The measurement of optical ultrafast laser pulses is done indirectly because the required bandwidth to measure these pulses exceeds the bandwidth of current electronics. As a result, this measurement problem is often posed as a 1-D phase retrieval problem, which is fraught with ambiguities. The phase retrieval method known as ptychography solves this problem by making it possible to measure ultrafast pulses in either the time domain or the frequency domain. One well known algorithm is the principal components generalized projections algorithm (PCGPA) for extracting pulses from Frequency-Resolved Optical Gating (FROG) measurements. Here, we discuss the development of the PCPGA and introduce new developments including an operator formalism that allows for the convenient addition of external constraints and the development of more robust algorithms. A close cousin, the ptychographic iterative engine will also be covered and compared to the PCGPA. Additional developments using other algorithmic strategies will also be discussed along with new developments combining optics and high-speed electronics to achieve megahertz measurement rates.

光学超快激光脉冲的测量是间接完成的，因为测量这些脉冲所需的带宽超过了当前电子设备的带宽。因此，这个测量问题通常被视为一维相位检索问题，其中充满了歧义。称为 ptychography 的相位检索方法解决了这个问题，它可以在时域或频域中测量超快脉冲。一种众所周知的算法是用于从频率分辨光选通 (FROG) 测量中提取脉冲的主成分广义投影算法 (PCGPA)。在这里，我们讨论了 PCPGA 的发展并介绍了新的发展，包括允许方便地添加外部约束和开发更强大算法的运算符形式。一个近亲，ptychographic 迭代引擎也将被涵盖并与 PCGPA 进行比较。还将讨论使用其他算法策略的其他发展以及结合光学和高速电子技术以实现兆赫测量速率的新发展。