## 倾斜波面干涉系统点源阵列选取的数学模型研究

Title Study on mathematical model of the selection of array source in tilt wavefront interference system
Abstract
Freeform optics is a new photoelectric element, in high performance and compact
optical system is a large number of applications, but the lack of high efficiency
and precision of the detection method restricts its further application. In many
current on the free surface element detection method, inclined wave interferometry
is the realization of free-form surface optical element surface shape measurement
with high precision is an effective way. Tilt phase-shifting interferometry method
compared to other methods of measurement, with fast speed, high precision, large
dynamic range, good generality and the advantages. In the study of tilt wavefront

interference system, arrangement of point source array is the key factors affecting
the detection range and detection of objects. In view of the different free surface
element surface gradient distribution and detection caliber, inclined wave
interference system of point source array arrangement must and adapt.
This paper according to the principle of inclined wavefront interferometry of point
source array arrangement and measured the mathematical relationship between free
curved surface gradient distribution and diameter, establishment of point source
array arrangement algorithm, for the design of the whole system with model parameters.
Keywords Optical freeform surface,Non-null interferometer,tilted wavefront

1 引言1
1.1 课题背景 1
1.2 国内外研究现状 1
1.3 干涉测量法 6
1.4 课题任务与要求 8
2 基于点源阵列的倾斜波面干涉系统 10
2.1 光学系统基本结构10
2.2 倾斜波面干涉法基本原理 11
2.3 基于点源阵列的倾斜波面非零位干涉系统的设计方法 12
3 倾斜波面干涉系统数学模型的建立 13
3.1 数学模型结构示意 13
3.2 数学模型坐标的选取以及最佳球面的拟合 14
3.3 球面上点的干涉情况的讨论15
3.4 利用光路可逆原理计算光路 16
4 基于 MATLAB 的点源阵列的排布算法 20
4.1 MATLAB点源阵列排布算法分析 20
4.2 利用 MATLAB 仿真及结果 21

1 引言
1.1 课题背景

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