| It is well-known that magnetic fields with different scale and strength exist widely in astrospace. Comparing with the magnetic fields in the neutron star andwhite dwarf of 10~7 Gauss, the magnetic fields in the solar atmosphere is much smaller. Even in the umbra of sunspots, the strongest region in the solar atmosphere, the magnetic field strength is only about 2000 Gauss. The magnetic field in the solar atmosphere, however, plays a significant role in solar activities. Observations and researchs of polarized spectra are basic methods to know the magnetic field in solar atmosphere and other remote stars. Since the introduction of Zeeman effect to the astrophysics in the first of 20th century, the polarization from the solar active region is always an important tool to explore the nature and regularity of the solar acitivities.Our investigation focuses on processing Stokes spectra to inverse the vector magnetic fields of sunspots. Assuming that the Muller matrix and Stokes ejection vector in the line formal region are constant, the absorption matrix is diagonalized and a model is developed on the basis of Landi Delg'Innocenti's formal solution of polarization radiative transfer equation. Using the model, we fit the Stokes profiles of sunspots and obtain the distributions of vector magnetic field in sunspots.In Chapter I, we firstly describe the sunspots' featurs and importance of vector magnetic field measurement. Secondly, we introduce the measurement theory of vector magnetic field and some optical essentials for the measurement. Lastly, theSolar Stokes Spectrum Telescop (S~3T) is described in detail, including its structure,feature, data reduction. S~3T is a complicated optical instrument whose optical system is mainly made up of primary mirror, second mirror, corrector,reflector, grating and CCD. It can simultaneously obtain the full Stokes spectra of the selected magneto-sensitive lines.
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