We present a new technique for radio frequency (RF) phase-shift amplification based on RF interferometry and demonstrate it in an optical system. A striking feature of this amplifier is that the input phase noise is not amplified together with the input phase signal, so the phase sensitivity improves with higher phase amplification. We also predict that in the case of correlated amplitude noise, the sensitivity is not affected by the amplitude noise. With 600 MHz of modulated light and a phase amplification of 100, we demonstrate a phase resolution of 0.2 mrad, giving a distance resolution of 8 μm. We postulate that nanometric distance resolution can be achieved with sub-gigahertz modulation.