Precise calibration of kilometer-scale interferometric gravitational wave detectors is crucial for source localization and waveform reconstruction. A technique that uses the radiation pressure of a power-modulated auxiliary laser to induce calibrated displacements of one of the ~10 kg arm cavity mirrors, a so-called photon calibrator, has been demonstrated previously and has recently been implemented on the LIGO detectors. In this paper, we discuss the inherent precision and accuracy of the LIGO photon calibrators and several improvements that have been developed to reduce the estimated voice coil actuator calibration uncertainties to less than 2% (1σ). These improvements include accounting for rotation-induced apparent length variations caused by interferometer and photon calibrator beam centering offsets, absolute laser power measurement using temperature-controlled InGaAs photodetectors mounted on integrating spheres and calibrated by NIST, minimizing errors induced by localized elastic deformation of the mirror surface by using a two-beam configuration with the photon calibrator beams symmetrically displaced about the center of the optic and simultaneously actuating the test mass with voice coil actuators and the photon calibrator to minimize fluctuations caused by the changing interferometer response. The photon calibrator is able to operate in the most sensitive interferometer configuration, and is expected to become a primary calibration method for future gravitational wave searches.