We present a systematic comparison of two complementary methods for determining the longitudinal charge density profile of the compressed electron bunches in the soft X-ray free-electron laser FLASH: a frequency-domain technique - coherent transition radiation (CTR) spectroscopy - and a time-domain technique - streaking of the electron beam with a transversely deflecting microwave structure (TDS). While the direct time-profile measurement with a TDS is a well-established method invented at SLAC, our group has pioneered high-resolution bunch shape analysis based on coherent radiation spectroscopy. We have developed a broadband spectrometer covering the wavelength range from $5$m to $433$m with two sets of remotely interchangeable staged reflection gratings. The measured spectral intensity allows to compute the absolute magnitude of the bunch form factor but not its phase which, however, is needed to retrieve the bunch profile. Two phase retrieval methods are investigated in detail: analytic phase computation by means of the Kramers-Kronig dispersion relation, and iterative phase retrieval. Several computational techniques are compared and evaluated in view of their applicability and efficiency. For a large variety of bunch shapes, the time profiles derived from the spectroscopic data are compared with the TDS profiles, and generally excellent agreement is observed down to the 10,fs level. For part of the measurements, two independent CTR spectrometer systems have been available, yielding almost identical bunch shapes. In summary, we demonstrate that using well calibrated and broadband spectroscopy data, a fast and reliable phase reconstruction algorithm leads to bunch profiles competitive to high resolution TDS measurements.

中文翻译：

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基准相干辐射光谱作为自由电子激光器高分辨率束形状重构的工具

我们对确定软X射线自由电子激光器FLASH中压缩电子束的纵向电荷密度分布的两种互补方法的系统比较：频域技术-相干跃迁辐射（CTR）光谱-和时间畴技术-用横向偏转微波结构（TDS）划线电子束。尽管使用TDS进行直接时间轮廓测量是SLAC发明的一种行之有效的方法，但我们小组已率先开发了基于相干辐射光谱的高分辨率束形分析。我们开发了一种宽带光谱仪，涵盖了从$5$米到 $433$m具有两组可远程互换的分阶段反射光栅。测得的光谱强度允许计算束形状因子的绝对大小，但不能计算其相位，但是要获得束轮廓，它的相位是绝对的。详细研究了两种相位检索方法：借助Kramers-Kronig色散关系的解析相位计算和迭代相位检索。考虑到几种计算技术的适用性和效率，对它们进行了比较和评估。对于各种各样的束形，将从光谱数据得出的时间轮廓与TDS轮廓进行比较，通常观察到在10，fs的水平上具有极好的一致性。对于部分测量，已经提供了两个独立的CTR光谱仪系统，产生的束形状几乎相同。综上所述，