Fast scaled cylindrical holography based on scaled convolution

Abstract

Recently, the 360°display of cylindrical holography has garnered significant attention. However, existing studies have been limited to concentric cylindrical surfaces with equal heights, which restricts the height of the objects. In this paper, a fast scaled cylindrical holography is proposed based on scaled convolution to break this constraint. Firstly, the scale cylindrical diffraction is derived using the Rayleigh–Sommerfeld diffraction formula for scaled cylindrical holography, in which the object’s height can be adjusted. Then, a method of fast scaled cylindrical diffraction is presented by scaled convolution based on scaled Fourier Transform, and it significantly reduces computational time, enhancing its practical feasibility. Furthermore, the proposed method is extended to 3D objects using a layer-oriented approach. Moreover, the effectiveness and feasibility of the proposed method are verified through numerical simulations and optical experiments. Therefore, the issue of the constraint on the object’s height in cylindrical holography is thoroughly discussed and effectively addressed for the first time. This breakthrough paves the way for the development of a zoom-able cylindrical holographic display with immense potential for applications in mixed reality and beyond.