Vibrational levels near the dissociation limit of NaK a (3) Sigma(+) + state are observed with an optical-optical double resonance technique. High resolution spectra are sensitively detected with the combination of perturbation facilitated polarization spectroscopy with frequency modulation spectroscopy. An electronically excited state, the B (II)-I-1 state, is mixed with the c (3) Sigma(+) State through spin-orbit interaction. The transition from the X (1) Sigma(+) state to the a (3) Sigma(+) State through the B 1II state is facilitated by the perturbation by the c(3) Sigma(+) state. Hyperfine structures of the a (3) Sigma(+)(v = 3-16,N = 4-25) state are resolved with this spectroscopic technique and found to be independent of vibrational and rotational quantum number. The a (3) Sigma(+) state can only be perturbed by the X(1) Sigma(+) state through the hyperfine interaction. The vibrational levels (v less than or equal to 16) of the a (3) Sigma(+) State are demonstrably not perturbed by the X(1) Sigma(+) state. The potential curve of the a (3) Sigma(+) state is determined by the near-dissociation expansion fitting of molecular constants and the inverse perturbation analysis method. The coefficients C-6, C-8, and C-10 of the potential function are determind to be (12.75 +/- 0.15) x 10(6) cm(-1) Angstrom(6), (2.22 +/- 0.19) x 10(8) cm(-1) Angstrom(8), and (1.100 +/- 0.061) x 10(10) cm(-1) Angstrom(10), respectively. The dissociation energy, D-e, is obtained to be 207.858 +/- 0.019 cm(-1), which is 2.8 cm(-1) above the highest observed vibrational level (v =16). determined