It is well known that the classical fundamental limit of phase measurement by optical interferometry is due to shot noise. Within this limitation, the sensitivity for measuring incremental changes in the optical path-length improves for higher optical power, reaching nanometric sensitivity in standard interferometers. Another well-known approach for monitoring displacement is to measure the RF phase-change of RF-modulated light. However due to the many orders of magnitude difference between the optical carrier frequency and RF frequencies, typical sensitivities of the RF phase-shift method are in the millimeter regime. We have recently reported a new technique for photonic RF phase-shift amplification based on RF interferometry (Ben Ayun et al, Opt. Lett. 40,4863 (2015)). A striking feature of this amplifier is that the input phase noise is not amplified together with the input phase-shift signal, so that the phase sensitivity improves with higher phase-shift amplification. With 600 MHz modulated light and a phase-shift amplification of 100, we have demonstrated a phase resolution of 0.2 mrad, giving 8 μm distance resolution. In this work we review the theory of Phase-shift Amplification by RF Interferometry (PARFI) and compare its' performance to that of optical interferometry at the shot-noise limit. It is shown that nanometric displacement sensitivity can be achieved with PARFI at sub-GHz modulation frequencies. The ability to reach ultra-high displacement sensitivity with incoherent light is an attractive alternative to optical interferometry.