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We model and demonstrate a novel concept for the Doppler-shift compensation of optical transmitters. Optical frequency offset locking is demonstrated using a simple Fabry-Perot laser diode transmitter and a frequency-lock loop. Our system simultaneously demonstrates a continuous tracking range of 21 GHz and a tracking speed of 44 THz/s. The transmitter frequency is adjusted over the entire 21-GHz range by merely adjusting the frequency of a microwave oscillator.