Mr. Rochester's has his vision improve after visiting a London occulist, in modern times one would say the person was an optometerist. Through newspaper clippings and research articles I have narrowed down the doctor that Rochester would have visited at the time in London. This would have been Dr. John Nottingham. Nottingham was a diciple of the first real 'occulist' who was the doctor for Queen Anne and King George III, this was Benedict Duddell, who was the father of 'modern occulism.' Duddell would've most likely taught the occulist that was most famous at the time of Jane Eyre: John Nottingham, who was based in London. Nottingham published one of the most important documents regarding the treatment of the eye titled: "Practical observations on conical cornea, and on the short sight, and other defects of vision connected with it." 

Churchill, J., and A. Churchill. “Clerical, Medical and General Life Assurance Society, Report of the Directors.” The Medical Times and Gazette, 1 Jan. 1855, p. 854.

Grzybowski, A. and McGhee, C. N. (2013), Early history of keratoconus. Clin Exp Optom, 96: 140-145. doi:10.1111/cxo.12035