Optical phased arrays (OPAs) have been a popular option to manipulate the spatial behavior of the free-space optical beams. Inspired by the success of the integrated circuits (IC) industry, photonic IC (PIC) based OPAs have been actively studied in the last decade. Due to the fabrication imperfection, light passing through different paths typically results in random phase errors. The phase errors can seriously deviate the interference pattern of an OPA, and radically change the spatial distribution of the optical field. This phenomenon will significantly degrade the performance for applications like image scanning and optical wireless communication (OWC). Thermally or electrically tunable phase shifters can be applied to compensate the phase errors through dedicated calibration algorithms. However, the complexity of the calibration processes quickly increases with the number of the OPA’s elements. Hence, the whole processing can be time-consuming and this significantly pushes the overall system cost. Besides, considering the potential dynamic factors such as thermal gradient and aging effects, continuous calibration may be necessary. This results in great demand for fast and efficient calibration processing for the practical applications. In this paper, novel and efficient radix-p calibration processing is proposed which can be directly combined with most of the already reported/developed optimization algorithms as a speed-up turbo. It is shown that the computation time of the proposed radix-p processing grows linearly with the number of the OPA’s elements. In comparison to the conventional particle swarm optimization (PSO) algorithm, which exhibits exponential computation time in our numerical results, the radix-p processing shows great efficiency improvement. In the numerical results, speed with more than 12 times faster is shown for the proposed radix-p processing compared to the traditional PSO algorithms.

中文翻译：

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通过 radix-p 优化处理快速校准相位误差

光学相控阵 (OPA) 已成为操纵自由空间光束空间行为的流行选择。受集成电路 (IC) 行业成功的启发，过去十年中一直在积极研究基于光子 IC (PIC) 的 OPA。由于制造缺陷，通过不同路径的光通常会导致随机相位误差。相位误差会严重偏离 OPA 的干涉图样，并从根本上改变光场的空间分布。这种现象将显着降低图像扫描和光无线通信 (OWC) 等应用的性能。热或电可调移相器可用于通过专用校准算法补偿相位误差。然而，随着 OPA 元件的数量增加，校准过程的复杂性会迅速增加。因此，整个处理过程可能非常耗时，这显着推高了整体系统成本。此外，考虑到诸如热梯度和老化效应等潜在的动态因素，可能需要连续校准。这导致实际应用对快速有效的校准处理的需求很大。在本文中，提出了一种新颖且高效的 radix-p 校准处理，它可以直接与大多数已经报告/开发的优化算法结合作为加速涡轮。结果表明，所提出的基数 p 处理的计算时间随着 OPA 元素的数量线性增长。与传统的粒子群优化（PSO）算法相比，在我们的数值结果中表现出指数计算时间，radix-p 处理显示出极大的效率改进。在数值结果中，与传统 PSO 算法相比，所提出的 radix-p 处理速度提高了 12 倍以上。