Dear Prof. Rasio,

first of all, we like to thank you and the reviewer for the detailed and
constructive comments on our manuscript.

The key issue with the manuscript is our statement that the
filtering technique can revive the interest of astronomy in intensity
interferometry again. We do agree that the proof of Hanbury Brown and others
that the signal to noise ratio for observing the photon bunching signature
from a star is independent from the filter bandwidth for intensity
interferometry in the traditional regime where the coherence time tau_c due to
filtering is much shorter than the detector resolution tau_d. The situation is
slightly less obvious in the regime we are working, where the temporal detector
resolution tau_d is smaller than the coherence time, mostly because the
"signal" of the bunching signature is not contained in a single time slot
anymore, but distributed over a part of a timing histogram. The original
argument of the SNR being independent of the filter bandwidth, however, should
still hold, at least for a probably reasonable definition of the signal as a
fit parameter of the visibility of the bunching signal. We therefore agree
that the filtering technique probably does not help to improve spatial
coherence measurements in comparison to the Narrabri results.

We do believe, however, that the temporal resolution of the photon bunching
signature may make this technique still interesting for the astronomy
community: Specifically, we feel that in a spectral assessment of Wolf-Rayet stars
with very narrow spectral emission features that the tool could be helpful, maybe
even in answering the question if the narrow-band emission can be attributed
to a laser-like enhancement process. There, the full temporal resolution of
the photon bunching signature may be helpful.

We also like to stress that, in comparison with measurements where the photon
bunching signature is very small compared the background (with the traditional
situations where tau_d >>tau_c), we can make a relatively precise statement on
the absolute peak value if the bunching signature. By now, we do have a better
quantitative understanding what reduces our observed g(2) to the extent that
we can probably make quantitative statements on the visibility of the bunching
signal. This also may help to understand the statistical properties of distant
light sources better, and possibly help in looking at decoherence properties
of light over longer distances.

We therefore changed this aspect of our manuscript completely by removing the
emphasis on intensity interferometry as a means to look at the spatial
coherence of stars, and putting an emphasis on spectral measurements and the
high absolute value of the observed photon bunching signal. We also made a
hopefully clear reference to the original argument of SNR being independent of
the filtering bandwidth in the text. We chose not to quote the complete
expression for the SNR, since only aspect that is important was the independence
of the filtering bandwidth, and we still have not fully sorted out how to
come up with a corresponding expression in the our regime where
tau_d<tau_c. The affected sections in the manuscript are the abstract, the
introductory background section, and the summary and outlook part.

(a) In the abstract, we removed the reference to spatial intensity
interferometry.
(b) In the introductory part, we significantly changed the reference to intensity
interferometry, included a brief comment on the SNR argument in spatial
coherence measurements, and explain briefly the difference of traditional HBT
measurements and our configuration (tau_c<tau_d vs. tau_d>tau_c). The new
section starts at "Yet, the comparatively simple optical intensity
interferometer...." To make the and added two new paragraphs on the narrow
features in Wolf-Rayet stars, and the high absolute visibility of the photon
bunching signature (which may also be useful to understand the light
generation process of these stars...)
(c) We removed statements on spatial coherence measurements in the summary.

We still believe that this work is of interest to the astrophysics community
for the reasons outlined above.

As for the other issues pointed out by the referee, we tried to address them
in the following way:

1. page 2, left column, first few lines of paragraph 1

Obviously the bunching has already been measured by the experiments of
Hanbury Brown. Admittedly the excess correlation was tiny, but the sheer
number of photons still made a measurement possible. (This is closely
related to the major issue described above.)

Reply: distinction between spatial(established technique in astronomy) and temporal(uncommon in astronomy)
"Therefore, empirical observation of temporal photon bunching from blackbody
light sources has been extremely difficult, with only recent breakthroughs
using two-photon absorption in semiconductors \citep{boitier:09}, and in
ghost imaging research using a narrowband Faraday anomalous dispersion optical
filter \citep{karmakar:12, liu:14}.

In this paper, we present a spectral filtering technique that significantly
increases the observed temporal photon bunching signature from a blackbody light
source."

2. page 2, left column, last paragraph, line 3

Please explain what "NA=0.13" means.

Reply: numerical aperture. This is now included in  the text.

3. page 2, Eq. (2)

Can you provide a reference for this equation? (Remember that ApJL is
read by astronomers who are not all experts in these optical devices.)

Reply: We added a hopefully easy accessible reference textbook: quantum optics: an introduction, by mark fox, oxford university press (2006)

4. page 3, left column, paragraph 4

The structure of the sentence "The temporal correlation..." is unclear.

 Reply: We elaborated slightly more on the measurement scheme using the
 oscilloscope. It making use of a measurement option of the device:
"The temporal correlation was carried out with a digital sampling
oscilloscope (4\,GHz analog bandwidth, 40\,Gsamples/sec, LeCroy) that recorded
the APD signals if two detection events fall within a coarse coincidence time
window of 20\,ns. The oscilloscope then evaluated the timing difference $\tau$
between the APD events with an uncertainty below 10\,ps, and generated a
histogram of all observed $\tau$. The temporal correlation function
$g^{(2)}(\tau)$ is just a normalized version of this histogram."

5. page 3, left column, line 5 from bottom

English is not my native language, but to me the word "convolved" would
seem more appropriate than "convoluted".

Reply: corrected, thanks!

6. page 3, right column, section 4

I assume that the PDF detectors were used here. This should be mentioned.

Reply: We inserted the reference there.

7. page 3, right column, last paragraph, lines 4-7

Can you be more specific on exactly which discrepancy you are referring two?

Reply: This is an instrument-related issue of the oscilloscope we use for
histograming. Depending on the acquisition mode, the device spends some time
in evaluating the time difference between the events where it can not record
pair events. This poses a problem when normalizing the g(2) function to what
we would expect from the individual detector event rates r1, r2, where we
expect a total number of r1*r2*Tm*tb events, where Tm is the whole acquisition
time (hours), and tb is the bin width of the histogram (few 10 ps). Because we
can not exactly measure what time the oscilloscope spends not measuring, we
need an independent source of information what the value of g(2)(tau) is for
tau>>tau_c. This is done with a separate time stamp unit that does not have this
duty cycle issue, but not enough time resolution to resolve the photon
bunching feature. We wanted the information being present, because the
normalization with the rates and total integration times we quote otherwise do
not seem to match. The most obvious point is a comparison with the Hg data,
and the sunlight data, where the Hg measurement took significantly longer,
even though we receive much more events at the detectors. There, the we had
chosen an acquisition mode of the oscilloscope that displays the two detector
signal traces after each pair event, which dramatically reduces the duty
cycle. In the arc discharge and sunlight measurement, we disabled this option
and acquired a large number of traces before processing. We believe this is a
very technical problem, related to some intricacies how the oscilloscope
evaluates time differences between events, so we thought it would clutter the
article if we detailed it too much.

We modified the statement there to be slightly more explicit:  

"unlike the oscilloscope with a varying dead time (and thus
integration time) which is dependent on the sampling mode and light
intensity},..."

8. page 3/4, section 4

It would be good to see a bit more discussion of the possible reasons
for g^(2) being lower than the expected value of 2. (As impressive as
the values are already!)
The width of the central peak of the response of the PDF (as shown in
red in Fig. 3) should not have much of an effect, but the broader wings
(as mentioned just before section 4) may well play a role. This would
also explain the apparent correlation between the peak value and the width.

I don't see immediately how atmospheric fluctuations can be responsible
for the reduced correlation in case of the Sun as mentioned just before
section 5. Would all these effects not vanish after the single-mode
fibre? In my understanding this fibre should produce pure thermal
radiation as if from a stochastic point-source.

Reply: We did a more careful characterization of the etalon, and could
identify one of the reasons for the reduction in the visibility
quantitatively. By now, we seem to fairly well understand the visibility from
the mercury light and the arch discharge, but
still see a lower visibility from sunlight. We understand the argument of the
referee about the single spatial mode, but we have not yet fully understood
the reduction of visibility from the sun light as compared to the arc
discharge. We carried out measurements at two different elevations above the
horizon, which may indicate that atmospheric effects may be an issue,
although we do not yet have a good understanding why. We added comments at the
various experimental result discussions outlining the effects of individual
contributions: 

For the detector resolution:
"A convolution of an ideal correlation
function from a finite-bandwidth thermal light source (where
$g^{{(2)}}(\tau=0)=2$) with the detector response recorded in
figure~\ref{fig:jitter} leads to $g^{{(2)}}(\tau=0)=1.85$. Thus, the mercury
lamp seems perfectly compatible with a thermal light source."

For the residual transmission in the "stop band" of the etalon:
"For an etalon of R $\approx97$\% and so an effective finesse of about
100, we expect a minimum transmission of $\approx0.1$\% over the whole grating
transmission of $\approx240$\,GHz (for 2 FWHMs). The etalon also has a
less-than-ideal peak transmission of approximately 50\% . The off-peak
transmission of the etalon effectively serves as an additional incoherent
light source that adds about 24\% more photons than a
singly-peaked transmission with exponential decay. These additional random
correlations should thus further reduce the measured $g^{(2)}(\tau=0)$
from 1.8 due to the detector
resolution down to $\approx1.5$, which is in good agreement with the
value of 1.45 measured for the Ar arc lamp."

For atmospheric effects:
"This apparent dependency of the measured visibility of the photon
bunching on the altitude of the Sun is possibly due to seeing-induced
atmospheric fluctuations in optical path
length differences \citep{dravins:07a}, where studies by
\citet{kral:04, blazej:08, ortolani:12} suggest that atmospheric
turbulence and scintillation may introduce jitter in photon timing
measurements and is strongly dependent on the altitude of the light
source."

9. page 4, section 5, paragraph 4

Note that very small tau_c and tau_t would also require a better control
of the optical light paths. In order to utilize a resolution of 40 psec,
light paths must be equal within about a cm. This is possible but more
difficult for very large collecting areas.

Reply: We fully agree with this comment. With the removal of the emphasis on
spatial coherence measurements this issue in the manuscript is not present
currently.


10. page 4, section 5, paragraph 4

On the issue of very long baselines in intensity interferometry: Just a
remark that there are doubts that this will be possible for thermal
sources due to SNR reasons. If compact sources are be resolved only with
kilometre baselines, they will as result of their small apparent size
only deliver small photon rates. The recent paper by Malvimat et al.
(2014) describes a fundamental limitation in this regime.

We thank the referee for pointing this out - again, with a removal of the
emphasis on spatial coherence measurement, this should not be an issue in the
manuscript anymore.


Additional changes:
We updated figure 5 with the g(2) function from sunlight with the data taken
from the zenith, because it shows a clearer photon bunching signature, and
have less noise due to a longer integration time compared to the original
figure. 

With this, we hope to have addressed the issues raised by the referee, and
would appreciate a kind reconsideration for publication in APJL.

With Best Regards on behalf of all authors,

Christian Kurtsiefer