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Successful recording I, Q, U, and V Stokes parameters of the faint objects near the bright ones, particularly, structures of the upper solar atmosphere in the range < 1.4 Rsun, is defined by the acceptable level of stray light in telescopes. Reducing the stray light by the Lyot method, a multiple cascade coronagraphic technique, the use of super-smooth or moderately smooth with a given profile of a micro-relief primary optics are briefly noted. The efficiency of the other two ways to reduce the stray light is analyzed. They are different from the classical coronagraphic one and allow the use of telescopes with a simplified optical scheme. Recent technology advances allow the consideration of a new generation coronagraph with a variable transmission of an entrance aperture. Calculated efficiency is at least 2-3 orders of magnitude higher than in a Lyot-type coronagraph. Another approach is based on ground and space total solar eclipses. “Polarization images” (2D distributions of the polarization degree, the polarization angle, and the sign of the angle) and 2D distributions of the relative color index of the K-corona are shown to demonstrate advantages of total solar eclipse programs. Calculated dependences of the expected level of the stray light on distance are compared for ground (scattering at the Moon “profile”) and artificial space total solar eclipses: Artificial Solar Eclipse Experiment during the Apollo-Soyuz Test Project, Proba 3, near Mercury orbits).