  We present exact solutions for rogue waves arising on the background of
periodic waves in the focusing nonlinear Schrodinger equation. The exact
solutions are obtained by characterizing the Lax spectrum related to the
periodic waves and by using the one-fold Darboux transformation. The
magnification factor of the rogue waves is computed in the closed analytical
form. We relate the rogue wave solutions to the modulation instability of the
periodic wave background.
