We study the effect of diffraction on the performance of microelectromechanical system Michelson interferometers. By using a simple Gaussian model, we calculate the degradation of the interferometer visibility due to the diffraction effect. We then use this model to estimate the optimum detector diameter to maximize the fringe visibility at the interferometer output and study its effect on the resolution of Fourier transform spectrometers based on Michelson interferometers.