  We present a frequency modulation technique for calibration of the
displacement actuators of the LIGO 4-km-long interferometric gravitational-wave
detectors. With the interferometer locked in a single-arm configuration, we
modulate the frequency of the laser light, creating an effective length
variation that we calibrate by measuring the amplitude of the frequency
modulation. By simultaneously driving the voice coil actuators that control the
length of the arm cavity, we calibrate the voice coil actuation coefficient
with an estimated 1-sigma uncertainty of less than one percent. This technique
enables a force-free, single-step actuator calibration using a displacement
fiducial that is fundamentally different from those employed in other
calibration methods.
