Adaptive interferometers based on dynamic holography within a nonlinear medium allow to precisely measuring phase modulations in noisy environments. Thanks to its adaptive behavior, the hologram follows slow external perturbations cancelling the low frequency phase mismatches between the two arms of the interferometer, while it appears static at high frequencies, hence, converting phase into intensity modulation. As a holographic medium, we use a liquid crystal light valve combining a photoconductor with a liquid crystal layer. The effective refractive index and, thus, the phase shift, depend both on the incident optical intensity and the bias voltage. By characterizing the response of the light valve, we show that low frequency noise can be filtered out within a voltage-controlled frequency bandwidth. This feature can be useful for applications where the signal of interest is limited by external noise such as temperature fluctuations and/or vibrations.