addenda and errata\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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ISSN: 1600-5775

Determination of X-ray pulse duration via intensity correlation measurement of X-ray fluorescence. Erratum

aRIKEN SPring-8 Center, 1-1-1, Kouto, Sayo, Hyogo 679-5148, Japan, and bJapan Synchrotron Radiation Research Institute, 1-1-1 Kouto, Sayo, Hyogo 679-5198, Japan
*Correspondence e-mail: inoue@spring8.or.jp

Edited by G. Grübel, HASYLAB at DESY, Germany (Received 25 September 2020; accepted 13 November 2020)

Corrections to equations and experimental results in the paper by Inoue et al. [(2019[Inoue, I., Tamasaku, K., Osaka, T., Inubushi, Y. & Yabashi, M. (2019). J. Synchrotron Rad. 26, 2050-2054.]). J. Synchrotron Rad. 26, 2050–2054] are made.

The correct versions of equations (2)[link] and (3)[link] in the paper by Inoue et al. (2019[Inoue, I., Tamasaku, K., Osaka, T., Inubushi, Y. & Yabashi, M. (2019). J. Synchrotron Rad. 26, 2050-2054.]) are as follows:

[{g}_{f}^{\left(2\right)} \left({{r}}_{1},{{r}}_{2}\right) = 1 + {{{1}\over{2}} \big|\,j\,\left({{r}}_{1},{{r}}_{2}\right)\big|}^{2} \int\Pi \left(\tau\right)\,{\big|\gamma\left(\tau\right)\big|}^{2} \,{\rm{d}}\tau, \eqno(2)]

[{g}_{f}^{\left(2\right)}\left({{r}}_{1},{{r}}_{2}\right) = 1 + {{1}\over{2}} {g}_{0}^{(2)} \exp\left(-{{\Delta{x}^{2}}\over{2{l}_{x}^{\,2}}}\right) \exp\left(-{{\Delta{y}^{2}}\over{2{l}_{y}^{\,2}}}\right). \eqno(3)]

The additional factors of 1/2 on the right-hand sides of these equations represent a decrease in intensity correlation of X-ray fluorescence due to the unpolarized nature of the fluorescence (Trost et al., 2020[Trost, F., Ayyer, K. & Chapman, H. (2020). New J. Phys. 22, 083070.]; Goodman, 2007[Goodman, J. W. (2007). Speckle Phenomena in Optics: Theory and Applications. Englewood: Roberts and Co.]).

Accordingly, the degree of intensity correlation [g0(2)] and the XFEL duration [[2\sqrt{2\ln2}\,{\sigma_t}]] evaluated by the experiment also need to be corrected; the values of g0(2) and [2\sqrt{2\ln2}\,{\sigma_t}] shown in Section 4 should be 0.0262 ± 0.008 and 5.1 ± 0.2 fs, respectively. The determined XFEL duration is consistent with previous estimations by other methods (Inubushi et al., 2017[Inubushi, Y., Inoue, I., Kim, J., Nishihara, A., Matsuyama, S., Yumoto, H., Koyama, T., Tono, K., Ohashi, H., Yamauchi, K. & Yabashi, M. (2017). Appl. Sci. 7, 584.]; Inoue et al., 2018[Inoue, I., Hara, T., Inubushi, Y., Tono, K., Inagaki, T., Katayama, T., Amemiya, Y., Tanaka, H. & Yabashi, M. (2018). Phys. Rev. Accel. Beams, 21, 080704.]), in which the XFEL duration was evaluated to be less than 10 fs. Although the determined XFEL duration is shorter than the electron bunch duration measured by a radiofrequency deflector (∼10 fs in FWHM), such discrepancy could be explained by insufficient time resolution of the deflector (∼10 fs) (Ego et al., 2015[Ego, H., Maesaka, H., Sakurai, T., Otake, Y., Hashirano, T. & Miura, S. (2015). Nucl. Instrum. Methods Phys. Res. A, 795, 381-388.]).

Acknowledgements

We thank the authors of Trost et al. (2020) for pointing out the errors in the original paper.

References

First citationEgo, H., Maesaka, H., Sakurai, T., Otake, Y., Hashirano, T. & Miura, S. (2015). Nucl. Instrum. Methods Phys. Res. A, 795, 381–388.  Web of Science CrossRef CAS Google Scholar
First citationGoodman, J. W. (2007). Speckle Phenomena in Optics: Theory and Applications. Englewood: Roberts and Co.  Google Scholar
First citationInoue, I., Hara, T., Inubushi, Y., Tono, K., Inagaki, T., Katayama, T., Amemiya, Y., Tanaka, H. & Yabashi, M. (2018). Phys. Rev. Accel. Beams, 21, 080704.  Web of Science CrossRef Google Scholar
First citationInoue, I., Tamasaku, K., Osaka, T., Inubushi, Y. & Yabashi, M. (2019). J. Synchrotron Rad. 26, 2050–2054.  Web of Science CrossRef IUCr Journals Google Scholar
First citationInubushi, Y., Inoue, I., Kim, J., Nishihara, A., Matsuyama, S., Yumoto, H., Koyama, T., Tono, K., Ohashi, H., Yamauchi, K. & Yabashi, M. (2017). Appl. Sci. 7, 584.  Web of Science CrossRef Google Scholar
First citationTrost, F., Ayyer, K. & Chapman, H. (2020). New J. Phys. 22, 083070.  CrossRef Google Scholar

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