The key physical processes of the laser fusion are well known and include the laser beam absorption, the heat transfer from the absorption zone to the ablation surface, the shell ablation acceleration and fusion fuel compression, the initiation of an effective thermonuclear burn. The first and second issues are investigated in detail on the small and moderate size facilities and high level of understanding is achieved on both phenomena. On the other hand, to study the thermonuclear burn seriously the large scale experiments should be carried out on the facilities of the next generation. Thus the efficiency and stability of the shell acceleration are today the main objects of experimental investigations in the majority of the laser fusion research laboratories. This paper is devoted to the development of the diagnostic methods just for studies of these problems.