Dear Editor,

we are glad the reviewers appreciate our work, and we welcome the constructive comments. In the following we address the points raised by the Reviewer 2.

- Section I: - "[...] to
work in different regions of the electromagnetic spectrum, from soft
X-rays to telecom wavelengths." TESs are also used in the hard X-ray and
even gamma-ray regime.

    We have extended the description of the wavelength range to include also gamma-rays and referenced a recent paper by Koyama et al. that describes its fabrication.

- Section IV: - The data shows good estimation up
to 3 photons. A comment on the performance beyond this limit would be
useful.

    We thank the reviewer for highlighting this point.
    We did not perform a systematic evaluation of the photon number resolution with our algorithm for larger nbar. From the performance for n=3, we expect to be able to demonstrate a reasonable energy resolution for larger photon numbers in the future, possibly matching the resolution obtained for pulsed sources.
    We included the following statement in the Sec.VII Conclusion:

    "Although we do not demonstrate photon number resolution for $n > 3$,
    transition edge sensors can resolve $n > 10$ photons from pulsed sources[24].
    We expect a similar extension to be possible for CW sources."

- Section V: - Equation (4): The left part has an extra ")"

    Corrected

- Section V.B: - Paragraph 3: "This matches the time accuracy expected
from the simple noise/slope estimation for the leading edge of the
single photon pulse, despite the overlapping pulses." This comparison
should be provided with other proofs, e.g. how the noise/slope
estimation was done, or a proper reference material.

    We included the noise / slope estimation and a relevant reference in Section III.

- Section VI: First paragraph: Although a reference was given, it might be helpful to briefly explain within the text why the author wanted to examine the
second order correlation function.

    We clarified the intent of the measurement of the second order correlation at the beginning of Section VI. We replaced "as another benchmark for the fitting algorithm" with "To examine the accuracy of the fitting technique over a continuous range of pulse separations".

- Section VII: Paragraph 5: In section V.B, it seems that this method is capable of handling events with 92 ns< delta t < 170 ns; and in section VI, the method seems capable down to 150 ns. In the conclusion, it is said "about 200 ns". Is there a specific reason why 200 ns is used? It is true that 150 and 200 are around the same order, but 200 seems to underestimate this method a
little bit.

    We thank the reviewer for pointing out this inconsistency.
    We corrected the relevant values in the Conclusion.

With this, we are looking forward for your consideration of publishing this
work in RSI.

With Best Regards on behalf of all authors,

Christian Kurtsiefer


List of changes:
Section I:
- replaced "soft X-rays" with "gamma-rays"
- added reference [3]

Section III:
- replaced
"An expected timing accuracy for single photon events that can be extracted
from the TES response would be given by the RMS noise (about 1.75 mV), and the
steepest slope of the response (0.11(9) mV/ns, estimated from an average of
10%-90% transitions of an ensemble of pulses) to be about
16 ns."
with
"We estimate a timing accuracy for single photon events [5] of $\sigma/(dv/dt) ~ 16 ns, from the RMS noise $\sigma = 1.75$ mV, and the
steepest slope of the response $dv/dt = 0.11(9)$ mV/ns (from the average of the 10%-90% transitions of an ensemble of pulses)."


Section V:
- added "(see section III)"

Section VI:
- replaced "As another benchmark for the fitting technique presented in here" with "To examine the accuracy of the fitting technique over a continuous range of time differences $\Delta t$"
- replaced "For a light field in a coherent state, this" with "This"

Section VII:
-added "Although we do not demonstrate photon number resolution for $n > 3$, transition edge sensors can resolve $n > 10$ photons from pulsed sources[24]. We expect a similar extension to be possible for CW sources."

- replaced "200ns" with "150ns"
- replaced "5 x 10^6 s^-1" with "6.7 x 10^6 s^-1"
- replaced "4 x 10^5 s^-1" with "4.0 x 10^5 s^-1"

References:
- added reference [3]