# Landsat Surface Product Validation Instrumentation:
## 5 Mirror Empirical Line Method (MELM)  
### UAS Experiment  
During the primary BigMAC validation studies, a preliminary experiment on reflectance retrieval using SPARC technology was performed for UAS-based platforms. The goals of this experiment were to validate the perceived reflectance of the mirrors from calibrated imagery (i.e., from a diffuse reflectance-based ELM) and an initial application of a MELM on hyperspectral imagery. During the primary activities, the mirrors were deployed on black felt panels for isolating the mirror signal and optimal contrast; Figure 16. Because the mirrors are on a uniform background (felt panels), isolating the mirror signal is carried out by simply averaging the black felt signal. The focus of this experiment was on the mirror signals highlighted in Figure 16, providing two points for the application of the MELM technique. \[LER(\lambda,\theta_{i}^{m})=\left[\frac{1}{\cos\theta_{o}}+\left(f-\frac{1}{ \cos\theta_{o}}\right)G(\lambda)\right]\cdot\frac{N\pi R_{c}^{2}}{4\,GSD_{x}\, GSDy}\cdot\rho_{m}(\lambda,\theta_{i}^{m}) \tag{1}\]  
where the following nomenclature holds:  
\(\theta_{o}\): Solar zenith angle (relative to a horizontal surface). \(\theta_{i}^{m}\): Solar angle of incidence on mirror surface (relative to mirror surface normal). \(\rho_{m}(\lambda,\theta_{i}^{m})\): Mirror specular reflectance spectrum measured in the laboratory at \(\theta_{i}^{m}\). \(R_{c}\): Mirror radius of curvature. \(GSD_{x}GSD_{y}\): Along-scan and cross-scan ground sample distance of imaging sensor. \(N\): Number of identical mirrors contained in the SPARC target. \(f=1-cos2\theta_{m}\): Fraction of the hemispherical sky reflected by the mirror of  
half angular width \(\theta_{m}\) (measured from the center of curvature). \begin{table}
\begin{tabular}{l l l l} \hline ColdPool (TidBit) & 11:52 AM & 15:14 [0.125] & 15:28 [0.20] \\ \hline AmbientPool (TidBit) & 11:52 AM & 26.3 [0.02] & 25.6 [0.495] \\ \hline \multicolumn{4}{l}{**Flight 3—Noon—30 August 2021 (Estimated Pass 12:33)**} \\ \hline Object & Time (CDT) & \begin{tabular}{l} Ground-reference \\ temperature (C) \\ \end{tabular}  & FLIR temperature (C) \\ \hline Concrete (contact \\ thermocouple) & 12:33 PM & 42:30 & 40.49 \\ \hline ColdPool (TidBit) & 12:33 PM & 13.23 & 13.11 \\ \hline AmbientPool (TidBit) & 12:33 PM & 27.07 & 25.12 \\ \hline \multicolumn{4}{l}{**Flight 4—Afternoon—30 August 2021–  
An initial validation of the mirror reflectance, or LER(\(\lambda\)), from the calibrated imagery was demonstrated to be within the expected uncertainty of 7.20% (Figure 17). This conservative uncertainty was calculated using the RSS method for the SPARC radiative transfer and LER(\(\lambda\)) equations [28]. The black curves are calculated using Equation (1) with N = 1 producing the predicted \"low\" LER SPARC target. Using N = 2 predicts the \"high\" LER SPARC target spectrum, both using the same specular reflectance spectrum, \(\rho_{m}(\lambda,\theta_{i}^{m})\), of the mirrors measured in the laboratory. Both of the black curves with 7.20% error bars. For the validation, these are compared to the \"high\" (blue) and \"low\" (orange) spectra derived from the drone image data based on the gain and offset coefficients derived from the ELM analysis of the Permaflect Lambertian targets using the same two-point linear regression procedure in each spectral band. The primary uncertainty contributions are the drone GSD, mirror reflectance factor, and focal length. The high LER(\(\lambda\)) of the mirror targets was expected but not designed for this UAS's GSD. Due to a faulty lens iris, the f-number (f/\(\sharp\)) was larger than expected, which resulted in an overall low signal. Thus, the mirrors meant for a larger GSD were within the dynamic range of this sensor and equally valid for calibration. After validation, a two-point MELM technique was applied to the imagery and compared to the collected ground truth data for the RIT red felt target (Figure 17(right)).