Doppler asymmetric spatial heterodyne spectroscopy (DASH) technique with the advantages of high spectral resolution and high phase sensitivity can be considered as a combination of the spatial heterodyne spectroscopy (SHS) technique and the Michelson interferometer technique, which is very suitable for high-precision passive measurement of Doppler velocity. Since a larger optical path difference offset in one of the spectrometer arms corresponds to a higher phase shift sensitivity while suffering a lower contrast of the interferogram, there is an optimum path difference offset for measuring the phase shift and thus the Doppler shift is most sensitive. By comprehensively considering the trade-off between the contrast and the phase shift sensitivity of the interferogram, in this paper we carry out theoretical analysis on the optimum path difference offset. Based on the efficiency function which is defined as the product of the optical path difference and the contrast of the interferogram, the mathematical expressions of the optimum path difference offset for the Gaussian and Lorentz type emission spectral lines are theoretically deduced, respectively. In order to verify these two mathematical expressions, a simulation analysis about the phase shifts of the interference fringes for a single Gaussian type emission spectral line is carried out. The simulation result is consistent with the theoretical value calculated by the deduced mathematical expression. In addition, concerning the complexity of the traditional data processing method for resolving the Doppler velocities of multiple spectral lines, a simplified data processing method based on partial interference fringes is proposed. In general, a single spectral line should be distinguished and isolated from multiple spectral lines in the traditional data processing method. If the distribution of the spectral lines in the passband is too dense, a DASH spectrometer with high enough spectral resolution will be needed. The proposed processing method, retrieving the Doppler velocity from multiple spectral lines without isolating a single line in frequency domain, can not only effectively reduce the calculation of data processing, but also lower the requirement for the spectral resolution of the DASH spectrometer. Combining it with the adaptive frequency-tracing algorithm, the simulation calculations of the Doppler velocity measurement process of the single and multiple spectral lines are conducted. The results show that without taking the noise into account, the maximum resolving errors derived from the proposed data processing method for single and multiple spectral lines are similar, both within 0.005 m/s. It indicates that the proposed data processing method can fully meet the accuracy requirement of practical application and shows the prospect of wide applications in the field of passive Doppler velocity measurement.