We calculate the root mean square (rms) value of the spectral noise caused by optical path phase measurement errors in a spatial heterodyne spectrometer (SHS) featuring a complex Fourier transformation. In our calculation the deviated phases of each Mach-Zehnder interferometer in the in-phase and quadrature states are treated as statistically independent random variables. We show that the rms value is proportional to the rms error of the phase measurement and that the proportionality coefficient is given analytically. The relationship enables us to estimate the potential performance of the SHS such as the sidelobe suppression ratio for a given measurement error.