Inferring Anthropogenic Space Object Characteristics via Quanta Photogrammetry (QPM)

Dr. Daniel Kucharski, my research associate, and I have been progressing what we are calling the Biometrically-Inspired Space Object Recognition (BISOR) method leveraging Quanta Photogrammetry (QPM) as a basis.

Claude Shannon was awarded the Kyoto Prize and made some seminal statements. He stated that communication is the transmission of information from one point to another, including computing the manipulation and transformation of information. He also said that the main problem of information engineers is in getting a wave from one point to another and understanding the knowledge it conveys about an entity or event. 

Information theory sets up quantitative measures of information and of the capacity of various systems to transmit, store, and process information. One meaningful question is, “What are the upper bounds on what is possible to achieve with a given information carrying medium (channel)?” We are specifically interested in casting the anthropogenic space object (ASO) characterization via remote sensing problem in an information system and theoretic framework and exploring the generalized mechanism to infer or reconstruct the characteristics of objects which have interacted with measured photons. Our research here can be summarized by one question: “What is the theoretical bound on information about ASOs that can be extracted from measured photons?” We wish to answer this fundamental theoretical question in conjunction with experimental research. We propose to use Quanta Photogrammetry (QPM) as an optical data registration and representation method that captures and conveys scientific information about a physical object through the process of detection and mapping single photons reflected or emitted off the ASO surface elements in the ASO’s body-fixed reference frame.

In general, an Information System has the following elements:

1. An information source that produces new information or "message" to be transmitted. In our case, this is any given ASO.
2. A transmitter that transforms or encodes this information into a suitable form for the channel. This transformed message is called the signal. In our case, information is encoded onto a photon at the moment of photon reflection and emission as a result of the interaction between the surface material and photon flux. 
3. The channel upon which the encoded information or signal is transmitted to the receiving point. During transmission the signal may be changed or distorted and these effects are generally treated as noise. For us, this is the so-called “free-space optical link.” The photon arrival rate (the signal) is affected by the atmospheric effects, attenuation, absorption, etc. We also suffer a significant loss in that we only measure a fraction of all reflected and emitted photons from any given ASO. However, our proposed framework is uniquely favored in addressing this problem since each measured photon is treated independently in its information carrying capacity. Typical optical sensors accumulate photons until a minimum threshold is reached. This accumulation effectively averages the information content of the individual photons and can be considered an information-diffusion process.
4. The receiver which decodes or translates the received signal back into the original message or an approximation of it. This is at the heart of the proposed work. To wit, the ability to not only measure individual photons but also interpret their information content so as to reconstruct the characteristics of the anthropogenic space object they interacted with. The decoding process is therefore both measuring and interpreting these photons via algorithms. 
5. The destination or intended recipient of the information.

The attached image is a QPM formed by processing hypertemporal single-pixel (for now) photon counting (>50KHz) of reflected photons off of the defunct TOPEX satellite in LEO. These are real data. The QPM is what is represented in the Mollweide projection (a 2D representation of a sphere). The polar plot is looking at the spacecraft’s south pole also assuming a Spacecraft Centered Celestial Sphere (SCCS). 

The first thing we do is infer the ASO inertial-to-body orientation and body rates. When we get it wrong, the QPM and Polar plots display blurring (wrong body rates) and distortion (wrong rotation axis). 

This is shown in the top plot. The middle and bottom plots show it when we get it correct. There is distortion because we have a rotation axis error to adjust but it’s mostly there. 0 longitude is the front of TOPEX, +/- 90 are the side, and +/-180 is the back. The bottom plot is the same as the middle except in a log scale that makes the specular returns even more salient. 

We will be submitting a journal paper on this soon. The more exciting thing for me to share with you is that we now have a way of displaying this in 3D. Someone in the Bahamas, Fanny Oldfield, has volunteered to generate a few 3D CAD models of satellites, TOPEX being one of them, in so called .obj file formats. We’ve taken this CAD model and represented the QPM in 3D in context of the model. See and share the following link. We’re just getting started. By leveraging the Texas Advanced Computing Center (TACC), once we have a method and process down…we will scale this to all ASO’s possible and automate this to be accessible to the widest possible community. We believe we are paving the way for a new way to represent and exchange information regarding the physical characteristics of all ASOs.

http://astria.tacc.utexas.edu/BISOR  

Enjoy the link…it will take 15 seconds or so to load. To be clear, the 3D QPM at the website is the same data as the QPM from the attached image (lower left plot). Use your mouse to zoom in, out, and all around.

We've added VR compatibility - a new button in the right bottom corner and when you click a point it will display the body-fixed location of the point (az/el in degrees) and the corresponding photon count intensity in Hz - meaning 'photon count per second'.