A Spatial 4-DOF Laser Collimation Measurement System

Comments 1: The  abstract content should be more general related to the main involved  ideas developed in the article and their motivation  rather than to be  focused on  insisting  very much in particular numerical values used in the experiments.

Response 1: Thank you for your suggestions. In response to your question, changes were made to the summary. The modified sentences are marked in yellow(see lines 11-25).

Comments 2: Sections 5 (Technical Approach in the Article) and 6 (Conclusions)  are not mentioned/described in the paper organization description given at the end of the introductory section.

Response 2: Thank you for your suggestions. In response to your question, I describe section 5 (the technical approach of the article) and section 6 (the conclusion) in the structure of the paper in the introduction. The modified sentences are marked in yellow(see lines 133-137).

Comments 3: Eqns. 4 and 8 : Should be "x" replaced with "y"?. Otherwise,  the  given  set of equations, including those above mentioned ones,  does not consider the coordinate"y".

Response 3: Thank you for your suggestions. In response to your question, α is the pitch angle, which corresponds to x. β is the yaw angle, which corresponds to y. Therefore, replacing x with y in equations (4) and (8).The modified sentences are marked in yellow(see lines 231-233).

Comments 4: It is not clear why (13), (15) and (17) of one hand , and (14), (16) and  (18) on the other hand  with respective distinct right-hand-sides have exactly the same left-hand-side.

Response 4: Thank you for your suggestions. In response to your question, Equations (11) and (12) of  and  are analyzing the actual crosstalk caused by yaw angle in X-direction straightness measurements, and yaw angle in Y-direction straightness measurements, and Equations (13) and (14) are simplifications of Equations (11) and (12) considering the condition that the angle change is very small. Equations (15) and (16) are treatments of equations (13) and (14) that take into account the fact that the angular cone prism doubles the straightness ranging results. Equations (17) and (18) are the crosstalk caused by the pitch angle for the X-direction and the crosstalk caused by the pitch angle for the Y-direction. Therefore,  and  of equations (11) and (12) are changed to  and , respectively,  and  of equations (13) and (14) are changed to  and , respectively,  and  of equations (15) and (16) are changed to  and , respectively, and  and  of equations (16) and (18) are changed to  and , respectively.The modified sentences are marked in yellow(see lines 283-292).

Comments 5: The six indexes mentioned previously to (21) are not described and they are not shown either. The corresponding supporting sentence of text  has also a bad syntax and needs some improvement.

Response 5: Thank you for your suggestions. In response to your question, The six metrics are the three straightness deviations and three angular deviations after the misalignment of the two coordinate systems described earlier, namely, i.e., the positional errors in the three directions of the XYZ axes of the two coordinate systems, //, and the angular errors in the three directions of the XYZ axes, //. Therefore, the last sentence is changed to the chi-square matrix H that contains these six metrics. Next, the bad syntactic structure of the corresponding supporting sentences in the text was improved. The modified sentences are marked in yellow(see lines 302-312).

Comments 6: The matrix P/Qds mentioned previous to (22) does not appear.

Response 6: Thank you for your suggestions. In response to your question,This is a clerical error on my part,  in equation (22) should be changed to  in equation (23), the reason for this error is that my photodetector was originally a four-quadrant detector QD, and I analyzed the error according to the four-quadrant detector QD, but later I found out that the measurement range, the price, and other factors, the four-quadrant detector has been changed to a CMOS detector, and I forgot to change the sign of QD, so I'm sorry for that. Please understand.The modified sentences are marked in yellow(see line 317).

Comments 7: The legends of Figs. 1-9 are currently quite short and should be extended with more details in.

Response 7: Thank you for your suggestions. In response to your question, it is true that more details should be added, for example, I have added the legend in Figure 6 to make the equation clearer to the reader.The modified sentences are marked in yellow(see line 222).

Comments 8: The translation errors (23)-(24) should be introduced better and more clearly . The current given  close explanation text is not clear to follow.

Response 8: Thank you for your suggestions. In response to your question, it was indeed not clear enough, and I have revised the text by better elaborating and explaining the interpretation of equations (23)-(24).The modified sentences are marked in yellow(see lines 321-325).

Comments 9: Eqn. (30) seems to use mixed notations DeltaX, Y ,... with Delta/sub X, Delta/subY, ...Please, revise the related  notation, if necessary.

Response 9: Thank you for your suggestions. In response to your question,, and denotes a change in position in the XYZ direction and should not be used with the increment X，Y and Z. Therefore the notation in equations (30) and (31) has been modified.The modified sentences are marked in yellow(see lines 349-353).

Comments 10: The novelty of the performed  research related to the multi- DOF measuremant system  is not sufficiently clear. The novelty , compared to the close or simialr methods available  n the background literature, should be emphasized in more detail.

Response 10: Thank you for your suggestions. In response to your question, include in the introduction the innovativeness of this system compared to similar or comparable methods already available in the background literature.The modified sentences are marked in yellow(see lines 90-105).

Comments 1: A dedicated section comparing the system with other existing 4-DOF or multi-DOF measurement systems could strengthen the paper.

Response 1: Thank you for your suggestions. In response to your question, Include in the introduction a comparison of the system with other existing four- or multi-degree-of-freedom measurement systems.The modified sentences are marked in yellow(see lines 90-105).

Comments 2: While the paper mentions crosstalk and installation error, a more in-depth analysis could benefit readers. Including methods for minimizing these errors in various environments, especially under thermal or mechanical stress, would strengthen the system robustness claims.

Response 2: Thank you for your suggestions. In response to your question, added the content of BP neural network error compensation model in section 3.2 to enhance the robustness of the system. The modified sentences are marked in yellow(see lines 358-384).

Comments 3: Including a comparison table that showcases this system performance metrics alongside those of laser interferometry and diffraction methods would clearly highlight its precision and cost advantages, particularly in terms of measurement stability and operational range.

Response 3: Thank you for your suggestions. In response to your question, added a comparison table of several optical measurements.The modified sentences are marked in yellow(see line 73).

Comments 4: Since environmental factors can impact laser-based measurements, adding a section on the system resilience in different environmental conditions could be useful.

Response 4: Thank you for your suggestions. In response to your question, the development of this thesis is the principle prototype, the laboratory does not have the conditions to do simulation tests (such as high and low temperatures, high and low speeds, etc.), later will coordinate the relevant resources to solve the simulation experiments, so as to make the system more robust. Please understand.