基于重心法哈特曼波前传感器光斑图像的质心计算

一、光斑图像的模拟

首先，仿真得到如下图所示的光斑阵列图像，仿真参数如下：微透镜数目为72×72，每个微透镜所占的像素数为36×36，CCD相机像素数则为2592×2592；
在这里插入图片描述

图1 仿真得到的光斑图像

二、重心法原理

在子孔径光斑质心计算方面，最为简单直接的方法是重心法，其计算公式如下:

式中[x(i),y(i)]分别表示第i个子孔径在x，y方向上的质心位置，

分别表示点(m,n)处的像素坐标， ${{I}_{mn}}$ 表示的是点(m,n)处像素的强度。通过将当前质心位置与标定质心位置进行比较，即可得到待测波前的斜率:

将图1所示的光斑阵列图像代入到上式中，即可求解得到XY方向上的质心数据，

X方向质心数据为72*72大小的矩阵，如下图所示：

在这里插入图片描述

图2 X方向质心数据

Y方向质心数据为72*72大小的矩阵，如下图所示：

在这里插入图片描述

图3 X方向质心数据

三、资源获取

上述matab程序可从如下链接处获取:

https://download.csdn.net/download/qq_36584460/82066235

资源中提供了仿真的参考质心光斑图像/偏移质心光斑图像，进而可求解波前斜率，进一步重构出待测波前。最后，提供其他技术支持，包括哈特曼波前传感仿真模拟，以及波前重构等算法。

------------恢复内容开始------------

一、光斑图像的模拟

图1 仿真得到的光斑图像

二、重心法原理

在子孔径光斑质心计算方面，最为简单直接的方法是重心法，其计算公式如下:

$\left. \begin{matrix}

x(i)=\frac{\sum\limits_{m=1}^{M}{\sum\limits_{n=1}^{N}{{{x}_{mn}}{{I}_{mn}}}}}{\sum\limits_{m=1}^{M}{\sum\limits_{n=1}^{N}{{{I}_{mn}}}}} \\

y(i)=\frac{\sum\limits_{m=1}^{M}{\sum\limits_{n=1}^{N}{{{y}_{mn}}{{I}_{mn}}}}}{\sum\limits_{m=1}^{M}{\sum\limits_{n=1}^{N}{{{I}_{mn}}}}} \\

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    \left. \begin{matrix} x(i)=\frac{\sum\limits_{m=1}^{M}{\sum\limits_{n=1}^{N}{<!-- -->{<!-- -->{x}_{mn}}{<!-- -->{I}_{mn}}}}}{\sum\limits_{m=1}^{M}{\sum\limits_{n=1}^{N}{<!-- -->{<!-- -->{I}_{mn}}}}} \\ y(i)=\frac{\sum\limits_{m=1}^{M}{\sum\limits_{n=1}^{N}{<!-- -->{<!-- -->{y}_{mn}}{<!-- -->{I}_{mn}}}}}{\sum\limits_{m=1}^{M}{\sum\limits_{n=1}^{N}{<!-- -->{<!-- -->{I}_{mn}}}}} \\ \end{matrix} \right\}
   
  
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margin-right: 0.0714286em;"><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 3.85002em;"><span style="top: -0.69999em;"><span class="delimsizinginner delim-size4"><span>⎭</span></span></span><span style="top: -0.69999em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -0.99999em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -1.29999em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -1.59999em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -1.89999em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -2.19999em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -3.15001em;"><span class="delimsizinginner delim-size4"><span>⎬</span></span></span><span style="top: -4.30001em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -4.60001em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -4.90001em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -5.20001em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -5.50001em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -5.80001em;"><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top: -6.10002em;"><span class="delimsizinginner delim-size4"><span>⎫</span></span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span></span></span></span></p>

式中[x(i),y(i)]分别表示第i个子孔径在x，y方向上的质心位置，

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</span><span class="katex-html"><span class="base"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right: 0.03588em;">y</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.151392em;"><span style="top: -2.55em; margin-right: 0.05em;"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span></span></span> 分别表示点(m,n)处的像素坐标， <span class="katex--inline"><span class="katex"><span class="katex-mathml">

 
  
   
    
     I
    
    
     
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</span><span class="katex-html"><span class="base"><span class="mord"><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right: 0.07847em;">I</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.151392em;"><span style="top: -2.55em; margin-right: 0.05em;"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s"></span></span></span></span></span></span></span></span></span></span>表示的是点(m,n)处像素的强度。通过将当前质心位置与标定质心位置进行比较，即可得到待测波前的斜率:</p>