评价函数构建：像差理论与评价函数的关系、常用评价函数、权重分配策略
评价函数，说白了就是光学设计的「裁判」。你优化了半天，系统好不好，总得有个打分标准吧？这个标准就是评价函数。我刚开始做设计那会儿，总觉得评价函数随便选一个就行，后来被一个项目狠狠教育了——选错了评价函数，优化出来的系统根本没法用。
今天咱们就聊聊，怎么给光学系统选对裁判、定好规则。
像差理论与评价函数的关系
先问一个问题：评价函数到底在评价什么？
答案是——像差。评价函数的本质，就是把各种像差量化成一个数值。你想想看，一个光学系统好不好，最终看的是成像质量。而成像质量差，说白了就是有像差。球差、彗差、像散、场曲、畸变、色差……这些像差越小，系统越好。
但问题来了：像差有几十种，怎么综合成一个分数？
这就是评价函数要做的事。它把各种像差加权组合，变成一个标量值。优化器的工作，就是让这个值尽可能小。
核心关系：
- 评价函数 = 像差的加权组合
- 优化方向 = 降低评价函数值
- 评价函数设计 = 决定哪些像差重要、重要到什么程度
我在项目中遇到过一件事：一个投影镜头，用RMS光斑半径优化，结果出来MTF很差。为什么？因为RMS光斑半径只关心几何光线，没考虑衍射效应。后来换成MTF做评价函数，问题就解决了。
所以，选评价函数不是随便挑一个，得看你的系统工作在什么场景。
常用评价函数
常用的评价函数主要有三种。我按使用频率排个序：
| 评价函数 | 适用场景 | 优点 | 缺点 |
|---|---|---|---|
| RMS光斑半径 | 几何光学主导的系统（照明、投影） | 计算快、直观 | 忽略衍射效应 |
| 波前差（RMS Wavefront） | 衍射受限系统（相机、显微镜） | 物理光学准确 | 计算稍慢 |
| MTF（调制传递函数） | 成像系统（镜头、望远镜） | 直接反映成像清晰度 | 计算最慢、优化难度大 |
RMS光斑半径
这是最基础的评价函数。它计算所有光线在像面上的分布，然后求均方根半径。说白了，就是看光斑有多大。
我个人的习惯是：在优化初期用RMS光斑半径。因为计算快，能快速找到大致方向。等系统接近目标了，再切换到更精确的评价函数。
# 在Zemax中设置RMS光斑半径评价函数
# 操作数：RSCE（RMS Spot Radius）
# 权重：根据系统要求设定
RSCE 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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