Unlike traditional images, light field images capture comprehensive scene information, enabling novel post-capture manipulations. However, this very richness makes them vulnerable to tampering. This paper proposes lossless copyright protection of light-field images based on a robust zero-watermarking algorithm without modifying the original image. First, the fractional-order radial harmonic Fourier moments (FrRHFMs) for light-field images were computed accurately. The FrRHFMs and chaotic Logistic and May maps (LOMAS) were combined to produce a light-field images robust zero-watermarking algorithm. Due to the excellent geometric invariance of FrRHFMs and the chaotic system's initial value sensitivity, the proposed algorithm's robustness to geometric attacks and security was improved. The experiments' results demonstrated that this algorithm outperformed other algorithms and was resilient to conventional image processing and geometry attacks.