标题： 傅里叶相关成像 显示英文标题

标题： Fourier-Correlation Imaging

摘要： 我们研究了在卫星飞越平面时，利用一维天线阵列测量电场波动的略微偏移频率的傅里叶分量之间的相关性，能在多大程度上将二维亮度温度作为平面上位置的函数进行测量。 我们发现，仅使用两个天线得到的可实现空间分辨率约为$h\chi$，其中$\chi=c/(\Delta r \omega_0)$，在卫星飞行方向和垂直于该方向上，其中$\Delta r$是天线之间的距离，$\omega_0$是中心频率，$h$是卫星相对于平面的高度，$c$是光速。 在以几公里每秒的速度飞行、高度约为1000公里、中心频率为千兆赫兹的卫星上，相距约100米的两个天线因此可以对地球表面的亮度温度进行分辨率为约1公里的成像。 对于单个点源，相对辐射分辨率约为$\sqrt{\chi}$，但对于卫星轨迹左侧或右侧半平面内的均匀温度场，其分辨率仅为$1/\chi^{3/2}$，这表明两个天线不足以精确重建温度场。 讨论了多种如何提高辐射分辨率的想法。 特别是，拥有$N$个天线，且所有天线之间的距离至少为波长的数量级，可以将信噪比提高约$N$倍，但需要对从相同数量天线对中获得的$N^2$个温度剖面进行平均。 显示英文摘要

摘要： We investigate to what extent correlating the Fourier components at slightly shifted frequencies of the fluctuations of the electric field measured with a one-dimensional antenna array on board of a satellite flying over a plane, allows one to measure the two-dimensional brilliance temperature as function of position in the plane. We find that the achievable spatial resolution resulting from just two antennas is of the order of $h\chi$, with $\chi=c/(\Delta r \omega_0)$, both in the direction of flight of the satellite and in the direction perpendicular to it, where $\Delta r$ is the distance between the antennas, $\omega_0$ the central frequency, $h$ the height of the satellite over the plane, and $c$ the speed of light. Two antennas separated by a distance of about 100m on a satellite flying with a speed of a few km/s at a height of the order of 1000km and a central frequency of order GHz allow therefore the imaging of the brilliance temperature on the surface of Earth with a resolution of the order of one km. For a single point source, the relative radiometric resolution is of order $\sqrt{\chi}$, but for a uniform temperature field in a half plane left or right of the satellite track it is only of order $1/\chi^{3/2}$, indicating that two antennas do not suffice for a precise reconstruction of the temperature field. Several ideas are discussed how the radiometric resolution could be enhanced. In particular, having $N$ antennas all separated by at least a distance of the order of the wave-length, allows one to increase the signal-to-noise ratio by a factor of order $N$, but requires to average over $N^2$ temperature profiles obtained from as many pairs of antennas.