We report high resolution sub-Doppler spectroscopy of molecular iodine hyperfine transitions around 541 nm. A novel solid state source, based on a diode laser, a Yb+ fiber amplifier and a periodically-poled KTiOPO4 crystal, was developed, having a continuous tunability range of 1.2 THz. The performance of this crystal for doubling 1083 nm laser radiation is demonstrated for the first time, as well as the use of a broad band Yb-doped fiber amplifier for Doppler-free spectroscopy. Preliminary results for the frequency stability of the 1083 nm diode laser locked to an iodine hyperfine line are reported. This source can be used as a compact frequency standard for precision measurements of the atomic helium and determination of the fine structure constant α.