Fig. 1. Principle of S-FFT and DSFD algorithms for lensless holographic projection. (a) S-FFT algorithm with plane wave illumination; the maximum projecting image size is limited by the Nyquist criterion. (b) DSFD algorithm with diverging point light source; the image size is larger.

Fig. 2. Projection image size of the S-FFT algorithm and DSFD algorithm, where the wavelength is 532 nm, pixel size is 8 µm, the number of pixels is 1920, and the distance between the point light source and the SLM plane is 2.6 cm.

Fig. 3. GS algorithm workflow for computing a phase-only CGH from target image.

Fig. 4. SGD algorithm workflow for computing a phase-only CGH from target image.

Fig. 5. Illustration of our wave propagation model. A target image is first converted to an amplitude value, and then is passed to a phase-encoder network (i.e., the U-Net). At the SLM plane, we display the CGH and propagate the light field to the target plane. During the training phase, the loss between the projection image and the target amplitude can be calculated and is then propagated back to train the phase-encoder network.

Fig. 6. Performance evaluation of the GS algorithm and the SGD algorithm.

Fig. 7. Performance evaluation of our U-Net and the iterative methods. The PSNR and MSE values indicate the reconstruction image quality of the algorithm.

Fig. 8. Comparison of average calculating speed and image quality achieved by several CGH techniques. (a) Images are reconstructed with similar quality at the same number of iterations by GS and SGD algorithms. (b) The SGD algorithm requires less time than the GS algorithm for high-quality reconstruction. The U-Net takes less than 0.05 s, which is far less than that of iterative methods. The horizontal of Fig. 8(b) is in logarithmic scale.

Fig. 9. Schematic of the experimental setup (P1, P2, polarizers; C&E, collimator and expander; L, lens; BS, beam splitter).

Fig. 10. (a) Simulated optical image and the experimental result based on U-Net. (b) Comparison of reconstruction quality of different encoding methods.