\" field of view. Thus, the DELTA \(C_{n}^{2}\) profile measurement method is not susceptible to large-scale effects on the \(C_{n}^{2}\) quantification since DELTA only uses the measured differential tilt variances for the various feature separations rather than feature positions within the field of view. Figure 11 shows \(C_{n}^{2}\) profiles for 15 July 2020 at 24.5 m above the surface using \(C_{T}^{2}\) or alternatively via direct calculation of the structure function \(C_{v}^{2}\) as was carried out for the 14 July 2020 profile. Figure 10: Representative, individual image frames recorded at multiple times on 14 July using the DELTA eight-inch aperture camera at 100 Hz frame rate. As noted earlier, the system measures the differential motion, or tilts between pairs of feature points on the target as a function of their angular separation. Figure 9: Profiles of \(C_{n}^{2}\) at 24.5 above the surface using in situ sonic anemometer measurements (derived from \(C_{V}^{2}\), \(\
abla\left(n^{\prime}\right)\), \(\frac{\partial\left(V\right)}{\partial z}\), mean = 1.3 \(\times\) 10\({}^{-14}\), std dev = 3.6 \(\times\) 10\({}^{-14}\)) as well as the DELTA system (mean = 4.8 \(\times\) 10\({}^{-15}\), std dev = 3.4 \(\times\) 10\({}^{-15}\)).