We have recently shown that for any oblique sample movement containing a transverse velocity component, the prevalent classic Doppler model assuming that the phase shift is proportional to the axial velocity component is erroneous for spectrometer-based FD OCT. While the previous derivation assumed a continuous integration of the photocurrent, we extend the new Doppler model for detectors with a shutter control by taking the detector dead time into account. Because an analytical solution for the new relation between phase shift and oblique sample displacement can not be given, numerically calculated universal contour plots, which are valid for any center wavelength and beam size, are presented for detector dead times ranging from 5 % to 90 %. Compared to systems with a duty cycle of 100 %, the average phase shift does not approach a constant value for large transverse displacements and high sample velocities. In contrast, at large detector dead times and with this small integration times, the numerically simulated phase shift corresponds almost to the assumed one according to the classic Doppler model for the investigated velocity range. The theoretical results were verified by using a flow phantom model.