  We demonstrate a three step laser stabilisation scheme for excitation to nP
and nF Rydberg states in 85Rb, with all three lasers stabilised using active
feedback to independent Rb vapour cells. The setup allows stabilisation to the
Rydberg states 36P3/2 to 70P3/2 and 33F7/2 to 90F7/2, with the only limiting
factor being the available third step laser power. We study the scheme by
monitoring the three laser frequencies simultaneously against a self-referenced
optical frequency comb. The third step laser, locked to the Rydberg transition,
displays an Allan deviation of 30 kHz over 1 second and < 80 kHz over 1 hour.
The scheme is very robust and affordable, and it would be ideal for carrying
out a range of quantum information experiments.
