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假设入射光束具有发散半角
$ \theta $ ,光束正入射和斜入射滤光片的情况如图1所示。正入射下的最大入射角是光束发散半角;在斜入射的情况下,最大入射角与入射角有关。为了方便起见,用
$ {\theta }_{max} $ 表示入射光束的最大发散半角;用函数$ C\left(\theta \right) $ 表示光束能量在发散角$ {2\theta }_{max} $ 中的分布。当发散光束以入射角$ {\theta }_{0} $ 入射在薄膜样品表面时,光谱特性可以近似为:$$ {F}_{1}\left(\lambda \right)=\frac{1}{{2\theta }_{max}}\underset{{\theta }_{0}-{\theta }_{max}}{\overset{{\theta }_{0}+{\theta }_{max}}{\int }}C\left(\theta \right)f(\lambda ,\theta ){\rm{d}}\theta $$ (1) 其中,薄膜样品光谱函数
$ f(\lambda ,\theta ) $ 可以从薄膜的特征矩阵中推导出来,在分光光度计中光束能量分布通常被认为是均匀的,即函数$ C\left(\theta \right) $ ≈1。在大多数情况下,光束很难严格保持单色性,总是具有一定的线宽。假设
$ \mathrm{\Delta }\lambda $ 代表光束的半线宽,函数$ D\left(\lambda \right) $ 表示为入射光在全线宽2$ \mathrm{\Delta }\lambda $ 中的能量分布。薄膜的光谱特性可以近似表达式为:$$ F\left(\lambda \right)=\frac{1}{2\Delta \lambda }\frac{1}{{2\theta }_{max}}\underset{\lambda -\Delta \lambda }{\overset{\lambda +\Delta \lambda }{\int }}D\left(\lambda \right)\underset{{\theta }_{0}-{\theta }_{max}}{\overset{{\theta }_{0}+{\theta }_{max}}{\int }}C\left(\theta \right)f(\lambda ,\theta ){\rm{d}}\theta {\rm{d}}\lambda $$ (2) 其中,在分光光度计中线宽的能量分布一般也认为是均匀的,即函数
$ D\left(\lambda \right) $ ≈1。
Influence of nonparallel beams on the spectral properties of the narrow-band filter
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摘要: 因为发散角和线宽效应的存在,非平行光束入射窄带滤光片时,滤光片的透射特性会发生变化。特别是在斜入射时,窄带滤光膜透射通带波形更易从矩形向三角形退化,并且伴随峰值透过率降低等负面现象。虽然已知的卷积模型可以对非平行光束入射窄带滤光片的情况进行数值模拟,但是由于制备和测量误差的阻碍,其正确性和数值模拟的准确性没有严格的实验进行验证。通过膜系优化和测量误差修正降低相应误差及其影响,并通过等离子体辅助反应磁控溅射 (PARMS) 的方法制备了工作角度为17°的1 064 nm高性能窄带滤光片。滤光片的透射光谱分别由两款分光光度计Cary 7000和Lambda 1050测量得到。在不同条件下测得的光谱与数值模拟结果吻合得很好,充分验证了卷积模型的有效性和数值模拟的准确性。Abstract: Because of the divergence angle and linewidth effects, the filter’s transmission characteristics will change when a nonparallel beam irradiates the narrow-band filter. Especially at oblique incidence, the passband waveform of the narrow-band filter film is more likely to degenerate from rectangular to triangular, and negative phenomena such as the transmittance peak decrease appear. Although the known convolution model can simulate this variation numerically, there is no strict experimental verification for the model’s correctness and the accuracy of numerical analysis due to obstacles of preparation and measurement errors. For this verification, the corresponding errors are overcome through film optimization and measurement error correction. A high-performance 1064 nm narrow-band filter at an incident angle of 17° was fabricated by plasma-assisted reactive magnetron sputtering (PARMS). The transmission characteristics were measured by two spectrophotometers, Cary 7000 and Lambda 1050, separately. The spectra are coincident with the numerical simulation under different conditions. Therefore, the validity of the convolution model and the high accuracy of the numerical simulation are adequately justified.
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Key words:
- narrow-band filter /
- numerical simulation /
- divergence-angle effect /
- linewidth effect
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