Holographic display with optical computational Fresnel convolution to broaden distance.

As a method of near-field diffraction in the condition of the paraxial approximation, the Fresnel convolution (FR-CV) method is widely used in hologram generation and other applications. However, it is applicable to near-field diffraction, and the quality of holographic reconstruction degrades seriously with the increase of diffraction distance. Moreover, its hologram generation speed is limited due to the use of three fast Fourier transforms in the convolution operation. Nevertheless, there are also many application scenarios that need longer distance diffraction. To achieve a holographic display in broadened distance with high generation speed and reconstruction quality, an optical computational Fresnel convolution method is proposed in this paper. Since an optical Fourier lens is used to perform optical calculations for Fourier transforms in our proposed method, the hologram generation speed of the proposed method is approximately 8 times faster than that of the FR-CV method. Moreover, the reconstructed image with our proposed method can be successfully and clearly displayed at both short and longer diffraction distance by changing focal lengths of the Fourier lens. The effectiveness and superiority of the proposed method have been validated by both numerical simulations and optical experiments.