凹非球面的非零位干涉检测技术 -

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凹非球面的非零位干涉检测技术

doi:10.37188/CO.2023-0042

西安工业大学光电工程学院, 陕西西安 710021

基金项目:陕西省科技厅项目（No. 2022GY-222，No. 2022GY-262）；基础科研（No. JCKY2020426B009）；“一带一路”外国专家创新人才交流项目（No. DL2022040006L）

详细信息

作者简介:
张旭（1998—），女，陕西渭南人，硕士研究生，2019年于西安工业大学获得学士学位，2021—至今于西安工大学就读硕士研究生，主要从事光学检测方面的研究。E-mail：zhangxu19982021@163.com
李世杰（1988—），男，四川广安人，博士，副教授，硕士生导师，2014年于中国科学院光电技术研究所获得博士学位，主要从事先进光学制造技术及先进光学系统研发等方面的研究。E-mail：lishijie@xatu.edu.cn

中图分类号:TN74
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出版历程
- 网络出版日期:2023-09-26

A non-null interferometryfor concave aspheric surface

School of Opto-electronical Engineering, Xi’an Technological University, Xi’an 710021, Shaanxi, China

Funds:Supported by Shaanxi Provincial Department of Science and Technology Project (No. 2022GY-222, No. 2022GY-262); Basic Scientific Research (No. JCKY2020426B009)、"The Belt and Road" Foreign Experts Innovative Talent Exchange Project (No. DL2022040006L)

More Information

Corresponding author:lishijie@xatu.edu.cn

摘要

摘要:
为了实现凹非球面的快速、高精度与通用化检测，文中提出了一种将非球面当做球面直接采用干涉仪检测的非零位干涉检测方法，并结合相应的数据处理方法，获得非球面的面形误差检测结果。首先介绍了该方法的检测原理，建立了回程误差、调整误差的计算与去除模型，研究了面形误差的数据处理方法。然后以两个不同非球面度的凹非球面为例，对其回程误差和调整误差进行了仿真计算，验证了该方法的有效性。最后搭建了凹非球面的非零位检测实验装置，成功测量得到其面形误差。通过与自准直零位检测法及LUPHOScan轮廓测量法检测结果的对比，发现两种方法测量得到的误差结果的面形分布和评价指标具有高度一致性，验证了该检测方法的正确性。该检测方法在保证高精度测量的同时兼备一定的通用性与便捷性，为凹非球面的通用化检测提供了一种有效手段。
- 非球面面形测量/
- 非零位干涉检测/
- 回程误差/
- 数据处理
Abstract:
In order to realize the rapid, high-precision, and universal testing of concave aspheres, a non-null interferometry is proposed in this paper, which takes the asphere as a sphere and measures it directly with an interferometer. Combined with the corresponding data processing methods, the test results of the aspheric are obtained. Firstly, the detection theory of this method is introduced, the calculation and removal models of retrace error and adjustment error are established, and the data processing method of shape error is studied. Secondly, taking two concave aspherical surfaces with different parameters as an example, the retrace error and adjustment error are simulated, which verified the effectiveness of the method. Finally, a non-null interferometric experimental setup of concave aspheric surface is performed, and its shape error is successfully obtained. By comparing the results with autocollimation method and LUPHOScan method, it is found that the surface distribution and evaluation indicators of the results are highly consistent, which verifies the correctness of this method. This method provides an effective measurement method for concave aspheric surface with high precision, universality, and convenience.
- aspheric surface shape measurement/
- non-null interferometry/
- retrace error/
- data processing

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图 1非零位干涉法直接检测非球面

Figure 1.Direct non-null interferometry of aspheric surfaces

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图 2非零位检测光线追迹模型

Figure 2.Non-null testing of ray-tracing model

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图 3调整误差的产生：（a）距离引起的离焦；（b）光轴倾斜引起的倾斜误差；（c）偏心引起的彗差

Figure 3.Generation of adjustment errors: (a) Distance induced defocusing; (b) Tilt error caused by optical axis tilt (c) Coma caused by eccentricity

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图 4非零位检测凹非球面：（a）非零位检测凹非球面光路图；（b）非零位直接检测凹抛物面的数据; （c）非零位直接检测凹椭球面的数据；

Figure 4.Non-null testing concave aspheric: (a) The light path diagram of non-null testing concave aspheric; (b) Data of concave paraboloid by non-null direct non-null interferometry (c) Data of concave ellipsoid by non-null direct non-null interferometry

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图 5非零位检测去除调整误差与回程误差：（a）凹抛物面处理后的面形结果；（b）凹椭球面处理后的面形结果；

Figure 5.Non-null testing removes adjustment error and retrace error: (a) Surface shape results after concave parabolic surface testing; (b) Surface shape results after concave ellipsoid surface testing

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图 6凹非球面的对比实验

Figure 6.Comparative experiment on concave aspheric

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表 1Zernike多项式的项数与像差的对应关系

Table 1.Correspondence between the number of terms of Zernike polynomials and aberrations

Term	Polynomial	Meaning
$ {Z_4} $	$ - 1{\text{ + }}2\left( {{x^2} + {y^2}} \right) $	Power
$ {Z_7} $	$ \left( { - 2 + 3{x^2} + 3{y^2}} \right)x $	Coma X
$ {Z_8} $	$ \left( { - 2 + 3{x^2} + 3{y^2}} \right)y $	Coma Y
$ {Z_9} $	$ 1 - 6\left( {{x^2} + {y^2}} \right) + 6{\left( {{x^2} + {y^2}} \right)^2} $	Primary Spherical

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表 2凹抛物面参数

Table 2.Parameters of concave paraboloid

Parameter	Value	Parameter	Value
Aspheric type	Concave paraboloid	Maximum sag	1.67 mm
Diameter	90 mm	Maximum slope	4.25°
Radius curvature of the vertex	606 mm	Maximum asphericity	0.575 μm
Conic coefficient K	−1	Best radius of the reference sphere	606.835 mm

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表 3凹椭球面参数

Table 3.Parameters of concave ellipsoid

Parameter	Value	Parameter	Value
Aspheric type	Concave ellipsoid	Maximum sag	2.91 mm
Diameter	90 mm	Maximum slope	7.39°
Radius curvature of the vertex	348 mm	Maximum asphericity	2.0154 μm
Conic coefficient K	−0.66	Best radius of the reference sphere	348.9615 mm

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表 4凹抛物面回程误差的仿真计算

Table 4.Simulation calculation of retrace error of concave paraboloid

OA/mm	$ O P D $	Power item $ Z_{OPD(4)} $	Primary Spherical $Z_{\Delta{OPD(9)}}$	Retrace error
605
606
606.835
607
608

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表 5凹椭球面回程误差的仿真计算

Table 5.Simulation calculation of retrace error of concave ellipsoid

OA/mm	$ O P D $	Power item $ Z_{OPD(4)} $	Primary Spherical $ Z_{\Delta{OPD(9)}}$	Retrace error
347
348
348.9615
349
350

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表 6实验中距离误差引入的离焦误差与去除

Table 6.Defocusing error introduced by distance errors in experiments and its removal unit: nm

Detection result	Power is adjusted to a minimum	Adjust the distanceL₁	Adjust the distanceL₂	Adjust the distanceL₃
Fringe pattern
Surface error before removing Power	PV=639.7608 RMS=135.4192	PV=4283.4232 RMS=1200.4216	PV=1833.8544 RMS=515.732	PV=1999.0152 RMS=523.3256
Surface error after removing Power	PV= 627.1048 RMS=135.4192	PV= 654.3152 RMS=133.5208	PV=721.392 RMS=132.888	PV=656.2136 RMS=137.3176

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表 7实验中倾斜/偏心误差引入的彗差与去除

Table 7.Comet error introduced by tilt/eccentricity error in experiments and removal of the error unit：nm

Detection result	Coma is adjusted to a minimum	Adjust the eccentricθ₁	Adjust the eccentricθ₂	Adjust the eccentricθ₃
Fringe pattern
Surface error before removing Coma	PV=722.6576 RMS=137.3176	PV=656.8464 RMS=133.5208	PV=641.6592 RMS=134.7864	PV=649.2528 RMS=136.6848
Surface error after removing Coma	PV= 510.6696 RMS=125.2944	PV= 489.7872 RMS=123.3960	PV= 491.0528 RMS=125.2944	PV= 488.5216 RMS=126.5600

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