对于归一化的方向图来说，比例因子并不重要，而是与辐射电场强度E(θ, ϕ)相关，即所谓的天线电压方向图：

Aside from scale factors, which areunimportant for normalized patterns, it is related to the radiated electricfield intensity E(θ, ϕ), known as the antenna voltage pattern, according to

对于在两个孔径维度上可分离的辐射函数的矩形天线阵列，P(θ, ϕ)能够被分解为两个一维方向图的乘积，即：

For a rectangular aperture with anillumination function that is separable in the two aperture dimensions, P(θ, ϕ)can be factored as the product of separate one dimensional patterns (Stutzmanand Thiele, 1998):

对于大多数的雷达应用，只有远场（也称为Fraunhofer）功率方向图是人们感兴趣的。

For most radar scenarios, only thefar-field (also called Fraunhofer) power pattern is of interest.

对于孔径大小为D的天线，一般将远场定义为D2/λ或2D2/λ之外。

The far-field is conventionally defined tobegin at a range of D2/λ or 2D2/λ for an antenna ofaperture size D.

考虑图1.5所示的一维线性孔径阵列的方位(θ)波束图。

Consider the azimuth (θ) pattern of theone-dimensional linear aperture geometry shown in Fig. 1.5.

Figure 1.5. 矩形孔径上一维电场计算的几何示意图Geometry for one-dimensional electric field calculation on arectangular aperture.

从信号处理的观点来看，孔径天线（如平板阵列和抛物面反射器）的一个重要特性是：远场条件下的电场强度作为E(θ)的函数，正好是方位面上跨孔径电流分布A(y)的逆傅立叶变换，即：

From a signal processing viewpoint, animportant property of aperture antennas (such as flat plate arrays andparabolic reflectors) is that the electric field intensity as a function ofazimuth E(θ) in the far field is just the inverse Fourier transform of thedistribution A(y) of current across the aperture in the azimuth plane (Bracewell,1999; Skolnik, 2001):

其中这里所谓的“频率”变量为(2π/λ)sinθ，对应单位为弧度/m。

where the “frequency” variable is(2π/λ) sinθ and is in radians per meter.

附录B中介绍了空间频率的概念。

The idea of spatial frequency is introducedin App. B.

为了更明确地说明这一点，定义s= sinθ，ζ = y/λ。

To be more explicit about this point,define s = sinθ and ζ = y/λ.

将以上定义代入方程（1.5）得到

Substituting these definitions in Eq. (1.5)gives

上式显然是傅立叶逆变换的形式。

which is clearly of the form of an inverseFourier transform.

（式中的有限积分范围是由于天线孔径的有限支撑，即天线孔径的实际尺寸是有限的）。

(The finite integral limits are due to thefinite support of the aperture.)

根据ζ和 s的定义，该变换通过非线性映射将电流分布作为由波长归一化孔径位置的函数与空间频率变量相关联，而空间频率变量与方位角相关。

Because of the definitions of ζ and s, thistransform relates the current distribution as a function of aperture positionnormalized by the wavelength to a spatial frequency variable that is related tothe azimuth angle through a nonlinear mapping.

由此得到

It of course follows that

式（1.7）中的无限积分是一种误导，因为变量s = sinθ的积分范围只可能是-1到+1。

The infinite limits in Eq. (1.7) aremisleading, since the variable of integration s = sinθ can only range from –1to +1.

正因为如此，-1到+1范围之外的积分值均为零。

Because of this, is zero outside of thisrange on s.

实际上，方程（1.5）是略微简化的表达式，它忽略了距离相关的总相位因子和幅度对距离变化的轻微依赖性（Balanis，2005）。

Equation (1.5) is a somewhat simplifiedexpression that neglects a range dependent overall phase factor and a slightamplitude dependence on range (Balanis, 2005).

——本文译自Mark A. Richards所著的《Fundamentals of Radar Signal Processing（Second edition）》

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