Rigorous Oversampling Correction for Landsat 8 Lunar Observations

Shuang Li, Jie Shan

Abstract: .Landsat 8 Operational Land Imager (OLI) has the capability to acquire Moon images in their orbits. These lunar images provide an additional option for on-orbit radiometric calibration using the Moon as a reference source. However, due to the slow scanning (attitude) rate of the satellite, the lunar images are usually elongated in the along-track direction making the shape of the Moon an ellipse instead of a circle. It is essential to correct such oversampling effect to obtain accurate digital numbers (DNs) or irradiance and pixel counts of the Moon disk.Existing Work.In general, when using lunar images for radiometric calibration, oversampling was accounted for by simply dividing the total irradiance by a certain ratio or oversampling factor [1] - [3]. However, this oversampling factor varies with the observers (sensors) and their attitude maneuver, such as 4.57 for Terra [4] and 8 for Landsat 8 [5]. Lunar edge points could be detected through edge detection [3], derivatives of the distribution of brightness [6], or gray-level based segmentation. Ellipse fitting was then applied to the extracted Moon edge to determine its semi-major and semi-minor. The semi-major axis was considered the elongated Moon radius in the image and the semi-minor axis was the actual radius. The oversampling factor was the ratio of these two axes [7] - [8]. Moreover, the oversampling factor can also be calculated using the average pitch rate [4] or roll angle [9] of the satellite when scanning across the Moon. However, the oversampling effect is different for each frame or among push-broom image lines since the viewing geometry and the oversampling factor are also changing during the Moon observation. All reported work produces a single oversampling factor and uses it for the oversampling correction of all lines in the image. Therefore, rigorous oversampling correction is needed.Fig. 1.(a) Flowchart of the proposed rigorous oversampling correction approach, including two main parts, i.e., line of sight intersection calculation and weighted interpolation-based oversampling correction, (b) illustration of the footprints of corrected and oversampled pixels in one column, and the calculation of the interpolation weights at a pixel based on a triangular function.Method.We propose a rigorous oversampling correction method for lunar images collected by Landsat 8 OLI. As shown in Fig. 1 (a), the variation of oversampling effect for each image line (row) is considered and corrected to produce a lunar image that would ideally be collected with non-overlapped and non-gapped footprints on the lunar surface. Due to the oversampling effect, the information from a single ground instantaneous field of view (GIFOV) is captured by the same detector in multiple adjacent image rows whose footprints overlap with the current row. In addition to oversampling between the same detector in different image rows, there are offsets between even and odd detectors in one image. Fig. 1 (b) shows an example of the GIFOVs of pixels collected by the same detector in three adjacent rows in one column of the corrected image (the red, green, and blue squares), denoted as the target footprints, and the footprints of pixels in the oversampled image (the gray windows). The cross signs in Fig. 1 (b) represent the centers of the gray windows. In the original image, the information collected by each pixel footprint is proportional to the overlapped area with the target footprints. Hence, the pixel value in the corrected image can be derived from the weighted interpolation of pixels in the oversampled image, where the weights are determined by the overlapped areas of their footprints on the lunar surface using a triangular function. An illustration for the calculation of the n-th pixel in a column of the corrected image is provided in Fig. 1 (b). The calculation of overlapped areas between pixel footprints is achieved by calculating the intersections of the lines-of-sight vector [10] with the lunar surface. The imaging time for each pixel is determined and used for the interpolation of the attitude and ephemeris data. The LOS vectors are constructed given the sensor imaging parameters, i.e., the coefficients of two groups of the Legendre polynomials for the along-track and across-track direction. The LOS vectors in the sensor coordinate system are then converted to the Earth-centered inertial (ECI) coordinate system. Based on the relationships between the satellite positions, LOS vectors, and Moon positions at specific observation time, the LOS intersection on lunar surface can be determined by solving a system of quadratic equations.Findings.The lunar images we used for this study were collected by Landsat 8 OLI on Jan. 29, 2021. The OLI consists of 14 sensor chip assemblies (SCAs), each of which has 9 bands. They observed the Moon in two orbits, producing 15 multi-spectral lunar images in total (one of the SCAs observed the Moon twice). The oversampling correction was conducted on each SCA and each band. Edge detection and ellipse fitting were conducted for evaluation. Since the ideal correction should result in a nearly circular Moon, the flattening and azimuth of the corrected Moon disk are calculated for assessment. The corrected Moon images showed that our method can achieve a near-circular Moon disk with ideally non-overlapped and non-gapped pixel footprints for all SCAs and bands. For example, Fig. 2 provides the oversample correction results for the images of SCA 5. The flattening of the Moon disk is less than 0.02 except for SCA 13. As for the consistency, the results of 9 bands in the same SCA are similar while larger difference is found for different SCAs. Overall, our method provides a rigorous solution to oversampling correction of Landsat 8 OLI lunar images. Variations of oversampling with different viewing geometries are considered, resulting in corrected images with desirable non-overlapped and non-gapped pixel footprints and more accurate DNs.Fig. 2.An example of Landsat 8 lunar images from band 1-9 (in the order of their placement on the SCA along track) of SCA 5 before and after correction.