A Practical Approach to Plate-Solving of Astronomical Images Based on Least-Squares Estimation
Year: 2025
Type: conference-paper
Abstract: A common task in astrophotography (i.e. imaging of space) is image registration, also referred to as plate solving. Broadly speaking, this is the task of determining the direction and orientation of an astronomical image with respect to the celestial sphere based on recognition of star patterns found in the image. The development of plate solving tools is generally in the domain of astronomers, and the most widely used method for the past several years is an application known simply by the name Astrometry. Plate solving is also required to determine a spacecraft’s attitude when utilizing a star tracker camera, and therefore a number of star tracker manufacturers have developed their own proprietary techniques. Most plate solving methodologies involve comparing stars in an image with a known database of simulated template images that are developed based on a variety of assumed fields of view, from narrow (e.g. 0.5 degrees or less) to wide (e.g. 20 degrees or greater). A typical plate solving run involves a search through the image database to find a match among asterisms (i.e. groups of stars) in the real image (which could be construed as mini-constellations). The runtime of this search can typically be improved if either (a) the camera’s parameters (e.g. focal length, focal plane dimensions, and pixel size) and/or (b) the approximate direction and orientation of the image are already known. Otherwise, a blind search proceeds, which can incur significant runtime. Depending on the platform, this could be upwards of several minutes, which is unacceptable for many realistic applications, such as processing a large number of images for various purposes. In this paper the authors develop an alternate approach to plate solving compared to those in current use or in the literature. This approach assumes the camera’s focal length and pixel size are known. The proposed procedure is as follows: -Given a space image, detect and localize each object (i.e. star) in the camera frame in terms of local (x, y) pixel coordinates (e.g. right-down-forward) -For each star detected, combine its (x, y) location with the above-mentioned camera parameters to calculate the unit vector from the camera (i.e. observing platform) to the star, expressed in the local coordinate frame (right-down-forward) -Compare the juxtaposition of unit vectors of the stars in the image with those contained in a standard star catalog (e.g. Tycho-2) to eventually yield a least-squares solution of the coordinate transformation (in terms of a direction cosine matrix) between the local camera frame and the inertial frame of the star catalog (e.g. J2000) This last step will be achieved by dividing the star catalog into sectors of right ascension and declination (RA and Dec), where the size of each sector in degrees will be roughly equal to the image’s known field of view. Proceeding one sector at a time, a comparison between the stars in an image and those in the star catalog can be conducted by solving the over-determined attitude navigation problem (more commonly known as Wahba’s problem) and calculating the residuals (i.e. RA and Dec pointing error) between the two sets of unit vectors. A “match” can then be assessed based on how close the residuals are to some chosen threshold in degrees. Anticipated advantages of this technique over other methods include: -Potentially faster runtime -Simplicity of the algorithm, leading to greater flexibility in terms of the platform (i.e. operating system) on which the algorithm can operate -Transparency of the code, leading to better general understanding of the process and more efficient troubleshooting if an image fails to solve The potential applications of this algorithm reach beyond general astrophotography; examples include onboard spacecraft attitude determination and optical space situational awareness. References to be cited in the paper will include: -Shuster, M.D., “The generalized Wahba problem,” The Journal of the Astronautical Sciences, 2006 -Lang, D. W. Hogg, K. Mierle, M. Blanton, and S. Roweis, “Astrometry.net: Blind astrometric calibration of arbitrary astronomical images,” Oct. 2009. -Curtis, D., “Orbital mechanics for engineering students,” 4th edition. -Hog E., Fabricius C., Makarov V.V., Urban S., Corbin T., Wycoff G., Bastian U., Schwekendiek P., Wicenec A., “The Tycho-2 Catalogue of the 2.5 Million Brightest Stars,” 2000.
DOI: 10.2514/6.2025-99706
Authors: Cindy Uyen Chi Nguyen, Thomas Alan Lovell
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4413191601