合成孔径激光成像雷达(V):成像分辨率和天线孔径函数

Synthetic Aperture Imaging Ladar(V): Imaging Resolution and Antenna Aperture Function

基于合成孔径激光成像雷达(SAIL)二维数据收集方程和成像算法,研究了圆形孔径和矩形孔径光学望远镜天线的方位向成像分辨率,导出了点扩展函数的解析表达式,分析了理想成像点尺寸及其光学足迹中心偏离、相位二次项匹配滤波失匹、空间采样宽度、采样周期等的影响;也研究了距离向成像分辨率并分析了非线性啁啾补偿等的影响。对于各种影响因素都给出了数学判据,特别是发现了矩形孔径的光学望远镜可以产生适合于SAIL扫描方式的矩形光学足趾并消除方位向分辨率不均匀降低,可以设计最佳的矩形孔径的尺度分别控制光学足趾在方位向及其垂直方向上的尺度,得到大扫捕宽度和高方位向分辨率;也发现了目标外差延时必须尽量小以克服非线性啁啾和初始光频不稳定性相位误差。

The azimuth imaging resolution of synthetic aperture imaging ladar （SAIL） using the telescopes with circular and rectangular apertures is investigated based on the point target SAIL data collection equation, and the analytic expressions of point spread function for imaging are correspondingly achieved. The ideal resolution spot and its degradation due to the target deviation vertically from the footprint center, the mismatch of matched filtering from the quadratic phase history, and the limited width and period for sampling are discussed. And the deficient compensation of phase errors of nonlinear chirping and the others related to range resolution are also detailed. Mathematical criteria are derived for all of these factors. Moreover, an explanation to the resulted azimuth resolution from the earlier experiment in our laboratory-scaled SAIL is given to verify the developed theory. As a conclusion, it is found that the antenna of rectangular aperture telescope can provide a rectangular footprint more suitable for the SAIL scanning format, and this leads not only to an elimination of resolution degradation but also to an optimal design of aperture to give both a fine resolution and a wide scan strip. And it is also found that the delay between the target and the local oscillator must be small enough to eliminate the phase errors from nonlinear chirping and optical frequency instability.