SOFT Plate Solver Simulation in One Dimension

Live Script simulating SO(3) Fourier transform (SOFT) plate solving in 1D.

A plate solver registers an image of the night sky using a catalog of known stars and discovers the camera pose while identifying the stars in the image. A companion script uses a 3D SO(3) Fourier transform (SOFT) method to solve real night sky images. This educational Live Script presents a 1D plate simulation (for a 'sky' that is a circle rather than a sphere) to illustrate the SOFT method in a way readily understood and visualized.

It creates a catalog of point sources with a realistic brightness (magnitude) distribution and a simulated Milky Way over-density, creates from a sub catalog with reduced magnitude an image of stars over a smaller image range, adds noise stars, drop-outs, and location jitter to the image, computes the Fourier coefficients of both the catalog and image points in closed form, cross-correlates these with a high-pass filter, normalizes, and then finds and interpolates the peak corresponding to the camera pointing direction and refines. It then identifies the image star candidates based on the final "camera pose."

A few failure modes that appear also in the 3D case are pointed out and may be explored. A random correlation of the image with stars in a crowded part of the sky can exhibit a higher value than the true correlation. This distraction can be eliminated by filtering out low frequencies. A catalog searched deeper than the image warrants can result in wrong chance identifications. The number can be reduced by requiring the magnitudes to match as well, but in reality the image candidate magnitude may be poorly determined.

This script will interest students and instructors of physics and astronomy. Calculus is assumed in some derivations but is not essential. Every governing parameter in the script is made available for tuning and study. 'Try this' suggestions, 'Challenges,' and references are included for further exploration.

Additional educational Live Scripts by the author are here.