Laguerre-Gaussian transform for rotating image processing.

In practical applications, it is often crucial to track high-speed rotating objects. However, the traditional Fourier transform techniques are not applicable under such circumstances because the Fourier spectrum of a rotating object is changing. Here, we propose a Laguerre-Gaussian (LG) transform to analyze the rotating object. The rotation provides a feasible way to acquire a LG-mode spectrum, which does not change even the object working at a high rotating speed. By analyzing the LG spectrum, one can perform image processing such as reconstruction, edge enhancement, and pattern replication. The LG transform makes it convenient for real-time monitoring of industrial and astronomical objects.