Sub-microdegree phase measurement technique using lock-in amplifiers

A phase measurement technique that is capable of measuring 100 nanodegree phase differences between sinusoidal electronic signals is presented. The technique can be implemented using a commercial lock-in amplifier and a computer to calculate the phase from the X and Y output lock-in channels. Whereas commercial lock-in amplifiers are typically limited to millidegree phase sensitivity, this technique can be used to improve their phase sensitivity up to 4 orders of magnitude. The technique is currently limited by the noise and thermal drift of the electronic components within the lock-in amplifier, limiting the maximum effective lock-in time constant to 30 sec. The technique is based on subtraction of the input signal and reference signal before using the lock-in amplifier to measure the phase. The improved phase sensitivity of several commercial lock-in amplifiers (analog and digital) are demonstrated using a simple RC low pass filter.