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1、第三章 SAR数据处理,几何分辨率,r,Nadir,航迹,x,柱坐标系,X=0，垂直于飞行方向的平面，为视角,如何与斜距分辨率联系起来？,将斜距转换为无量纲参数,合成孔径雷达是通过对回波信号的处理来获得图像的高分辨率的。从信号处理的角度出发，合成孔径雷达对目标的观测过程等效为一个二维卷积过程：,雷达回波信号,目标的散射系数,点目标的响应信号,从另一个角度思考，合成孔径雷达的成像处理过程可以等效为一个重建地面目标散射系数的二维反卷积过程,Effective range dimension,如果,Point target spread function in range direction exp
2、ressed in decibels,如果两个点目标具有相同的强度信息,Superposition of the point spread functions of two targets located at r=r1 and r=r2, respectively, with,如果 ，则可以区分这两个目标,连续分布的散射体,2、方位向,方位相关量为,合成 2Nd=X,参考函数,多普勒观点,R0,散射体,航迹,由于,这个不断变化的相位，代表回波信号相对发射信号的频率偏移，即多普勒偏移,频率是相位的时间变化率,其多普勒增量为,多普勒频率分辨率与滤波器时间常数T存在如下关系,当天线发射波束与飞机速
3、度矢量之间的夹角相等时，所得的多普勒频率也相同,SAR成像原理,R,点目标A（时间零点）,点目标B,Le,y,x,由几何关系可知,在y=0处点目标回波信号的双程超前相位为：,假设发射脉冲信号的脉冲重复频率（PRF）足够高，以至于回波信号可以被认为是连续信号，那么回波信号响应就可以利用在时间段-T/2 T/2 积分来处理回波信号 。如果假设在积分时间T内为均匀照射，那么在y处的目标回波响应可表示为,包含了,功率响应为,时的合成波束半功率点波束宽度，,方位向分辨率,是由于平台沿直线运动产生的，可以将其从总超前相位中减去，以产生所谓的聚焦合成孔径,归一化后的天线功率增益为,回波响应,方位向分辨率,合
4、成孔径雷达成像处理过程,合成孔径雷达是通过对回波信号的处理来获得图像的高分辨率的。从信号处理的角度出发，合成孔径雷达对目标的观测过程等效为一个二维卷积过程：,雷达回波信号,目标的散射系数,点目标的响应信号,从另一个角度思考，合成孔径雷达的成像处理过程可以等效为一个重建地面目标散射系数的二维反卷积过程,如果点目标能够在距离向和方位向可分，则,当点目标响应信号在距离向和方位向不可分时，则可以先进行一定的转换，使之在距离向和方位向可分，然后通过两个一维反卷积运算来完成成像处理运算。,合成孔径雷达是一种脉冲方式工作的雷达系统，其信号在沿距离向和沿方位向的变化程度是不同的，沿距离向是快变化，沿方位向慢变
5、化。这些特点为简化合成孔径雷达的成像处理过程提供了依据。,SAR成像算法,目标,1、斜距向,改善距离向分辨率脉冲压缩技术 为了既能提高信号噪声比又不至于对发射信号要求过大的峰值功率。常常采用脉冲压缩技术。利用线性调频信号作为发射信号，再进行距离向压缩处理,(脉冲宽度):是指脉冲90%幅度点之间的时间宽度（单位为秒）,如何使发射脉冲持续足够长的时间以维持信号的功率水平，同时还能不降低距离分辨率呢？现代雷达和通讯系统（包括SAR系统）普遍采用脉冲压缩技术解决这一问题：发射脉冲不是简单脉冲，而是幅度或相位按波形调制，而是幅度或相位按波形调制，在接收端经过压缩处理使得接收脉冲仿佛是由短脉冲发生的。这样
6、在时间上即使是重叠的脉冲也能经压缩处理而区分开。,一般脉冲雷达，发射脉冲信号是对载频波进行方波调制，载频是固定的。线性调频信号是载频随时间线性变化，线性增加或线性减小。,chirp,矩形函数,脉宽内的线性调频速率 （Hz/s）,回波相位,The quadratic phase behaviour corresponds to a linear change in the received azimuth frequency , the so-called DOPPLER-effect.,This linear DOPPLER-effect is only present as long as
7、x is really small in comparison to . Otherwise high order components are occuring and the correct hyperbolic phase history has to be taken into account. Particularly, this is the case for SAR sensors with very long apertures and for those operating not exactly perpendicular to the flight direction b
8、ut under a so-called squint-angle.,频率是相位的时间变化率,The maximal illumination time of a point target is defined by the extension of the antenna footprint in azimuth,The bandwidth of the signal in azimuth,信号理论指出带宽为B的信号可以等价处理为持续时间为=1/B的脉冲,Processing in azimuth,The echo of a single point target is contained
9、in may received radar pulses and appears therefore defocused. The aim of SAR processing, also called compression, is to focus all the received energy of a target, distributed over the illumination time, on one point at t=0 .,the received signal in azimuth direction can be written as,点目标的后向散射强度,The i
10、dea of azimuth compression is now to adjust all these phase value to the same value, followed by a coherent summation.,As the length of the synthetic aperture and with that also the length of the signal is limited, it makes sense to limit also the length of the reference function by a box-like wheig
11、hting function :,The correlation result can be written,Signal compression. Real part of the complex signal of an ideal point target response (left) and amplitude of the compressed signal (right).,The received signal, also called chirp, has a constant amplitude and a parabolic phase behaviour (shown
12、is only the real part of the complex signal). The reference function has an amplitude of one and exactly the opposite phase than the signal itself. After the correlation with the signal appears well located at . Its maximum amplitude increased from to and the peak phase is zero. In reality, the negl
13、ected phase term proportional to the two-way sensor object distance as well as the object phase appear here.,t,孔径,V（t）,DIRAC 函数,instead of using a box-like weigthing function, often instead other shapes are used, whose FOURIER-transform shows a better Peak-Sidelobe Ratio (PSLR). A very common functi
14、on for this is the so-called HAMMING-weighting:,Signal compression using a HAMMING weighting function.,为了提高运算效率，利用卷积定理,Processing in range,To achieve a high resolution in the direction perpendicular to the flight direction, only a short pulse duration is necessary. In practice, it can be problematic
15、 to generate a very short and high power pulse, as the resulting energy densities are hard to handle. In the spectral domain, with short pulse duration a higher signal bandwidth can be observed. A high resolution is therefore tantamount with a high signal bandwidth. A second possibilty to generate a high signal bandwidth is to use a long, but frequency modulated pulse. It is common to use for this a linear frequency modulation (called chirp),The resulting resolution in range direction,Two-dimensional point target response (without weighting),Structure of a SAR-processor,
