# Analysis of MTF in TDI-CCD Subpixel Dynamic Super-Resolution Imaging by Beam Splitter
## 1 Introduction  
Obtaining high resolution is an important goal of optical satellite remote-sensing technology. At present, the second-generation transmission type of remote sensing satellite is equipped with discrete imaging sensors, such as time delay integration charge coupled device (TDI-CCD). However, the under-sampling effect caused by the pixel size and sampling interval restricts the resolution of the image according to Shannon sampling theorem [1]. Although the resolution of the image can be improved by improving the area and spatial density of the optical sensor or using various complex optical systems such as free surface design [2; 3], the expense is excessive. The technique of subpixel dynamic super-resolution imaging can overcome the under-sampling effect partially without changing new charge coupled device (CCDs) [4; 5]. It use a set of undersampled (aliased) low-resolution (LR) images with subpixel shift to reconstruct a high-resolution (HR) image [6; 7], namely oversampling operation (Figure 1). It aims to reconstruct the high-frequency contents which are commonly confused with the low-frequency contents in the LR images accessed by oversampling operation [8]. There have been proposed many subpixel imaging systems according to the oversampling operation formats. For example, the Canadian Defense Research Organization developed a high-performance micro-scanning imaging system for the application of infrared focal plane devices [9], which is a type of technique that doubles the resolution of the staring array imaging device. This technique can acquire multi-frame images of the same scene and detect the phase shift at each time. The French National Center for Space Research (CNES) applied the technique of subpixel imaging to Systeme Probatiore d'Observation dela Tarre 5 (SPOT5) satellites [10], which resulted in an increase in imaging resolution from 5 m to 3 m. The hot spot recognition system (HSRS) [11] sensor,which was developed by German Aerospace Center, and ADS40 [12] digital aerial remote-sensing camera, which was developed by the Lycra company, have adopted the similar technique of subpixel imaging. There are lots of analyses that come forth to evaluate the performance of such subpixel imaging methods. [PERSON] discussed qualitatively the effect of micro-scanning modes on the quality of the image [13; 14; 15]. [PERSON] [16] introduced a super-resolution imaging system with oversampling technique. [PERSON] [17] analyzed the sampling performance of the CCD. However, this study did not mention the conditions under which the CCD reaches its sampling limit, and there was no analysis of the super-resolution reconstruction performance for multiple subpixel images. [PERSON] [18] proposed another subpixel imaging technique (Figure 2) using a beam splitter to divide the light into two orthotropic beams. A pair of linear array CCD detectors are set up in the two imaging plane positions around the beam splitter with the staggered subpixel-level distance in the linear array direction. So a pair of conjugate images (called a subpixel image pair) would be simultaneously got by the CCD pair via this linear push-broom imaging system for the moving scenes. Through super-resolution processing, a new image with higher spatial resolution in the linear array direction would be constructed [19; 20; 21]. However, [PERSON]'s work [18] only focused on the CCD sensors. Our subsequent research has updated the subpixel imaging system with TDI-CCDs. Considering MTF is the popular evaluating indicator for the imaging system, this paper proposes MTF analysis method based on discrete spatial oversampling for TDI-CCD subpixel imaging system. In Section 2, the improvement performance of MTF under  
Figure 1: Schematic of super-resolution technique. Figure 2: Schematic of sub-pixel imaging using beam splitter. the over-sampling conditions of subpixel dynamic super-resolution imaging is analyzed for CCD and TDI-CCD linear array in turn.