# Application of Matched-Filter Concepts to Unbiased Selection of Data in Pump-Probe Experiments with Free Electron Lasers

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## Abstract

**:**

## 1. Introduction

- validate the scans to be included or excluded from averaging
- determine the weight with which each scan should enter the average
- determine, if desired, by how much to temporally shift a scan prior to averaging

## 2. Results

## 3. Discussion

## 4. Materials and Methods

#### 4.1. Experimental

#### 4.2. Data Acquisition

#### 4.3. Data Reduction

**Figure 4.**Schematic representation of the generation of a delay scan $\left\{{S}_{i}\right\}$, as a function of pump-probe delay $\left\{{d}_{i}\right\}$ from single-shot data ${a}_{j}$. The green (red) dots symbolize shots that pass (fail) the filter conditions.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

EUV | Extreme Ultra Violet |

FEL | Free Electron Laser |

FERMI | Free Electron laser Radiation for Multidisciplinary Investigations (this acronym identifies the Free Electron Laser facility in Trieste, Italy) |

FWHM | Full Width at Half Maximum |

I0 | FEL energy per pulse |

LINAC | Linear Particle Accelerator |

$SNR$ | Signal-to-noise Ratio |

TOF | Time-of-flight |

UV | Ultra Violet |

## Appendix A

## References

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**Figure 1.**(

**a**) Three representative delay scans and (

**b**) their autocorrelation curves. We use the autocorrelation curves ($q=0$ excluded) as a criterion to classify scans as good (black), drifting (red), or pure noise (blue). The autocorrelation curve of a good scan is well approximated by a gaussian (green). In panel (

**a**), traces have been offset for clarity, and the shaded curve is the weighed average Equation (7); in panel (

**b**), the green curve is a gaussian fit of the black autocorrelation trace; the gray curve is the same, scaled to the height of the red autocorrelation trace (white-noise peak excluded). The calculated signal-to-noise ratio $\left(SNR\right)$ for the three scans are 1.30, 0.52, and 0.20.

**Figure 2.**(

**a**) Signal-to-noise ratio plotted versus scan index. (

**b**) Same data as (

**a**) sorted by increasing value, to highlight the gap between $\mathit{SNR}>0.25$ and $\mathit{SNR}<0.45$.

**Figure 3.**Single-shot ion-TOF trace (gray) and average over $12,200$ shots (red). One in three shots is a blank shot (no gas sample), which is subtracted from the average to eliminate spurious signals, such as that at $m/z=28$ in the single shot spectrum, due to residual nitrogen gas. Note that for $m/z>25$ both spectra are magnified by a factor 5.

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## Share and Cite

**MDPI and ACS Style**

Callegari, C.; Takanashi, T.; Fukuzawa, H.; Motomura, K.; Iablonskyi, D.; Kumagai, Y.; Mondal, S.; Tachibana, T.; Nagaya, K.; Nishiyama, T.;
et al. Application of Matched-Filter Concepts to Unbiased Selection of Data in Pump-Probe Experiments with Free Electron Lasers. *Appl. Sci.* **2017**, *7*, 621.
https://doi.org/10.3390/app7060621

**AMA Style**

Callegari C, Takanashi T, Fukuzawa H, Motomura K, Iablonskyi D, Kumagai Y, Mondal S, Tachibana T, Nagaya K, Nishiyama T,
et al. Application of Matched-Filter Concepts to Unbiased Selection of Data in Pump-Probe Experiments with Free Electron Lasers. *Applied Sciences*. 2017; 7(6):621.
https://doi.org/10.3390/app7060621

**Chicago/Turabian Style**

Callegari, Carlo, Tsukasa Takanashi, Hironobu Fukuzawa, Koji Motomura, Denys Iablonskyi, Yoshiaki Kumagai, Subhendu Mondal, Tetsuya Tachibana, Kiyonobu Nagaya, Toshiyuki Nishiyama,
and et al. 2017. "Application of Matched-Filter Concepts to Unbiased Selection of Data in Pump-Probe Experiments with Free Electron Lasers" *Applied Sciences* 7, no. 6: 621.
https://doi.org/10.3390/app7060621