Application of Radon Transform to Multi-Angle Measurements Made by the Research Scanning Polarimeter: A New Approach to Cloud Tomography. Part I: Theory and Tests on Simulated Data

The Research Scanning Polarimeter (RSP) is an airborne along-track scanner measuring the polarized and total reflectances in 9 spectral channels. The RSP was a prototype for the Aerosol Polarimetery Sensor (APS) launched on-board the NASA Glory satellite. Currently the retrieval algorithms developed for the RSP are being adopted for the measurements of the space-borne polarimeters on the upcoming NASA’s Plankton, Aerosol, Cloud Ocean Ecosystem (PACE) satellite mission. The RSP’s uniquely high angular resolution coupled with the high frequency of measurements allows for characterization of liquid water cloud droplet sizes using the polarized rainbow structure. It also provides geometric constraints on the cumulus cloud’s 2D cross section yielding the cloud’s geometric shape estimates. In this study we further build on the latter technique to develop a new tomographic approach to retrieval of cloud internal structure from remote sensing measurements. While tomography in the strict definition is a technique based on active measurements yielding a tomogram (directional optical thickness as a function of angle and offset of the view ray), we developed a “semi-tomographic” approach in which tomogram of the cloud is estimated from passive observations instead of being measured directly. This tomogram is then converted into 2D spatial distribution of the extinction coefficient using inverse Radon transform (filtered backprojection) which is the standard tomographic procedure used e.g., in medical CT scans. This algorithm is computationally inexpensive compared to techniques relying on highly-multi-dimensional least-square fitting; it does not require iterative 3D RT simulations. The resulting extinction distribution is defined up to an unknown constant factor, so we discuss the ways to calibrate it using additional independent measurements. In the next step we use the profile of the droplet size distribution parameters from the cloud’s side (derived by fitting the polarized rainbows) to convert the 2D extinction distribution into that of the droplet number concentration. We illustrate and validate the proposed technique using 3D-RT-simulated RSP observations of a LES-generated Cu cloud. Quantitative comparisons between the retrieved and the original optical and microphysical parameters are presented.

Tomographic Proximity Imaging Using Conductive Sheet for Object Tracking

This paper proposes a proximity imaging sensor based on a tomographic approach with a low-cost conductive sheet. Particularly, by defining capacitance density, physical proximity information is transformed into electric potential. A novel theoretical model is developed to solve the capacitance density problem using the tomographic approach. Additionally, a prototype is built and tested based on the model, and the system solves an inverse problem for imaging the capacitance density change that indicates the object’s proximity change. In the evaluation test, the prototype reaches an error rate of 10.0–15.8% in horizontal localization at different heights. Finally, a hand-tracking demonstration is carried out, where a position difference of 33.8–46.7 mm between the proposed sensor and depth camera is achieved at 30 fps.