Rolling shutter strobe pattern
No matter when the camera shutter is active, if the frequencies of the video vertical timing (the frame rate) and the laser pulse are not congruent, you'll see partial exposures as they drift apart.

The solution is to trigger the laser pulse on every other vertical sync time. The details on extracting the vertical interval will depend on the camera, and how to trigger the laser will depend on the details of that device. But some sort of forced sync is the only way to get exactly what you want.