On-Orbit Calibration of Danuri/PolCam. I. Geometric Calibration

TL;DR

This paper presents a comprehensive on-orbit geometric calibration for Danuri/PolCam, addressing severe obliquity-induced distortions by building a large tie-point network with the Kaguya MI map and refining both observation timing and the camera model. The authors use SPICE-based geometry and high-resolution DEMs (SLDEM) to convert 2D image coordinates into 3D lunar coordinates and generate patch-orthorectified products, achieving RMSEs of about $0.87$ px cross-track and $1.48$ px along-track, comparable to previous lunar orbiters. The calibration enables accurate orthorectification and inter-channel co-registration across PolCam’s six channels, establishing a foundational framework for geometrically-corrected polarimetric data products and cross-mission comparisons. The study also highlights residual along-track errors due to sparse sampling and outlines plans to leverage higher-resolution extended-mission data to further improve accuracy.

Abstract

The wide-angle Polarimetric Camera (PolCam) onboard South Korea's first lunar orbiter, Danuri, is a pioneering instrument designed to conduct the first global polarimetric and high-phase-angle survey of the Moon. Precise geometric calibration is critical for this mission, particularly due to PolCam's highly oblique viewing geometry, which introduces significant topographic distortion. We present a comprehensive on-orbit geometric calibration that relies on 160,256 tie points derived from matching features between PolCam images and the well-orthorectified global map of the Kaguya Multiband Imager (MI). This dataset allows us to address two fundamental challenges: (1) the accurate reconstruction of the observation time for each line of an observation strip via a simple linear model, and (2) the refinement of the precise camera model, geometric model for PolCam optics. Our optimization method for these two challenges transforms the 2D image coordinates of identified features into 3D lunar coordinates and minimizes the reprojection error against the reference coordinates provided by the Kaguya MI map. From the refined observation time and camera model, we compute the precise longitude, latitude, and elevation of each pixel of an observed image. These estimated 3D coordinates are then used to generate orthorectified images, the final product of the geometric calibration. The resulting calibration achieves a geometric precision comparable to that of previous lunar orbiters and establishes the foundational framework necessary to produce geometrically-corrected data products of PolCam.

Figures (9)

• Figure 1: Schematic diagram of the PolCam observation geometry in lunar orbit. The inset in the top-left corner details the central wavelength and polarizer orientation for the six channels on the $1024\times1024$ CCD. Data are acquired from only six specific lines (one line per channel) of the 1024 lines
• Figure 2: A subset of tie points extracted by feature detection and matching techniques. (Left) A sub-region of a PolCam raw image. (Right) The corresponding sub-region of the Kaguya MI map. Circular symbols in both images mark the locations of detected tie points, with numeric labels identifying the matched pairs.
• Figure 3: Schematic of the PolCam instrument frame and its camera model. (a) Frame orientation of PolCam $(x_\mathrm{P}, y_\mathrm{P}, z_\mathrm{P})$, PolCam-L $(x_\mathrm{PL}, y_\mathrm{PL}, z_\mathrm{PL})$, and PolCam-R $(x_\mathrm{PR}, y_\mathrm{PR}, z_\mathrm{PR})$ relative to the spacecraft frame $(x_\mathrm{S}, y_\mathrm{S}, z_\mathrm{S})$. (b) A view of the PolCam-L $(y_\mathrm{PL})$ and PolCam-R $(y_\mathrm{PR})$ cameras along the flight direction. (c) The simplified pinhole camera model, which defines the ideal projection geometry. Optical distortion presents a misalignment between this ideal projection and the actual observed pixel location.
• Figure 4: Flowchart of the camera calibration process.
• Figure 5: Time offset between the Danuri spacecraft clock and ephemeris time from Feburary 2023 to February 2025.