Cubic spline interpolation is able to recover temporally and spectrally resolved soft x-ray fluxes from an array of K-edge filtered x-ray diodes without the need for a priori assumptions about the spectrum or the geometry of the emitting volume. The mathematics of the cubic spline interpolation is discussed in detail. The analytic nature of the cubic spline solution allows for analytical error propagation, and the method of calculating the error for radiation temperature, spectral power, and confidence intervals of the unfolded spectrally resolved flux is explained. An unfold of a blackbody model demonstrates the accuracy of the cubic spline unfold. Tests of cubic spline performance using spectrally convolved detailed atomic model simulation results have been performed to measure the method's ability to conserve spectral power to within a factor of 2 or better in line-dominated regimes. The unfold is also demonstrated to work when information from the x-ray diode array is limited due to high signal-to-noise ratios or the lack of signal due to over-attenuation or over-filtration of the x-ray diode signal. The robustness of the unfold with respect to background subtraction and raw signal processing, signal alignment between diode traces, limited signal information, and initial conditions is discussed. Results from an example analysis of a halfraum drive are presented to demonstrate the capabilities of the unfold in comparison with previously established methods.

中文翻译：

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使用三次样条的 K 边滤波 X 射线二极管阵列的软 X 射线谱展开

三次样条插值能够从 K 边滤波 X 射线二极管阵列中恢复时间和光谱解析的软 X 射线通量，而无需对发射体积的光谱或几何形状进行先验假设。详细讨论三次样条插值的数学。三次样条解的解析性质允许解析误差传播，并解释了计算辐射温度、光谱功率和展开光谱解析通量的置信区间的误差的方法。黑体模型的展开展示了三次样条展开的准确性。使用光谱卷积的详细原子模型模拟结果对三次样条性能进行了测试，以测量该方法。s 能够将频谱功率保持在 2 倍以内或在线主导状态下更好。当来自 x 射线二极管阵列的信息由于高信噪比或由于 x 射线二极管信号的过度衰减或过度过滤而缺乏信号时，展开也被证明是有效的。讨论了展开在背景扣除和原始信号处理、二极管迹线之间的信号对齐、有限信号信息和初始条件方面的稳健性。介绍了半腔驱动器的示例分析结果，以证明与以前建立的方法相比展开的能力。当来自 x 射线二极管阵列的信息由于高信噪比或由于 x 射线二极管信号的过度衰减或过度过滤而缺乏信号时，展开也被证明是有效的。讨论了展开在背景减法和原始信号处理、二极管迹线之间的信号对齐、有限信号信息和初始条件方面的稳健性。介绍了半腔驱动器的示例分析结果，以证明与以前建立的方法相比展开的能力。当来自 x 射线二极管阵列的信息由于高信噪比或由于 x 射线二极管信号的过度衰减或过度过滤而缺乏信号时，展开也被证明是有效的。讨论了展开在背景减法和原始信号处理、二极管迹线之间的信号对齐、有限信号信息和初始条件方面的稳健性。介绍了半腔驱动器的示例分析结果，以证明与以前建立的方法相比展开的能力。并讨论了初始条件。介绍了半腔驱动器的示例分析结果，以证明与以前建立的方法相比展开的能力。并讨论了初始条件。介绍了半腔驱动器的示例分析结果，以证明与以前建立的方法相比展开的能力。