This study focuses on improving the accuracy of the energy distribution in directional wave spectra from temporal sequences of marine radar images. Wave spectra are obtained by converting the image spectrum to a wave spectrum by employing a modulation transfer function (MTF). While the imaging mechanism in the plane of the radar beam has received much attention, the effect of the combination of different beam positions has been largely neglected. Herein, we demonstrate that any MTF can only be valid for a limited azimuthal coverage. However, the proposed directional MTF is well suited for small windows for which it corrects the relative projection between the average radar beam position and the wavenumber vector. Spectra of different sea states are compared, using the derived MTF and the established MTF. The analysis shows a significant improvement in the energy distribution in the directional wave spectra when the directional spreading is high. It is suggested that future work should aim to remove the necessary restriction to small windows by synthesizing the full directional spectrum from multiple small windows in different directions. In this way, marine radars are suitable to better reproduce sea states with extreme directional spreading, including multi-modal seas (https://doi.org/10.1016/j.oceaneng.2024.118126).