We propose a swept source optical coherence tomography that uses an original external-cavity laser diode and demonstrate measurements of thickness distribution in two dimensions using this equipment. We first conducted high-speed, wide-range wavelength scanning with an external-cavity laser diode that was equipped with a special antireflection-coated laser diode working at 770 nm. Using an acousto-optic deflector enabled a tuning range and rate of 22 nm and 20 kHz, respectively, with no mechanical elements. Next, we applied this source to an optical coherence tomography and measured the two-dimensional distribution of thickness of a thin glass plate.