# Small Target Radiometric Performance of Drone-Based Hyperspectral Imaging Systems
## 1 Introduction  
For drone-based imaging platforms, radiometric calibration is accomplished using Lambertian targets (i.e., Empirical Line Method (ELM) [1, 2]) or a physics-based approach (i.e., At-Attitude Radiance Ratio (AARR) [3, 4]). Both techniques have the goal of compensating for and calibrating remote sensing imagery to surface reflectance. The transformation of remote sensing imagery to surface reflectance more readily aids in the identification of materials. During typical field data collection campaigns, the relative reflectance of Lambertian calibration targets are measured with respect to reference panels of high reflectivity (e.g., 99% SpectralonTM). The absolute radiometric information of these panels, albeit being calibration targets or reference panels, requires additional effort and complexity, however. The complexities reside in the understanding of the true reflectance of any Lambertian panel (in the field) in the presence of directional and hemispherical sources of illumination, for example [5]. That said, an advantage of field-deployed Lambertian targets is their large spatial extent, where statistical averaging can be employed to improve the signal-to-noise (SNR) of calibration curves for reflectance transformation. Even though high SNR can be achieved over Lambertian targets, these calibration curves are blindly applied to spatially unresolved targets and often not Lambertian [6]. Assessing the small target radiometric performance from Lambertian calibration targets cannot be achieved due to their needed size and because many sub-pixel limitations are hidden within their high uniformity. A physics-based approach to reflectance calibration uses remote sensing principles to transform imagery from entrance aperture-reaching spectral radiance to surface reflectance without in-scene calibration targets. The AARR technique uses the fundamental assumption that all objects in the scene are Lambertian reflectors such that the instantaneous measurements of the downwelling spectral irradiance (with a spectroradiometer) and object spectral radiance (with HSI system) can be used to estimate surface reflectance [4]. An advantage of this technique is the ability to correct hyperspectral (HS) imagery without in-scene calibration targets. However, this heavily relies on the calibrability of both instruments and the ability to accurately match different instruments (e.g., spectroradiometer to an HSI system). This calibration approach is limited to surface reflectance transformation, and no research has demonstrated the ability to examine HS radiometric performance. Key design trade-offs for HSI systems prioritize radiometric sensitivity and spectral resolution over spatial acuity, resulting in spatially aliased imagery [6]. This puts more reliance on the spectral identification of spatially unresolved objects within the scene. The application space that challenges HSI systems is within the detection of sub-pixel or small targets [7]. Within this application space, small targets cannot be averaged over multiple pixels like an extended target (e.g., Lambertian calibration target). Furthermore, extracting small target radiometric performance from Lambertian targets does not provide adequate analysis in comparison to the application space [8]. Thus, an emphasis now exists on the radiometric performance of HSI systems in the presence of sub-pixel or small targets. The deployment of point targets allows users the ability to radiometrically examine collected imagery for troubleshooting both their instrument and post-processing techniques (e.g., orthorectification process). From what we have seen, no other vicarious technique can support the analysis and understanding of HS imagery for applications involving small targets. Furthermore, there is a lack of vicarious techniques for assessing the radiometric accuracy and performance of orthorectified products at the pixel level for drone-based HSI systems.