# Image Motion Measurement and Image Restoration System Based on an Inertial Reference Laser
## 1 Introduction  
With the increasing application of space technologies, the requirements for the function and performance of spacecrafts have also become increasingly strict. In response to these requirements, a series of high-resolution optical remote sensing satellites with large apertures have been developed, such as GeoEye-1 [1], WorldView-4 [2], and GF-4 [3]. However, satellites have multiple frequency disturbance sources, such as the solar wing driving mechanism, antenna driving mechanism, control moment gyroscope, thruster, and refrigerator [4]. Coupled with the attitude instability of the satellite, these sources cause on-orbit flutter, which covers a wide band of frequency, from extremely low to high frequencies of thousands of Hz [5, 6, 7, 8]. All of these factors will lead to the jitter of the optical axis of the optical payload and move or rotate the imaging focal plane, thereby reducing the quality of the remote sensing images [9, 10, 11, 12]. The NASA Goddard Space Center has revealed that the energy of flutter is mainly concentrated in the middle- and low-frequency regions [13]. The flutter can be partly eliminated by setting a vibration isolation mechanism [14]. To measure the effect of flutter on imaging, a variety of image motion measurement methods have been proposed. The method based on joint transform correlator (JTC) has been widely used in camera image motion measurement [15; 16; 17; 18; 19; 20; 21; 22; 23]. The authors in [24] proposed an approach to restore a motion-blurred image in real time using optoelectronic hybrid joint transform correlation. This method requires several detection equipment, including a high-speed charge coupled device (CCD) camera and optical JTC. The two adjacent images measured by the high-speed CCD are processed by the JTC to obtain the corresponding image motion, which, in turn, is fed back to the image stabilization mirror to ensure relative stability between the imaging and CCD, as well as to achieve excellent imaging. In this method, the measuring device is placed at the focal plane, and the image motion is measured with a high accuracy and speed. The authors in [25; 26; 27; 28; 29; 30] adopted an image motion detection method based on remote sensing images. In the camera exposure process, a high-speed camera was used to record multiple frames of consecutive images, and the displacement between adjacent frames was measured using a registration algorithm to realize the image motion measurement. The point spread function (PSF) for the image restoration was constructed based on image motion, and image restoration was carried out via post-processing. Despite accurately measuring the real state of image motion at the focal plane, this method could not measure the image motion at the blind spot frequency, and demonstrated hysteresis [31]. Both the image motion measurement method based on JTC and the image motion detection method based on remote sensing images require a rich image level of the object to be photographed and a high signal-to-noise ratio [17]. Ensuring accuracy becomes difficult when the remote sensing image is smooth or the signal-to-noise ratio is low. In addition, reference [32] proposed a system to measure image motion using a position sensitive detector (PSD), which depends on a strong point light source placed around the object to be photographed. Reference [33] measured image motion using inertial measurement sensors, but the line of sight could not be measured directly. To address the above problems, this paper proposes a high-precision image motion measurement method based on an inertial reference laser. This method depends on neither the characteristics of the ground scenery nor the lighting conditions. The reference provided by this method ensures that the image motion measurement system can work effectively all day under any weather condition. The PSF is obtained by normalizing the image motion data, and the obtained PSF is used for restoration in order to obtain an excellent image. The rest of this paper is organized as follows.