From an Analytical Formulation to a Digital Image Processing Strategy for Contour Hologram Synthesis

The generation of structured light beams with prescribed shapes, such as Bessel or Gaussian beams, is typically achieved through analytical formulations based on known parametric expressions. However, when synthesizing beams with arbitrary, free-form contours, these methods require a laborious process to first analyze and determine the specific parametric equations that compose the desired shape. This traditional, continuous approach is not only computationally intensive but also time consuming, limiting its application in scenarios demanding rapid responses.

In this work, a novel strategy is proposed, departing entirely from this analytical framework by adopting a digital image processing approach. The method works directly from a binary mask of the target shape, where the algorithm detects the contour edges and performs all subsequent operations in the discrete domain. By replacing symbolic parameterization and continuous integration with discrete differentiation and cumulative integration, it can achieve a substantial reduction in computational complexity. Numerical simulations demonstrate that this new method achieves high fidelity synthesis for a wide range of arbitrary contours, with the resulting light beams accurately tracing the input shapes. This research provides a new pathway for synthesizing complex light beams, transitioning from a time intensive analytical formulation to a streamlined image based process that enhances both computational efficiency and flexibility.