# Small Target Radiometric Performance of Drone-Based Hyperspectral Imaging Systems
## 1 Introduction
The only vicarious method that can investigate the radiometric performance of HSI systems to radiometrically known small targets is the SPecular Array for Radiometric Calibration (SPARC) technique [9]. The SPARC technique produces a radiometrically accurate point target for assessing the small target radiometric performance of imaging systems. More importantly, when assessing the small target radiometric performance of a drone-based HSI system, we note that orthorectification is required as a post-processing step for mapping pixel location to a true ground position at a uniform pixel scale. Unfortunately, there are inaccuracies within this post-processing step from interpolation schemes (e.g., nearest neighbor) related to the assumption of a uniform pixel scale (i.e., that every pixel is square) [10]. Furthermore, inaccuracies accumulate from platform motion, HS mounting schemes, boresight offsets, sensor models, resolution scales within Digital Elevation Models (DEMs), and the absolute accuracy of Global Positioning Systems (GPSs)/Inertial Measurement Units (IMUs). All these inaccuracies manifest into an aggregate system level problem that requires evaluation utilizing field experiments and cannot be addressed separately due to the unforeseen correlations. Testing, characterizing, and understanding these system level effects using the SPARC method, as it relates to small target radiometric performance, is thus the subject of this paper. The objective of this work is to demonstrate the extraction of small target radiometric performance for drone-based HSI systems through the use of convex mirrors. The SPARC technique offers a unique advantage over Lambertian targets since convex mirrors provide a radiometrically known point target. The deployment of characterized convex mirrors with supporting field spectroradiometers tested the absolute radiometric response and repeatability of a drone-based HSI system to small targets. When compared to Lambertian targets, the radiometric repeatability varied significantly from image to image, even though the HS instrument was radiometrically accurate. In general, the experiment demonstrated that the HS instrument tends to overestimate the radiometric signal from small targets due to errors introduced in the orthorectification process. The interpolation schemes used within orthorectification is theorized to account for many artifacts, which can change the spectral signature and introduce energy that was never imaged. This paper is outlined as follows. Section 2 gives a background overview of our drone-based imaging platform and laboratory validation efforts of the HSI system. It then goes into detail about the theory behind the quantities that formulate the SPARC technique from a radiometric and spatial perspective. Section 3 speaks to the experiment overview, including the methodologies used in the field measurements and extraction of the radiometric signals related to Lambertian and point targets. Section 4 presents the results, where Lambertian and point targets are assessed over the entire experiment. In this section, the radiometric performance of small targets, after orthorectification, is scrutinized. Lastly, Appendix A and Appendix B outline a full derivation of the SPARC equation (i.e., entrance aperture-reaching spectral radiance) and the propagated uncertainty.