準確的決定太陽大氣結構的特性對於了解太陽活動的機制非常重要。然而現今的觀測技術無法直接量測太陽大氣結構的特性，必須從電磁波(具體來說是偏振光)的觀測反推而得。而透過偏振光推斷介質的特性的研究/技術稱為Spectropolarimetry(分光偏振法)。
本研究主要目的是透過數值模擬的方式尋找大氣結構變化與輻射光譜變化之間的關係，其結果可做為調整太陽大氣模型時，使其更符合真實太陽時調整的方向。具體來說，本研究利用梯形法求解輻射傳遞方程式(Radiative Transfer Equation, 簡稱RTE)，計算Rempel(2012)的太陽黑子模型中6302.5Å光譜在本影區、半影區與寧靜區的斯托克斯參數。在不同深度擾動不同的物理參數(磁場強度、粒子密度、溫度和視線速度)並研究其對不同的斯托克斯參數(Stokes I、Q、U、V)造成的影響。結果顯示在太陽表面附近(光深度=0.1~10)的擾動對於斯托克斯參數的影響最大，溫度在所有研究區域中，都是對所有斯托克斯參數影響最大的物理量，而其他物理參數的相對重要性會因斯托克斯參數及不同區域有所差異。這些結果可以幫助研究太陽模型的科學家調整模型，減小模擬與觀測資料之間的差異。如果光譜解析度足夠高的情況下，RTE的數值解與小擾動假設下的解析解的結果會一致，這是因為光譜解析度不足會造成斯托克斯參數不正確，而這種不正確會使數值解與解析解都不正確而導致其結果不一致。

Accurate determination of the properties of the solar atmosphere is very important for the understanding of the physical mechanisms of solar activities. However, the properties of the solar atmosphere cannot be directly measured by current observational techniques, and have to be inferred from the directly detected electromagnetic waves, specifically, polarized light. The technique to infer the properties of the medium from the observed polarized spectra (Stokes parameters) is called Spectropolarimetry.
The main objective of this research is to examine the relationships between the variations of the properties of the medium and the variations of the profiles of the Stokes parameters by a numerical simulation method. The results can provide a guideline on how to adjust the solar atmosphere models to be more consistent with the real Sun.
In this research, we use the sunspot model by Rempel(2012) and choose 6302.5Å absorption line for our study. The Stokes parameters profiles the absorption line in the umbra, penumbra and quiet Sun regions of are computed by solving the Radiative Transfer Equation (RTE) using the trapezoidal method. Different physical parameters (magnetic field, temperature, number density and line-of-sight velocity) are perturbed at different depths, and their effects on the profiles of different Stokes parameters are investigated.
The results indicate that Stokes parameters are mainly affected by the perturbation in the depth 〖log〗_10⁡〖τ_c 〗=-1~1. The temperature causes the largest variation in all four Stokes parameters in all studied regions. The relative importance of other physical quantites is different in different regions for different Stokes parameters at different wavelength. The results can help solar modelers to adjust their models to reduce the difference between the model-predicted and observed Stokes parameters.
In addition, to reduce computation time, we examine the consistency between the numerical solution of RTE and an analytical solution derived under the assumption of small perturbation. The results indicate that the analytical solution, which can be computed much faster, is consistent with the numerical solution if the spectral resolution is sufficiently high.

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