It looks like that this solution corrects for dispersion in group velocity [1], but it's unclear that it can correct for dispersion in phase velocity at the same time [2]. My intuition that the latter is not possible this way, but optics is not my field.

Correcting for dispersion in group velocity seem to have applications in pulsed-laser experimental setups (as presented), but correcting for dispersion in phase velocity would be required for correcting for the more conventional chromatic aberration people are familiar with in photography.

[1] https://en.wikipedia.org/wiki/Group_velocity [2] https://en.wikipedia.org/wiki/Phase_velocity