Review Reports

Round 1

Reviewer 1 Report

Sea the attached file.

Comments for author File: Comments.pdf

Author Response

Response to Reviewer 1 Comments

Point 1: The primary deficiency of the paper is the absence of the discussion on how their concept to make the TTL coupling to vanish differ from the concept used for the same purpose in Ref. [11]. I emphasize that such discussion should not be about the difference in the setup between their paper and Ref. [11], but rather about the difference in the concept used to make the TTL coupling to vanish.

Response 1: We very much appreciate your careful reading and valuable suggestions. Your suggestions really mean a lot to us. As you said, the concept of our paper made the TTL coupling to vanish is different from the concept used in Ref. [11]. In our paper, TTL noise is made be removed by the offset between two different optical path noises which have same magnitude but a different sign. However, the author in Ref. [11] adopts an imaging system which based on Fermat’s principle to image the point of rotation onto the detector to eliminate the TTL noise. Based on your suggestions, we add the relevant content “.This provides a different approach to use of an imaging system[11] which based on Fermat’s principle to image the point of rotation onto the detector to eliminate the TTL noise” in the revised manuscript.

Point 2: the comments (1)~(8) and (10) in several minor deficiencies.

Response 2: Thanks for your careful reading and suggestions. We feel sorry for the improper wording and unclear expression again. Based on your suggestions, we have corrected the above contents in the revised manuscript.

Point 3: The legend explaining that numerical results are presented by * and the analytical results by the solid line, is given only for Fig. 2, but not for Figs. 3 – 6. The authors should either provide this info for Figs. 3 – 6 in the captions to these figures or state in the text after Fig. 2 (not in the caption to Fig. 2) that in Figs. 3 – 6 the numerical and analytical results are designated in the same way as in Fig. 2.

Response 3: Your suggestions really mean a lot to us. Because it is difficult to obtain analytic solutions for the diffraction model, so there are only numerical results in Figs. 3 – 6. Based on your suggestions, we also did some changes in the captions to made them be more clear.

Reviewer 2 Report

The authors consider the elimination of tilt-to-length noise in long
distance interferometers. The interference comes for the superposition
of a flat top beam (far field of a Gaussian beam) and a Gaussian beam
with a waist not too far from the interference interface.

The essential idea is to move the waist of the Gaussian beam to the
pivot point (around which the tilt occurs) of the Gaussian beam. Then
at far distance there are spherical wave fronts, hence the interference
between the spherical wave and the flat wave front is which a less
sensitive to the tilt of the plane wave.

The idea is elegant and the derivations seem sound. It is difficult to
follow a bit the numerous abbreviations. On Fig. 3 the letters are too
small. Fig. 4 is hard to understand: where is the detector ? There are
several strange English phrasings in the test, hence I suggest a
careful read-through of the manuscript.

I have one relevant question: the authors worked out some examples to
demonstrate the effectiveness of their method. What would be the
result for realistic systems ? Isn't it possible to reformulate the
expressions for scale free quantities.

In summary I support the publication of the manuscript in the journal
MDPI Applied Science after the authors consider my suggestions and make
appropriate changes.

Author Response

Response to Reviewer 2 Comments

Point 1: The idea is elegant and the derivations seem sound. It is difficult to follow a bit the numerous abbreviations. On Fig. 3 the letters are too small. Fig. 4 is hard to understand: where is the detector? There are several strange English phrasings in the test, hence I suggest a careful read-through of the manuscript.

Response 1: Thank you for confirming that the idea in our manuscript is elegant and the derivations seem sound. It makes us very happy. And we are so sorry that there are too many abbreviations in the previous manuscript. The reason is that we want the article to be more concise. Here we will give you the full names of some abbreviations of the article again: Tilt-to-length(TTL); quadrant photo-diode(QPD); LISA Pathfinder (LPF); The longitudinal pathlength signal(LPS). And based on your suggestions, we modified Fig.3 and Fig.4 and did a careful read-through of the manuscript and corrected all strange English phrasings in the revised manuscript.

Point 2: I have one relevant question: the authors worked out some examples to demonstrate the effectiveness of their method. What would be the result for realistic systems? Isn't it possible to reformulate the expressions for scale free quantities.

Response 2: Your suggestions really mean a lot to us. The relevant questions above are what we are studying and now we are doing related experiments to verify the effectiveness of the idea of this paper for realistic systems. In this paper, we just want to focus on the theoretical analysis of the idea. We hope you can continue to pay attention to our research work.