From Analytical to Discrete Image-Based Contour Hologram Synthesis: A Comparative Analysis

A computational comparison between analytical and discrete image-based formulations for contour hologram synthesis is presented. The analytical approach relies on contour parameterization and Fourier-descriptor reconstruction to compute the phase accumulated along a closed contour, while the proposed discrete image-based approach performs contour extraction and phase accumulation directly on sampled spatial grids without explicit parametric modeling. Both methods were implemented under identical computational conditions and evaluated through numerical propagation in the Fraunhofer regime using representative contour geometries of increasing spatial complexity. Reconstruction quality was assessed using the Structural Similarity Index (SSIM), phase topology analysis, and hologram generation time measurements. Results show that both approaches successfully reconstruct the target contours while preserving the prescribed topological charge and phase winding behavior. High structural fidelity was obtained in all cases, with SSIM values above 0.93. The discrete image-based approach consistently produced slightly higher similarity values and achieved substantial reductions in computational cost, with speed-up factors ranging from approximately 120× to more than 1600×, depending on contour complexity. These results demonstrate that direct operation on sampled contour representations provides an efficient alternative to analytical contour parameterization while maintaining reconstruction quality and topological consistency.