Angle of incidence sampling technique for stray light rejection performance estimation of lunar terrestrial imagers

Abstract

The primary mission of the two Lunar Terrestrial Imagers (LUTIs) onboard the Korea Pathfinder Lunar Orbiter (KPLO) is to obtain high-resolution images of the Moon that will enable landing site identification and certification and target observation of interesting places. The two LUTIs are panchromatic push-broom line scanners, with an instantaneous field-of-view (IFOV) of 25-microradians. The two LUTIs are designed to provide 2.5 m scale panchromatic images over a combined 9.75 km swath from the nominal 100 km orbit. Each LUTI utilized a 400 mm focal length Ritchey-Chretien telescope that images onto a 2048-pixel charge coupled device (CCD) line array, providing an IFOV of 25-microradians and a cross-track field-of-view of 2.88° each. The design also incorporates a 131 mm long sunshade to prevent illumination of the primary mirror by rays more than 12.4° off axis. There are key parameters to quantify stray light effects by external sources, i.e., ray paths, irradiance distribution at the focal plane arrays, point source transmittance and radiometric error due to the stray light. All the parameters can be simulated using the forward ray tracing computation with the stray light model and the extended scene integration. The stray light model is the surface-based three-dimensional geometry for ray tracing computation using opto-mechanical design and those optical properties including reflection-, transmission-, absorption-coefficients, and bi-directional scattering distribution function (BSDF) models. After building the stray light model, ray sets are prepared and located at the entrance aperture (EA) to conduct the forward ray tracing computation towards the focal plane (FP). For this, incident angle boundaries are limited in consideration of the viewing geometry and each angle of incidence (AOI) is weighted by the backward ray tracing computation results, then representative AOIs are selected considering sampled regions for extended scene integration. In the ‘Sampling AOIs’ process, weighting factors are to be assigned to each incident angle. The backward ray tracing computation can be also used as possible ray paths investigation from the EA towards the FP. Assuming that a ray leaving from the FP is reflected or transmitted on the optical or mechanical surfaces along the mth and nth ray paths including scattered at an intervening object I and finally arrived at the EA, the mth and nth ray paths combination could be one of stray light ray paths having kth direction at the EA if it is not normal optical ray path. In this case, the ray fluxes can be changed by transmittance between the FP and the intervening object l along the mth ray path, TI_m, that between the intervening object l and the EA along the nth ray path, TI_n, BSDF of the intervening object I, and geometric configuration factor between the intervening object I and other surface illuminated by randomly distributed scatter rays in consideration of the mth and nth ray paths. Total flux with kth direction at the EA can be obtained by iterative backward ray tracing computation and summation of ray fluxes by kth incident angle. The kth incident angle weighting factor is a normalization of kth ray fluxes. Assuming that the single LUTI telescope observes the Moon, which is a spheroid having 3,474 km in diameter, from the nominal 100 km orbit at (0°, 90°) nadir angle, incident angle boundaries are limited less than 70°, latitudes and longitudes of the boundary region on the Moon are ±13.60° and 76.40°~103.60°, respectively. Directional weight distributions within 70° incident angles were obtained with the backward ray tracing computation technique. And then AOIs were sampled by dividing into far- and near-field based on the directional weight map. Each AOI represents each sampled region and summation of directional weights within the region is used a criterion for AOI selection. In this report, we present LUTI stray light rejection performance estimation focusing critical AOI sampling technique in detail.