Ultra-fast optical pulses are the most ephemeral sensing paradigm ever devised, examining events over incredibly brief timescales with broadband illumination. A consequence of sensing at timescales lower than a picosecond is that pulse characterization cannot be done with traditional analog-to-digital samplers and must be ascertained from integrating intensity sensors. Techniques for pulse characterization have been constructed using combinations of time-invariant and time-variant filter responses to create non-linear but invertible intensity datasets (Walmsley & Dorrer, 2009). In this paper, we develop a novel high-order phase retrieval technique to perform pulse characterization from a single-pixel integrating sensor measuring integrated intensity of auto-convolution (IIAC). We examine gradient descent’s ability to recover signals as a function of signal dimension and measurement count, and we demonstrate the effective use of iterative hard tensor thresholding as an initializer. Finally, we demonstrate IIAC recovery in a laboratory setting to recover the time profile of a complex laser pulse. We assert that the IIAC recovery solution demonstrated here simultaneously provides the optics community with a pulse characterization technique that scales to low-power microscopy systems and provides the optimization community with a physically motivated high-order phase retrieval problem enhanced by low-rank tensor processing.

中文翻译：

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从自动卷积的积分强度进行相位检索

超快光脉冲是迄今为止设计的最短暂的传感范例，利用宽带照明在极其短暂的时间尺度上检查事件。在低于皮秒的时间尺度上进行传感的结果是，脉冲表征无法使用传统的模数采样器来完成，必须通过集成强度传感器来确定。脉冲表征技术是使用时不变和时变滤波器响应的组合来构建的，以创建非线性但可逆的强度数据集（Walmsley & Dorrer，2009）。在本文中，我们开发了一种新颖的高阶相位检索技术，用于从测量自动卷积积分强度（IIAC）的单像素积分传感器执行脉冲表征。我们检查梯度下降恢复信号作为信号维度和测量计数的函数的能力，并且我们演示了迭代硬张量阈值作为初始化器的有效使用。最后，我们在实验室环境中演示了 IIAC 恢复，以恢复复杂激光脉冲的时间轮廓。我们断言，此处演示的 IIAC 恢复解决方案同时为光学界提供了可扩展到低功率显微镜系统的脉冲表征技术，并为优化界提供了通过低秩张量处理增强的物理驱动的高阶相位检索问题。