https://zhuanlan.zhihu.com/p/624292239
Goodman, J. W. (2004). Introduction to Fourier Optics.

RS type 1 衍射空间像计算

$$U_1(P_0)=\frac{1}{j\lambda }\int {\int }_{\Sigma }U(P_1)\frac{exp(jk{r}_{01})}{r_{01}}\cos (\vec{n},\overrightarrow{r_{01}})ds$$

直接计算该积分，需要二重循环，然后再二重循环遍历观测屏上的点，效率低下

傅里叶变换

二重积分在$\Sigma$上进行计算。将ds写为dxdy的形式，z为观测平面与源平面的距离，有
$$\cos (\vec{n},\overrightarrow{r_{01}})=\frac{z}{r_{01}}$$
$$r_{01}=\sqrt{(x-x_0{)}^2+(y-y_0{)}^2+(z-z_0{)}^2}$$

$$\begin{array}{rl}{U}_1(P_0)& =\frac{1}{j\lambda }\int {\int }_{\Sigma }U(x,y)\frac{exp(jk{r}_{01})}{r_{01}}\cos (\vec{n},\overrightarrow{r_{01}})dxdy\\ & =\int {\int }_{\Sigma }U(x,y)V(x,y)dxdy\end{array}$$

V ( x , y ) = 1 j λ e x p ( j k ( x − x 0 ) 2 + ( y − y 0 ) 2 + ( z − z 0 ) 2 ) ( x − x 0 ) 2 + ( y − y 0 ) 2 + ( z − z 0 ) 2 z ( x − x 0 ) 2 + ( y − y 0