A novel synchronous real-time analog sampling method for obtaining the sum and difference interferograms in double modulation Fourier transform infrared absorption experiments is described, and the application of this sampling methodology to polarization-modulation FTIR measurements of thin films at metal surfaces is demonstrated. A quadratic approximation of the background signal is used to calculate the difference interferogram. The demodulation of a test waveform with the real-time sampling electronics reveals how the bandwidth limitations of previous double modulation experiments on FTIR interferometers that employed lock-in amplifiers have been eliminated.