Laguerre-Gaussian single-pixel imaging for ultra-high-speed rotating objects based on the rotational Doppler effect

Imaging of high-speed rotating objects holds significant importance for both scientific research and industrial applications. The emerging single-pixel imaging (SPI) technique in recent years has provided a novel solution to accomplishing this task. However, it still faces limitations when dealing with ultra-high-speed rotation. This paper proposes a new SPI method for ultra-high-speed rotating objects based on the rotational Doppler effect (RDE). The method utilizes the rotational Doppler frequency shift generated by the interaction between Laguerre-Gaussian (LG) modes and the rotating object to acquire the LG spectrum, thereby enabling image reconstruction. By establishing a quantitative model of the relationship between the rotational Doppler frequency shift and the LG spectrum coefficients, the experiment successfully achieved imaging of a high-speed rotating object with a rotational speed of 444 revolutions per second (rps). The analysis indicates that the imaging performance is independent of the rotational speed, and the upper limit of the maximum rotation speed for imaging is determined solely by the maximum frequency shift that can be detected, as only the amplitude and phase of frequency shift are of interest in our measurement paradigm. Notably, the imaging time exhibits an inverse proportionality to the rotational speed. Such characteristic renders our methodology particularly advantageous for ultra-high-speed rotational imaging applications, where conventional approaches often encounter temporal resolution limitations.