For any oblique sample movement containing a transverse velocity component, the commonly used linear relationship between the phase shift and the axial velocity component is erroneous for spectrometer-based optical coherence tomography (spectral domain OCT, SD-OCT). We recently proposed a new Doppler model that assumes a continuous integration of the photocurrent. In this research, we extend the model for detectors with a shutter control by taking detector dead time into account. We present the new relation between phase shift and oblique sample displacement as well as the correlation of the phases of consecutive depth scans, in dependency on the detector dead times ranging from 5% to 90%, as numerically calculated universal contour plots, which are valid for any center wavelength and sample beam size. We found that detector dead time is recommended, especially for oblique sample motion. The reason for this recommendation is the achieved linear relation between the phase shift and the axial velocity component in the velocity range relevant for in vivo measurements, despite the signal damping due to shorter exposure time of the line detector. The theoretical Doppler model is verified using a 1% Intralipid flow phantom model. Because of the results of this research, we believe future measurements in Doppler SD-OCT can be more simple and more accurate by setting a shutter control for the line detector used.