Aim of this paper is formation of single focused diffraction order using binary amplitude modulation for digital micromirror device (DMD) applications. This can be achieved by using inline binary Fresnel holograms with divergent incident beam. However, extremely low reconstruction quality and diffraction efficiency of such holograms, synthesized by conventional means, prevent it. Here, we present new iterative method of synthesis of binary inline Fresnel holograms with much higher image reconstruction quality and diffraction efficiency compared to standard technique of hologram direct calculation. Synthesis procedure was carried out in two stages. The first stage of the new technique is based on Gerchberg-Saxton algorithm with two principal differences. First one is that synthesized diffractive optical element (DOE) is not a phase one, but an inline binary amplitude hologram. And second difference is that incident wavefront is spherical instead of a plane one. The second stage includes an application of the direct search with random trajectory method which greatly improves hologram characteristics by consequent processing of every pixel in it. The resulting binary inline Fresnel holograms in comparison to ones, synthesized using direct calculation method, have up to 11 times lower reconstruction error and up to 4 times higher diffraction efficiency. Results of optical reconstruction using DMD also demonstrate superiority of the new approach.

本文的目的是使用二进制幅度调制为数字微镜器件 (DMD) 应用形成单聚焦衍射级。这可以通过使用具有发散入射光束的内联二进制菲涅耳全息图来实现。然而，通过传统手段合成的这种全息图的重建质量和衍射效率极低，从而阻止了它。在这里，我们提出了合成二进制内联菲涅耳全息图的新迭代方法，与全息图直接计算的标准技术相比，该方法具有更高的图像重建质量和衍射效率。合成过程分两个阶段进行。新技术的第一阶段基于 Gerchberg-Saxton 算法，但有两个主要区别。第一个是合成衍射光学元件 (DOE) 不是相位元件，但内联二进制振幅全息图。第二个区别是入射波前是球形的而不是平面的。第二阶段包括应用随机轨迹直接搜索方法，通过对其中的每个像素进行后续处理，极大地改善了全息图的特性。与使用直接计算方法合成的二元内联菲涅耳全息图相比，其重构误差降低了 11 倍，衍射效率提高了 4 倍。使用 DMD 的光学重建结果也证明了新方法的优越性。第二阶段包括应用随机轨迹直接搜索方法，通过对其中的每个像素进行后续处理，极大地改善了全息图的特性。与使用直接计算方法合成的二元内联菲涅耳全息图相比，其重构误差降低了 11 倍，衍射效率提高了 4 倍。使用 DMD 的光学重建结果也证明了新方法的优越性。第二阶段包括应用随机轨迹直接搜索方法，通过对其中的每个像素进行后续处理，极大地改善了全息图的特性。与使用直接计算方法合成的二元内联菲涅耳全息图相比，其重构误差降低了 11 倍，衍射效率提高了 4 倍。使用 DMD 的光学重建结果也证明了新方法的优越性。