Analysis of Imaging Limit Capability for Natural Rendezvous of Low Earth Orbit Debris
In order to achieve precise attitude monitoring of large-sized space debris,the spatial resolution of cameras is continuously improving.However,this improvement leads to an increasing blurring effect caused by relative motion during exposure time.It is particularly important to research on how to balance camera resolution and the issue of image blur caused by motion-induced displacement.For low earth orbit natural rendezvous imaging scenarios,changes in the camera's observational angle before and after the rendezvous lead to variations in the position and orientation of the target in the camera line of sight.The image motion generated as a result of this is referred to as intrinsic image motion in the natural rendezvous imaging scenario.This passage establishes the equation for the image plane position through the mapping relationship between the points of space target objects and their corresponding image points.The equation involves the transformation of coordinates in seven different coordinate systems.In theory,taking the derivative of this equation with respect to time yields the instantaneous velocity equation for image motion.However,due to the immense computational complexity of the matrix and numerous parameters involved(including the orbital parameters of the imaging platform and target,spatial resolution of the camera,exposure time,etc.),it is impractical to provide an exact expression for intrinsic image motion.Therefore,we obtain the image plane positions at different time points based on specific orbital and imaging parameters,calculate the intrinsic image motion within the exposure time,and then employ a data fitting method to obtain a model for the intrinsic image motion function.Through analyzing the relative radial velocity of the target with the camera and the displacement of the target along the optical axis at the rendezvous moment,it can be understood that the rotational image motion of the target around the optical axis is a primary factor in intrinsic image motion.Therefore,this intrinsic image motion is directly correlated with the relative rotational angular velocity between the target and the camera,exposure time,angular separation between the target and the camera,and the spatial resolution of the camera.Taking into consideration these influencing factors,this paper calculates the intrinsic image motion for specific imaging orbits and various influencing factors using the image plane position equation.The obtained data is utilized as a training set for fitting the intrinsic image motion function.The fitting correlation coefficient for the training set is 0.99,with a root mean square error of 0.12.Subsequently,intrinsic image motion calculated with different orbital parameters is used as a test set to validate the accuracy of the fitting function.The correlation coefficients for different independent variables are all greater than 0.9,and the root mean square error are all less than 0.2.This indicates that the fitting accuracy of the intrinsic image motion function is high,and the fitting results are reliable.The intrinsic image motion function model reveals that intrinsic image motion is linearly correlated with relative rotational angular velocity,exposure time,and the angular separation between the target and the camera.It is also exponentially correlated with the spatial resolution of the camera.This paper analyzes the impact of this image motion on the modulation transfer function.When the image motion is greater than 0.5 pixels,the modulation transfer function decreases by approximately 10％,failing to meet the overall system design requirements.Therefore,this paper takes an image displacement of 0.5 pixels as the maximum allowable displacement and establishes a constraint on the camera's spatial resolution at the time of natural intersection.This constraint illustrates the relationship between camera resolution and the relative angular velocity,exposure time,and angular separation between the target and the camera under the condition of satisfying the maximum allowable image motion.Taking a specific set of imaging orbits as an example,we demonstrate the method of calculating the maximum resolution of the camera at the rendezvous moment using this constraint condition.We point out that in low earth orbit rendezvous imaging scenarios,even if the spatial camera resolution exceeds this limit,there is no improvement in image quality.This indicates that the constraint condition has a significance for the design of imaging cameras and the selection of exposure parameters.
Image motionImage plane position equationFunction fitting modelConstraint conditionLimiting resolution
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