An underwater planar covering problem is studied where the coverage region consists of polygonal cells, and line sweep motion is used for coverage. In many subsea applications, sidescan sonar has become a common tool, and the sidescan sonar data is meaningful only when the sonar is moving in a straight line. This work studies the optimal line sweep coverage where the sweep paths of the cells consist of straight lines and no turn is allowed inside the cell. An optimal line sweep coverage solution is presented when the line sweep path is parallel to an edge of the cell boundary. The total time to complete the coverage task is minimized. A unique contribution of this work is that the optimal sequence of cell visits is computed in addition to the optimal line sweep paths and the optimal cell decomposition.