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如图1所示,H-V消偏器由两块厚度一定的光楔晶体组成,这两块晶体的晶轴一个为水平方向,另一个为垂直方向。左、右晶体楔角相同、符号相反。
z轴表示光线传播方向,x‐y平面为消偏器截面,入射光沿光轴z方向垂直入射,由于双折射特性,光线进入晶体1后分解为o光和e光,由于两块晶体的光轴相互垂直,晶体1出射的光进入晶体2后o光变为e光,e光变为o光。
则在坐标x处出射光的o光和e光两分量的相位延迟(即入射光通过H-V消偏器的相位延迟)为[8]:
式中:λ为波长;no,ne分别为晶体o光和e光的折射率;x为归一化光瞳坐标;R为光瞳半径;t1、t2为两个晶体的中心厚度。
H-V消偏器的Muller矩阵为:
通常t1=t2,公式(1)可简化为:
将其带入H‐V消偏器穆勒矩阵,再对入瞳面积分得Muller矩阵(通常入瞳为圆形):
式中:J1(δ)为一阶贝塞尔函数。令矩阵参数η=2J1(δ)/δ,可得典型波长下,η与相位δ的变化关系如图2所示。
结合图2及公式(1)可以看出如下规律:
(1)波长越短相位δ越大,H-V消偏器性能越好;
(2)一定范围内,楔角β越大δ越大,H-V消偏器性能越好;
(3)光瞳半径R越大δ越大,H-V消偏器性能越好;
(4)当相位延迟量大于5.8π时,矩阵参数绝对值小于0.02,能够满足大部分应用场合。通常光学系统确定后,波长及光瞳半径已经确定,可根据需要选择合适的楔角及晶体类型以满足应用需求。
由公式(4)可知,不同类型的偏振光经H-V消偏器后,其残余偏振态有不同的形式,表1给出了典型偏振光经H-V消偏器后残余偏振度计算结果。
可知单个H-V消偏器不能对所有类型偏振光起到消偏效果,尤其对水平和垂直线偏光没有消偏作用。在使用上有一定局限性。
Types of incident light Stokes expression of incident light Stokes expression of output light DOP Horizontal-linear polarized light (1,1,0,0)′ (1,1,0,0)′ 1 Vertical-linear polarized light (1,−1,0,0)′ (1,−1,0,0)′ 1 45° linear-polarized light (1,0,1,0)′ (1,0, η,0)′ η −45° linear-polarized light (1,0,−1,0)′ (1,0,− η,0)′ η Left-rotated circular-polarized light (1,0,0,1)′ (1,0, 0, η)′ η Right-rotated circular-polarized light (1,0,0,−1)′ (1,0, 0, −η)′ η Table 1. Polarization degrees of a H-V depolarizer
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基于上述理论分析文中研制了一款应用于某光谱仪的双巴比涅型消偏器,基底材料为石英晶体,工作波长0.4~0.9 μm,结合空间结构布局及光学设计结果,消偏器光瞳有效口径为Φ20.6 mm,单个晶体中心厚度为2 mm,胶合后中心厚为8 mm,晶体楔角为0.6°,图8为研制的消偏器实物及根据实测光谱计算得出的消偏器残余偏振度,可以看出,消偏器残余偏振度≤3%满足指标,整体趋势为波长越短偏振度越小。0.4 μm端残余偏振度有较大起伏是因为选用的晶体间粘接胶在该波长附近吸收较大,P光、S光在该波段透过率较低所致,其余位置偏振度有较小起伏主要受粘接胶吸收率及测试设备误差影响。双巴比涅消偏器楔角产生的最大像分离计算公式为
$(\sqrt 2 + 2)f*\tan \beta $ [10],表2所示为计算得到的不同波长对应像分离列表,最大像分离出现在0.4 μm处,此时像分离为25.4 μm,探测器有效像元尺寸为104 μm×104 μm,像分离值小于(1/3)×104 μm,可以认为对系统MTF影响较小。Wavelength/nm |ne-no| HV_s/μm DB_s/μm 400 0.009 562 1 7.450 01 25.435 88 500 0.009 259 5 7.214 25 24.631 00 600 0.009 092 9 7.084 40 24.187 65 700 0.008 984 1 6.999 61 23.898 18 800 0.008 903 0 6.936 50 23.682 68 900 0.008 836 2 6.884 43 23.504 93 Table 2. Imaging separation of different wavelengths
Study on depolarizers applied for a grating spectrometer
doi: 10.3788/IRLA20190544
- Received Date: 2019-11-10
- Rev Recd Date: 2020-03-14
- Available Online: 2020-07-23
- Publish Date: 2020-07-23
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Key words:
- depolarizer /
- quartz crystal /
- Muller matrix /
- residual polarization
Abstract: The image quality of the grating spectrometer is often affected by the polarization characteristics of the incident light. In order to solve this problem, a depolarizer is usually added to the spectrometer to reduce the polarization response of the instrument. The birefringence property of the crystalline material can produce a depolarization effect on the optical principle, therefore it is often used to process into various types of depolarizers. Based on the principle of the matrix optics, the Muller matrix and residual polarization theoretical expression of a H-V depolarizer and a double Barbinet depolarizer were deeply discussed. The relationship among residual polarization of a double Barbinet depolarizer and working wavelength, its wedge angle, entrance pupil diameter and incident light polarization angle was given respectively. Based on these theories, a double Barbinet depolarizer applied for a grating spectrometer was developed. It could be obtained by calculation that when the wedge angle and the pupil diameter of the double Barbinet depolarizer was 0.6° and 20.6 mm respectively, the residual polarization of the depolarizer was better than 3% in the wavelength range of 0.4-0.9 μm. What’s more, the double image distance met the application requirements, so it can be widely used in engineering practice.