澄清经典文献上洛匈棱镜分束角公式的问题

李东风; 李如意; 杨春旺; 周珺; 陆守香

doi:10.37188/CO.2025-0036

澄清经典文献上洛匈棱镜分束角公式的问题

doi: 10.37188/CO.2025-0036

cstr: 32171.14.CO.2025-0036

李东风^{1, 2},
李如意²,
杨春旺²,
周珺³,
陆守香^1,

1.
火灾科学国家重点实验室, 安徽合肥230037
2.
安徽芯核防务装备技术股份有限公司, 安徽合肥230088
3.
公安部第一研究所, 北京 100048

基金项目: 公安部科技计划项目“基于激光热效应的爆炸物非接触快速检测智能识别技术与装备研究”（No. 2022ZB12）基金支持。

详细信息

作者简介:
李东风：正高级工程师，中国科学技术大学火灾火灾安全全国重点实验室博士研究生在读，现任公司董事长、总经理、党支部书记，入选第二批合肥市学术和技术带头人后备人选、安徽省国资委第五批538英才工程人才计划、安徽军工集团第三批学术带头人；主持研究国家重点研发项目、高新工程2项、公安部科技计划重点项目2项、公安部科技强警及成果引导计划项目各1项，上述参与的科研计划项目均已通过验收；获得安徽省科学技术三等奖1项，获得公安部科技技术进步奖2项，另获得发明专利5项，实用新型专利15项，论文在国家级刊物上发表并收录

陆守香：中国科学技术大学火灾安全全国重点实验室教授，博士生导师，主要从事应急技术理论，火灾科学与消防技术应用研究；先进火灾探测技术研究与开发，高效环保灭火装备及核心部件研究；智慧消防物联网系统开发。先后发表SCI学术论文200余篇，合著《火灾风险评估方法学》，获授权专利13项、软件著作权6项

中图分类号: O436.3;O439;
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出版历程
- 网络出版日期: 2025-08-21

Clarify the problem of the beam deviation angle formula of a Rochon Prism in classical literatures

1.
State Key Laboratory of Fire Science, Hefei 230037, China
2.
Anhui Core Defense Equipment Technology Co., Ltd, Hefei 230088, China
3.
The First Research Institute of the Ministry of Public Security, Beijing 100741, China

Funds: This paper is supported by the Science and Technology Program Project of the Ministry of Public Security, “Research on Intelligent Recognition Technology and Equipment for Non-contact Rapid Detection of Explosives Based on Laser Thermal Effects” (No. 2022ZB12).

More Information

Corresponding author: xxxxxx@xxx.xxx

摘要

摘要:
在科研项目研发过程中发现经典光学文献上的洛匈棱镜（Rochon Prism）的分束角公式（是针对负晶体）是错误的，为此推导了准确的洛匈棱镜分束角表达式（分布针对负晶体、正晶体），并解决了科研项目中包含洛匈棱镜的光学系统设计错误问题。针对一般洛匈棱镜产品的输出2束光的夹角较小的问题，分析推导了分别由负晶体、正晶体构成洛匈棱镜的分束角表达式，另外对由异种晶体材料构成洛匈棱镜的分束角进行了分析以及推导出表达式。通过用实际数据计算和比较知道，由异种晶体材料构成洛匈棱镜的分束角比由同种晶体材料构成洛匈棱镜的分束角有很大的提高。对于在紫外波段的应用，具体给出一种由异种晶体材料构成洛匈棱镜的较大分束角的设计实例。这种由异种晶体材料构成洛匈棱镜，按照合适的晶体排列顺序，可以在合理的晶体厚度的限制下获得相对较大的分束角度，这显然是有利于偏振仪器设备的结构设计。
- 洛匈棱镜 /
- 石英晶体 /
- 氟化镁晶体 /
- o光 /
- e光
Abstract:
During the research and development process of the scientific research project, it was found that the beam deviation angle formula of a Rochon Prism in classical optical literature (for negative crystals) was incorrect. Therefore, an accurate expression for the beam deviation angle of a Rochon Prism was derived (distributed for negative and positive crystals), and the problem of design in the optical systems containing a Rochon Prism in the scientific research projects was solved. In response to the problem of small angles between the output two beams of light in general a Rochon Prism products, the expressions for the deviation angles of a Rochon Prism composed of negative and positive crystals were analyzed and derived. In addition, the deviation angles of a Rochon Prism composed of different crystal materials were analyzed and the expression was derived. By calculating and comparing with actual data, it is known that the beam deviation angle of a Rochon Prism made of different crystal materials is significantly higher than that of a Rochon Prism made of the same crystal material. For applications in the ultraviolet band, provide a specific design example of a large beam deviation angle for a Rochon Prism composed of heterogeneous crystal materials. This type of a Rochon Prism is composed of heterogeneous crystal materials, and according to the appropriate crystal arrangement order, a relatively large beam deviation angle can be obtained under the limitation of reasonable crystal thickness, which is obviously beneficial for the structural design of the polarization instruments and equipments.
- Rochon prism /
- quartz /
- MgF2 crystal /
- o ray /
- e ray

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图 1 洛匈棱镜的原理（由负单轴晶体构成）

Figure 1. Principle of Rochon prism (negative uniaxial crystal)

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图 2 切割角和分束角之间的关系@方解石晶体

Figure 2. Relationship between cutting angle and beam deviation angle

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图 3 切割角和分束角之间的关系@方解石晶体

Figure 3. Relationship between cutting angle and beam deviation angle

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图 4 切割角和分束角之间的关系（全部）

Figure 4. Relationship between cutting angle and beam deviation angle

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图 5 切割角和分束角之间的关系(局部)

Figure 5. Relationship between cutting angle and beam deviation angle

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图 6 洛匈棱镜的原理（由正单轴晶体构成）

Figure 6. Principle of a Rochon prism (composed of positive uniaxial crystals)

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图 7 切割角和分束角之间的关系@193 nm波长

Figure 7. Relationship between cutting angle and beam deviation angle @ 193 nm wavelength

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图 8 两种正晶体构成的洛匈棱镜：(a)氟化镁+石英；(b)石英+氟化镁

Figure 8. A Rochon prism made of two types of positive crystal: (a) magnesium fluoride and quartz; (b) Quartz and magnesium fluoride

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图 9 正晶体洛匈棱镜的分束角

Figure 9. Beam deviation angle of a Rochon prism (positive uniaxial crystal)

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图 10 由石英和氟化镁晶体构成的洛匈棱镜

Figure 10. A Rochon prism made of Quartz and magnesium fluoride crystals

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表 1 各种洛匈棱镜分束角的比较

Table 1. Beam deviation angle of several kinds of a Rochon Prisms（RP）

Rochon prisms (RP)	Beam deviation angle (degree)
Prism cutting angle (degree)	30.78	32	37	42	47
RP made of Quartz and MgF2	9.9474	4.1185	1.7548	1.1850	0.8897
RP made of MgF2	1.2914	1.2324	1.0257	0.8605	0.7237
RP made of Quartz	1.2974	1.2380	1.0298	0.8637	0.7262
RP made of MgF2 and Quartz	1.0550	1.0213	0.8925	0.7767	0.6717

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