Dear Editor,

we would first like to thank the referee for the careful reading the and very constructive feedback, and for providing suggestions of possible future follow-ups to this work.

We respond to the comments or questions raised in the referee's report below:

1) "The authors motivate their interferometric photon correlation technique by emphasizing that no filtering is needed. This is indeed a relevant point as being able to investigate the whole signal is relevant for a precise characterization of light sources. However, the authors  might want to provide a somewhat broader explanation of how the authors avoid the need for filtering. As pointed out correctly by the authors, filtering is mostly of interest to increase the effective coherence time of light fields when the temporal resolution of the detectors used is not sufficient to resolve the true photon correlations. However, the authors do not explain in detail how the temporal resolution of their detectors changes the results of their interferometric photon correlations if the coherence time of the signal is shorter than the temporal resolution. As the authors use this question as an important part of the motivation, at least a brief qualitative discussion of signals with coherence time shorter than the temporal resolution of the detectors might be helpful for the reader."

Reply:
Indeed, if the coherence time of coherent light is shorter than the temporal resolution of the detectors, there dip feature would not be well resolved, and results in the fraction of coherent light extracted to be smaller than what it may be. 

The assumption we have made is that the coherence time of coherent light is typically much longer than the timing resolution of the detectors used in our technique. 

Even if the coherence time of the incoherent light component is shorter than the timing resolution of the detectors, the technique is able to estimate the fraction of coherent light solely from resolving the dip feature in g(2X) associated with coherent light.
We have revised the last paragraph of the introduction to explain how the technique avoids spectral filtering.


2) "When discussing the context of the results presented here, it might be helpful if the authors provided a slightly broader context of light fields that are coherent-incoherent mixtures. E.g., an early summary was given by Jakeman and Pike in J. Phys. A 2, 115 (1969). Also, it might be helpful to compare their approach to other measurements of coherent fractions, e.g., Phys. Rev. B 81, 165314 (2010)."

Reply:
We were previously unaware of this fundamental scientific interest in coherent-incoherent mixtures by a broader community than those working on semiconductor lasers. We are grateful for these references, and have revised the introduction to cite these earlier works. 

According to our understanding, the method of measuring coherent fractions demonstrated in Phys. Rev. B 81, 165314 (2010) is for pulsed lasers. The method in our manuscript complements their technique, by measuring coherent fractions on continuous wave lasers.

We thank the referee for bringing these works to our attention and have cited these works in our revised manuscript.  


3) "For example, the authors consider a mixture of two states: a coherent and an incoherent one. However, for real light sources of course also three or more modes may be present simultaneously. Would the authors be able to distinguish them or do they obtain the fraction of one mode considered as the coherent one and the fraction of all other modes?"

Reply: 
In this technique, we only distinguish one coherent mode from all other modes. Specifically if multiple uncorrelated coherent modes are present, we only distinguish the brightest coherent mode.

We have revised the first paragraph of Section III to clarify this.


4) "In equation 3, the normalization seems to be missing."

Reply:
The normalization should be 1/4 for all terms, upon evaluating Eqn. 2 using Eqn.1. In Eqn. 3, this 1/4 has been factorized out to be placed before the square parentheses. 


5) "Is equation 9 general or does it depend on the line shape of the signal under investigation?"

Reply:
Indeed, the expression  depends on the line shape of the signal in general. We have assumed that the laser has a Lorentzian line shape, typical of lasers.

We have amended the text to state this dependency explicitly.


Additionally, we fixed a number of typos and tried to adapt a more coherent spelling in the revised manuscript. For easier reference, we added a diff file to identify the detailed changes in the manuscript.

With this revision, we hope to have addressed the points raised by the referee, and look forward for further consideration in Physical Review A.

With Best Regards on behalf of all authors,

Christian Kurtsiefer