High-speed, high-resolution optical coherence tomography (OCT) imaging of the human retina is demonstrated using a frequency-swept laser at $850\mathrm{nm}$ . A compact external cavity semiconductor laser design, optimized for swept-source ophthalmic OCT, is described. The laser enables an effective $16\mathrm{kHz}$ sweep rate with $>10\mathrm{mm}$ coherence length and a tuning range of $\sim 35\mathrm{nm}$ full width at half-maximum, yielding an axial resolution of $<7\mu \mathrm{m}$ in tissue.