Vortex beams with orbital angular momentum (OAM) have attracted much attention in classical and quantum optics due to their infinite spatial states. In recent years, fractional OAM vortex beams have been introduced to increase the multiplexing ability of OAM mode dimensions. However, how to efficiently detect fractional OAM patterns is still a problem to be solved. This paper uses reverse design combined with coordinate transformation to identify fractional OAM patterns. Firstly, the fractional OAM mode is modulated by sector conversion to obtain a light field with a spiral phase gradient that increases exponentially. Secondly, the light field is re modulated by a logarithmically converted converted conversion phase superimposed on a reversely designed compensation phase. Finally, the recognition of a 21 order OAM pattern with a topological charge interval of 0.1 is realized. Moreover, it was found that after two multiplexed fractional OAM beams pass through the system, the minimum spacing at which the light spots can be separated is 0.6. At the same time, the system can still maintain a high diffraction efficiency of 83%. This provides an effective solution for solving the field of high efficiency and ultra high dimensional optical processing.