  We report the reduction of the thermal lensing in cryogenic sapphire mirrors,
which is planed to be used in the Large scale Cryogenic Gravitational wave
Telescope (LCGT) project. We measured three key parameters of sapphire
substrate for thermal lensing at cryogenic temperature. They are optical
absorption coefficient, thermal conductivity and temperature coefficient of
refractive index at cryogenic temperature. On basis of these measurements, we
estimated the shot noise sensitivity of the interferometer with thermal lensing
by using a wave-front tracing simulation. We found that thermal lensing in
cryogenic sapphire mirrors is negligible.
