变间距光栅设计、制作及其在位移传感器中的应用研究
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摘要
自从19世纪末Henry Rowland发明衍射光栅刻划机和凹面光栅分光装置以来，光栅分光仪器就已成为光谱分析领域的主角。光栅是光谱分析研究中的重要色散元件，其作用与棱镜相似，但在许多方面光栅的性能更好，并且使用方便。在许多光谱仪器中，光栅成本仅占总成本的一小部分，但衍射光栅的质量却从根本上决定了整个系统所能达到的光谱性能。
理论分析表明，有目的的改变光栅的线密度分布(即周期分布)或者改变光栅基底的面形，有可能使光栅具有自动聚焦和消像差的能力，从而可以减少系统中的光学元件，提高仪器的分辨率。变间距光栅(Variable-Line-Space Gratings或Varied-Line-Space Gratings，简称VLS光栅)也叫做消像差光栅，其线密度分布一般用线密度分布方程来表示，它直接影响VLS光栅的聚焦性能和像差两个主要参数。广义上任何变周期的光栅都可以称为VLS光栅。VLS光栅在19世纪末就被提出，上世纪五六十年代激光的出现，使我们可以利用全息的方法来制作VLS光栅。目前VLS光栅已广泛应用于同步辐射光束线、光纤通信、光电探测、等离子体物理研究、空间光谱仪、表面干涉计量等领域，深入研究VLS光栅的设计、制作及其应用，具有非常重要的意义。
国外研究VLS光栅已经有多年的历史，国内相关研究很少，其设计、制作以及应用仍需进一步研究。本文第二章介绍了衍射光栅原理、分类及其应用简介。在第三章中，我们简述了以光程函数为基础的全息变间距光栅几何理论，研究利用遗传算法对全息VLS光栅光路进行优化计算，推导出了目标函数的积分形式；计算了球面波干涉及球面波与非球面波干涉情况下的全息记录参数，给出了线密度误差曲线；分析了记录参数误差对线密度分布的影响；由于一维线密度分布方程相同的VLS光栅，其刻线弯曲程度可能会有很大的差异，因此还研究了不同记录参数情况下的刻线弯曲程度，并给出了用于评价光栅刻线弯曲程度的表达式，指出球面波与非球面波干涉得到的光栅线条并不一定比球面波干涉得到的线
Diffraction gratings are wide used to disperse light, which is to disperse incident light into angular directions corresponding to the wavelength of incident light. At the end of the 19th century Henry Rowland invented the ruling machine of diffraction gratings and the concave grating mounting, henceforth diffraction gratings have replaced prisms in most fields of spectral analysis. Subsequent production of high quality gratings led to significant advances in analytical spectroscopy. It has found a wide application from the fundamental research to the application study.
Theoretic analysis show that the changes of groove density, line-profile and grating substrate(blank) shapes endow gratings the ability of focusing and reducing aberration, so the amount of reflective mirrors are decreased, the efficiency and resolving power of instruments are improved. The flat CCD is used in modern spectrograph. VLS gratings give the spectrum on a flat field, which is more suitable for CCD array instruments.
Although variable-line-space gratings (VLS gratings) are wide used in spatial spectrum and synchrotron radiation devices, but the design and fabrication methods of them are difficult. Some abroad scholars studied VLS gratings year after year, but only a few papers about VLS gratings have been found in China. The test, fabrication, principle and applications of VLS gratings need more research. This dissertation is engaged in the study on design and fabrication of holographic VLS gratings and its application to position sensor.
In chapter 2, the principal of diffraction grating and its application are introduced.
In chapter 3, the geometry theory of aspheric wave-front recording optics is briefly described. The genetic algorithm is introduced to the recording parameters optimization of holographic VLS gratings; the integral expression of the merit function is also derived to improve the efficiency of calculation. Design example of holographic variable-line-space gratings is given to demonstrate the capability of this method, the groove density error curves are also given. The line-profiles of VLS plane gratings with two spherical wave-front recording are a family of confocal hyperbola, while the line-profiles of VLS plane gratings with spherical and aspheric wave-front recording are very complex. VLS plane gratings with the same grooves distribution maybe have different line-profiles. The merit function of the curve tendency is derived. Design example of holographic VLS plane gratings is given to demonstrate the capability of our method, which shows that the curve tendency is in very good agreement with the merit function. We analyze the relationship between the recording parameters and the coefficients of groove density distribution of VLS plane gratings. The curve by optimizing the groove density error with genetic algorithm is given, which validates the theory analysis.
理论分析表明，有目的的改变光栅的线密度分布(即周期分布)或者改变光栅基底的面形，有可能使光栅具有自动聚焦和消像差的能力，从而可以减少系统中的光学元件，提高仪器的分辨率。变间距光栅(Variable-Line-Space Gratings或Varied-Line-Space Gratings，简称VLS光栅)也叫做消像差光栅，其线密度分布一般用线密度分布方程来表示，它直接影响VLS光栅的聚焦性能和像差两个主要参数。广义上任何变周期的光栅都可以称为VLS光栅。VLS光栅在19世纪末就被提出，上世纪五六十年代激光的出现，使我们可以利用全息的方法来制作VLS光栅。目前VLS光栅已广泛应用于同步辐射光束线、光纤通信、光电探测、等离子体物理研究、空间光谱仪、表面干涉计量等领域，深入研究VLS光栅的设计、制作及其应用，具有非常重要的意义。
国外研究VLS光栅已经有多年的历史，国内相关研究很少，其设计、制作以及应用仍需进一步研究。本文第二章介绍了衍射光栅原理、分类及其应用简介。在第三章中，我们简述了以光程函数为基础的全息变间距光栅几何理论，研究利用遗传算法对全息VLS光栅光路进行优化计算，推导出了目标函数的积分形式；计算了球面波干涉及球面波与非球面波干涉情况下的全息记录参数，给出了线密度误差曲线；分析了记录参数误差对线密度分布的影响；由于一维线密度分布方程相同的VLS光栅，其刻线弯曲程度可能会有很大的差异，因此还研究了不同记录参数情况下的刻线弯曲程度，并给出了用于评价光栅刻线弯曲程度的表达式，指出球面波与非球面波干涉得到的光栅线条并不一定比球面波干涉得到的线
Diffraction gratings are wide used to disperse light, which is to disperse incident light into angular directions corresponding to the wavelength of incident light. At the end of the 19th century Henry Rowland invented the ruling machine of diffraction gratings and the concave grating mounting, henceforth diffraction gratings have replaced prisms in most fields of spectral analysis. Subsequent production of high quality gratings led to significant advances in analytical spectroscopy. It has found a wide application from the fundamental research to the application study.
Theoretic analysis show that the changes of groove density, line-profile and grating substrate(blank) shapes endow gratings the ability of focusing and reducing aberration, so the amount of reflective mirrors are decreased, the efficiency and resolving power of instruments are improved. The flat CCD is used in modern spectrograph. VLS gratings give the spectrum on a flat field, which is more suitable for CCD array instruments.
Although variable-line-space gratings (VLS gratings) are wide used in spatial spectrum and synchrotron radiation devices, but the design and fabrication methods of them are difficult. Some abroad scholars studied VLS gratings year after year, but only a few papers about VLS gratings have been found in China. The test, fabrication, principle and applications of VLS gratings need more research. This dissertation is engaged in the study on design and fabrication of holographic VLS gratings and its application to position sensor.
In chapter 2, the principal of diffraction grating and its application are introduced.
In chapter 3, the geometry theory of aspheric wave-front recording optics is briefly described. The genetic algorithm is introduced to the recording parameters optimization of holographic VLS gratings; the integral expression of the merit function is also derived to improve the efficiency of calculation. Design example of holographic variable-line-space gratings is given to demonstrate the capability of this method, the groove density error curves are also given. The line-profiles of VLS plane gratings with two spherical wave-front recording are a family of confocal hyperbola, while the line-profiles of VLS plane gratings with spherical and aspheric wave-front recording are very complex. VLS plane gratings with the same grooves distribution maybe have different line-profiles. The merit function of the curve tendency is derived. Design example of holographic VLS plane gratings is given to demonstrate the capability of our method, which shows that the curve tendency is in very good agreement with the merit function. We analyze the relationship between the recording parameters and the coefficients of groove density distribution of VLS plane gratings. The curve by optimizing the groove density error with genetic algorithm is given, which validates the theory analysis.
引文
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