A brief history of the solar diameter measurements: a critical quality   assessment of the existing data
  The size of the diameter of the Sun has been debated for a very long time. First tackled by the Greek astronomers from a geometric point of view, an estimate, although incorrect, has been determined, not truly called into question for several centuries. The French school of astronomy, under the impetus of Mouton and Picard in the XVIIth century can be considered as a pioneer in this issue. It was followed by the German school at the end of the XIXth century whose works led to a canonical value established at 959".63 (second of arc). A number of ground-based observations has been made in the second half of the XIXth century leading to controversial results mainly due to the difficulty to disentangle between the solar and atmospheric effects. Dedicated space measurements yield to a very faint dependence of the solar diameter with time. New studies over the entire radiation spectrum lead to a clear relationship between the solar diameter and the wavelength, reflecting the height at which the lines are formed. Thus the absolute value of the solar diameter, which is a reference for many astrophysical applications, must be stated according to the wavelength. Furthermore, notable features of the Near Sub-Surface Layer (NSSL), called the leptocline, can be established in relation to the solar limb variations, mainly through the shape asphericities coefficients. The exact relationship has not been established yet, but recent studies encourage further in-depth investigations of the solar subsurface dynamics, both observationally and by numerical MHD simulations. 
Jean Pierre Rozelot, Alexander G. Kosovichev and Ali Kilcik
astro-ph.SR