## 1 Introduction  
In order to ensure the effective working state of an optical RS imaging system, it is necessary to monitor its on-orbit imaging performance in real-time. Spatial resolution represents the ability to capture or distinguish fine spatial details, and it is closely related to the Ground Sampling Distance (GSD) and the Instantaneous Field of View (IFOV) [1]. However, the spatial resolution is more complicated than the concept of GSD or IFOV. Most agree that the effective spatial resolution is due to three features of the sensor: the instantaneous field of view (IFOV), the MTF, and the signal-to-noise ratio (SNR) [1]. Moreover, MTF is the most commonly used imaging quality assessment indicator for various imaging fields. MTF is used to characterize the ability to faithfully reproduce the scene spatial frequency content of an imaging system or its components [2]. The imaging system for MTF analysis must be approximately linear and shift invariant. Furthermore, to preserve the convenience of the transfer function approach for a sampled imaging system, it is assumed that the target being imaged has spatial frequency components with random phases that are uniformly distributed with respect to the sampling sites [2]. For a sampled imaging system, it is convenient to express the unit of spatial frequency as line pair/pixel (lp/pix) with the Nyquist and sampling cutoff frequencies corresponding to 0.5 lp/pix and 1 lp/pix, respectively. According to the different structural characteristics of the target, MTF measurement methods mainly include the point source method, pulse method, edge method,and contrast method, which involve the analysis of the responses of points, lines, edges, and periodic bar patterns in the target image. Point source and pulse methods are closest to the MTF definition in principle, but the used target size of the point and line affects the accuracy of MTF measurement, which limits the application in orbit. The contrast method is mostly used for laboratory measurements due to the demand for periodic stripe targets, which is usually easy to realize in the laboratory. Among them, the edge method has high practicability and the widest application, which is not only widely used for laboratory measurements under various implementation manners but also has been used for numerous space sensors in orbit [1,3]. The existing modified edge methods are mainly based on ISO 12233: 2017 e-SFR algorithm [4]. The ISO 12233 standard, which is also known as the edge method, slanted-edge method, or knife-edge method, is intended to characterize the spatial resolution of digital still cameras with two-dimensional photo element arrays that respond to light in proportion to the intensity of the light. The spatial frequency response is measured to approximate the MTF as a function of the horizontal or vertical spatial frequency by analyzing a near-vertical or near-horizontal bi-tonal edge image, respectively. However, it cannot be directly used for multidirectional MTF estimation. Recently, research into the edge method has mainly focused on improving the accuracy and practicability of MTF measurement. Relevant scholars pay more attention to the following five topics: the accurate and stable detection of edge angle, the accurate and effective construction of Edge Spread Function (ESF), the accuracy and error analysis of edge method, the practical research of MTF measurement method, and the transformation and acquisition of MTF [5,6]. Edge detection mainly adopts the row difference method [4] or the parameter fitting method [2]. ESF construction mainly adopts discrete oversampled binning method [4,7] or appropriate model fitting method [3,8,9]. The application of the model fitting method is an effective and excellent means for accurate edge detection and ESF construction, which is more suitable for the field of ground image processing than aerospace on-orbit processing. The research on the accuracy and error analysis of the edge method is comprehensive and in-depth [10,11,12,13].