光学学报, 2017, 37 (12): 1211002, 网络出版: 2018-09-06  

利用统计矩计算的图像运动光学传递函数 下载: 840次

Calculation of Optical Transfer Function for Image Motion Based on Statistical Moments
作者单位
1 中国科学院西安光学精密机械研究所检测技术服务所级中心, 陕西 西安 710119
2 中国科学院大学, 北京 100049
摘要
为准确评价跟踪成像平台对图像调制传递函数的影响,提供确定平台技术指标的理论依据,建立了利用图像运动函数直接计算运动光学传递函数的解析及数值计算模型,并给出了有限项的截断误差,取7阶近似时,截断误差小于10%。利用所建模型给出了低频正弦运动和高频正弦运动光学传递函数的解析式。对某跟踪成像平台的跟踪角速度误差进行了频谱分析,主要分量由多个低频正弦振动分量组成;在曝光时间的尺度上,跟踪角速度误差引起的图像运动可近似为匀速直线运动。利用统计矩法计算的调制传递函数,与利用跟踪角速度误差的均方根值计算的调制传递函数相当,200 mrad -1频率下计算结果偏差小于0.01,因此,跟踪角速度误差均方根值是表征跟踪成像平台的跟踪稳定度的合理参数。
Abstract
In order to evaluate the influence of the tracking and imaging platform on the modulation transfer function of the image accurately and provide a theoretical basis for the determination of the platform’s technical specifications, an analytical and numerical model is established, which is used to calculate the movement optical transfer function by the image motion function. The truncation error of the finite term is given, and the truncation error is less than 10% when the 7 order approximation is taken. The proposed model includes analytic expressions of low frequency sinusoidal motion and high frequency sinusoidal motion. The tracking angular velocity errors of a tracking imaging platform are analyzed by frequency spectrum. The fundamental components of frequency spectrum are composed by multiple low frequency sinusoidal vibration components. Image motion caused by the tracking angular velocity error can be approximated to uniform linear motion at the exposure time scale. The modulation transfer function is calculated by the statistical moment method, and is almost equal to that calculated by the root mean square of the tracking angular velocity error. The calculated deviation is less than 0.01 at 200 mrad -1 frequency. Therefore, the root mean square error of the tracking angular velocity is a reasonable parameter describing the tracking stability of the tracking imaging platform.

田留德, 王涛, 赵怀学, 刘艺宁, 赵建科, 周艳, 刘朝晖. 利用统计矩计算的图像运动光学传递函数[J]. 光学学报, 2017, 37(12): 1211002. Liude Tian, Tao Wang, Huaixue Zhao, Yining Liu, Jianke Zhao, Yan Zhou, Zhaohui Liu. Calculation of Optical Transfer Function for Image Motion Based on Statistical Moments[J]. Acta Optica Sinica, 2017, 37(12): 1211002.

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