大部分的太陽活動是由太陽磁場主導的，因此充分了解太陽磁場對於正確地預測太陽活動非常重要，但是太陽表面上有許多結構尺度小於觀測儀器的鏡頭解析度，目前提高儀器解析度的研究主要利用Artificial Neural Network，但此方法需用大量的影像資料訓練，且訓練好的模型只適用於與訓練資料相同的影像，因此本研究提出一方法藉由像素分割來縮小像素以提高解析度，其原理為是平面光到達不同角度之觀測者的投影光強度不同，利用不同角度觀測者量到之投影光強度，可還原出像素中的次像素的真實光強度。由於太陽磁場是由可直接被觀測的Stokes parameters所推算而得的，我們使用Sunspot model (Rempel 2012)中提供的參數，再利用Radiative Transfer Equation來模擬觀測到的Stokes parameters，再將此法應用到此參數以測試可行性及優缺點。結果顯示此方法可以對Stokes parameters的譜線與2D影像達到縮小像素大小的目的，其中在2D影像結果顯示，縮小像素水平方向的大小適合用來分辨水平切線上的結構變化；縮小垂直方向的大小適合分辨垂直切線上的結構變化，另外此方法所還原的值與原來的強度值表現出高度相關的結果，表示此像素分割法可以合理地得到次像素的真實光強度。

Most of the solar activity is dominated by the solar magnetic field. Therefore, in order to accurately predict the solar activities, it is important to correctly determine all the solar magnetic structures. In addition, there are many structures on the solar surface with scales smaller than the resolution of even the best observing instrument to-date. To improve the spatial resolution, many studies have developed various Artificial Neural Network (ANN) models. However, ANN models require large amount of data for training, and the trained model can only be applied to the same type of images as the training data. In this study, we propose a new non-ANN method which improves the spatial resolution by reducing the size of pixel. This pixel reduction method is based on the idea that the intensity of a plane wave detected by the observers of different viewing angles is different because of projec-tion. By using concept, we can in principle recover the true intensities of the point light sources comprising the area of the observed pixel. The solar magnetic fields are not di-rectly measureable but have to be derived from the directly observed Stokes parameters, which are a set of parameters that fully describe the intensity and polarizations of elec-tromagnetic waves. To test the pixel reduction method, we first simulate the observed Stokes parameters by using the physical parameters provided in a sunspot model and solving the Radiative Transfer Equation, and apply the method to both the spectral lines and the 2D images to evaluate its performance. The results show that this method can re-duce the pixel size for both spectral line of Stokes parameters and 2D images. In the image results, reducing the horizontal pixel size can better resolve the structures along the hori-zontal cross section, and reducing the vertical pixel size can better resolve the structures along the vertical cross section. The recovered intensities show a high correlation with the original intensity, indicating that this pixel segmentation method can reasonably obtain the true light intensity of sub-pixels.

[1] Stokes, G.G. (1852). On the composition and resolution of streams of polarized light from different sources. Trans. Cambridge Phil. Soc. 9, 399.
[2] Chandrasekhar, S. (1946). On the radiative equilibrium of a stellar atmosphere. X.
Astrophys. J. 103, 351.
[3] Chandrasekhar, S. (1946). On the radiative equilibrium of a stellar atmosphere. XI.
Astrophys. J. 104, 110.
[4] Chandrasekhar, S. (1947). On the radiative equilibrium of a stellar atmosphere. XV.Astrophys. J. 105, 424.
[5] Hale, G.E. (1908). On the probable existence of a magnetic field in Sun-spots. Astro-phys.J. 28, 315.
[6] Vögler. A, et al. (2005) Simulations of magneto-convection in the solar photosphere. A&A 429, 335-351.
[7] Unno, W. (1956). Line formation of a normal Zeeman triplet. Publ. Astron. Soc. Japan 8,108.
[8] Rachkovsky, D.N. (1962a). Magneto-optical effects in spectral lines of sunspots (in
Russian). Izv. Krymsk. Astrofiz. Obs. 27, 148.
[9] Rachkovsky, D.N. (1962b). Magnetic rotation effects in spectral lines (in Russian). Izv. Krymsk. Astrofiz. Obs. 28, 259.
[10] Landi Degl’Innocenti, E. and Landi Degl’Innocenti, M. (1972). Quantum theory of line formation in a magnetic field. Solar Phys. 27, 319.
[11] A. Tritschler, et al,(2016) Daniel K. Inouye Solar Telescope: High-resolution observ-ing of the dynamic Sun. Astron. Nachr. 337, 1064–1069
[12] de Wijn, A. G., et al.(2022) The Visible Spectro-Polarimeter of the Daniel K. Inouye Solar Telescope. SoPh, 297, 22.
[13] de Wijn, A. G., et al. (2012) Preliminary design of the Visible Spectro-Polarimeter for the Advanced Technology Solar Telescope. Proc. SPIE, 8446,84466X
[14] Scherrer, P. H., Schou, J., Bush, R. I., et al. (2012). The Helioseismic and Magnetic Imager (HMI) Investigation for the Solar Dynamics Observatory (SDO). Sol. Phys., 275, 207
[15] Erin E. Wilson and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.
[16] Leslie Stroebel; Richard D. Zakia (1995). The Focal encyclopedia of photography. Focal Press. p. 507. ISBN 978-0-240-51417-8.
[17] Philippe Cattin (2012-04-24). "Image Restoration: Introduction to Signal and Image Processing". MIAC, University of Basel. Retrieved 11 October 2013.
[18] Junichi Nakamura (2005). Image Sensors and Signal Processing for Digital Still Cameras. CRC Press. ISBN 0-8493-3545-0.
[19] S´anchez Almeida, J. & Landi Degl’Innocenti, E.(1996) Micro-structured magnetic atmospheres, Solar Phys., 164, 203–210.
[20] S´anchez Almeida, J., et al, (1996) Line Asymmetries and the Microstructure of Pho-tospheric Magnetic Fields, Astrophys. J., 466, 537–548
[21] Sobotka, M, & Puschmann, K. G (2009). Morphology and evolution of umbral dots and their substructures. A&A, 504, 575
[22] Stenflo. J. O. (1973). Magnetic-field structure of the photospheric network. SoPh, 32, 41.
[23] Bellot Rubio, L., & Orozco Suárez, D. (2019). Quiet Sun magnetic fields: an observa-tional view. Living Reviews in Solar Physics, 16, 1.
[24] Díaz Baso, C. J., & Asensio Ramos, A. (2018). Enhancing SDO/HMI images using deep learning. A&A, 614, A5.
[25] Deng, J., Song, W., Liu, D., et al. (2021). Improving the Spatial Resolution of Solar Images Using Generative Adversarial Network and Self-attention Mechanism. ApJ, 923, 76.
[26] David Kliger, James Lewis. (1990). Polarized Light in Optics and Spectroscopy.
[27] Born, M. and Wolf, E. (1993). Principles of optics, 6th edition (Pergamon Press: Ox-ford). Historical introduction.
[28] Lorentz, H. A. (1909). The theory of electrons and its applications to the phenomena of light and radiant heat. Vol. Bd. XXIX, Bd. 29. New York; Leipzig: B.G. Teubner.
[29] Bochner, S.& Chandrasekharan, K. (1949), Fourier Transforms, Princeton University Press.
[30] Zeeman, P. (1897). On the influence of magnetism on the nature of the light emitted by a substance. Astrophys. J. 5, 332. See also Phil. Mag. 43, 226.
[31] Mihalas, D. (1978). Stellar atmospheres (W.H. Freeman and Company: San Francis-co).
[32] Atkinson, K.E. (1989). An Introduction to Numerical Analysis New York: John Wiley & Sons.
[33] Burden, R.L. & Faires, J. D. (2000) Numerical Analysis.
[34] Rees, D.E., Murphy, G.A., and Durrant. (1989). Stokes Profile Analysis and Vector Magnetic Fields. II. Formal Numerical Solutions of the Stokes Transfer Equations. C.J. 1989, Ap. J., 339, 1093.
[35] Rempel. M. (2012) Numerical sunspot models: robustness of photospheric velocity and magnetic field structure. ApJ, 750, 62.
[36] J,Sanchez Almeida,et al (1996), Heights of formation for measurements of atmos-pheric parameters A&A, 314, 295.
[37] Riethmuller, T. L, et al. (2008) Brightness, distribution, and evolution of sunspot um-bral dots ¨ A&A, 492, 233
[38] del Toro Iniesta JC. (2003). Introduction to Spectropolarimetry. Cambridge: Cam-bridge Univ. Press
[39] Jason W. Ferguson,et al. (2005). Low-Temperature Opacities. ApJ, 623, 585
[40] Socas Navarro, H (2011). A high-resolution three-dimensional model of the solar photosphere derived from Hinode observations. A&A, 529, 37