Development of a Compact Three-Degree-of-Freedom Laser Measurement System with Self-Wavelength Correction for Displacement Feedback of a Nanopositioning Stage

Round  1

Reviewer 1 Report

Interesting design application.

I think that an experiment which shuts down the laser diode and then turns it back on before the next measurement would add impact to the paper by showing the necessity or capability of the system to only need to be calibrated once with an external reference (effectively assigning the initial angle of teh grating output)

I would like to see a replacement or corresponding graph to Table 1 which shows a plot of the deviation of the MM1 reference  slope change/correction against the measurement of the angle change from the detector. The slope  and variance of this can then be compared to the theoretical value from the math.

A comment on corrections to the dead-path error from the interferometer to the mirror on the stage at the beginning of travel should also be given so that the effect can be accounted for.

In the Figure 6 on page 7 the noise for one angle seems to be correlated to the inverse of the other angle. A discussion of this should be in the text indicating possible causes such as intensity variations of ground noise etc.

In the text below "Jones vector should be "Jones Calculus" or "Jones Matrices Math"

150 interference. Analyzed by the Jones vector, the intensity of each photodetector can be expressed as

A note concerning the below statement that it is easier to get the deviation of the angles than it is to determine the actual value of the angle.

181 calculated if the +1st order diffraction angle can be measured at known incident angle and grating

Is the 0,25 mm correct below? Seems small.

207 high precision QPD (OSI Co., USA, model SPOT-4DMI) with an active area of 0.25 mm, an element 208

Author Response

Response to the comments from the Reviewer 1 Thank you very much for your careful review of our paper. Your precious comments and suggestions, which have greatly helped us to improve the quality of this paper, are highly appreciated. The manuscript has been revised based on the comments and suggestions. The responses to the comments and questions are listed as follows. Interesting design application. I think that an experiment which shuts down the laser diode and then turns it back on before the next measurement would add impact to the paper by showing the necessity or capability of the system to only need to be calibrated once with an external reference (effectively assigning the initial angle of the grating output) Thank you for your kind suggestions. We are sorry for not making it clear in our previous version. Yes, this is just the way we are using. In the revised version, we have added the below description. “From the above experiments, it can be realized that a special feature of this 3DOFLM system is that it only needs to calibrate and store the nominal wavelength and the corresponding initial diffraction angle once by using a reference. With these stored parameters, the system can automatically correct the wavelength by itself in the rest measurements.” (Lines 318-321) I would like to see a replacement or corresponding graph to Table 1 which shows a plot of the deviation of the MM1 reference slope change/correction against the measurement of the angle change from the detector. The slope and variance of this can then be compared to the theoretical value from the math. Thank you for your kind suggestions. A corresponding graph to Table 1 has been added in the revised manuscript, as shown in figure 16. And we have added the description as follows: “Figure 16 shows the relationship between the calibrated laser wavelength λcal and the variation of slope kp obtained from the displacement measurement results of the NMM-1 and the MMI kit. The relationship between the measured laser wavelength λmea and the variation of drift +1st order diffraction angle detected by the AC2 was also plotted in figure 16. For the sake of comparison, λcal and λmea were listed in Table 1.” (Lines 305-309) A comment on corrections to the dead-path error from the interferometer to the mirror on the stage at the beginning of travel should also be given so that the effect can be accounted for. Thank you for your kind suggestions. We are sorry for not making it clear in our previous version. Yes, the dead-path error from the interferometer to the mirror on the stage at the beginning of travel will influence the measurement accuracy. In the revised version, we have added the below description. “It should be noted that due to the space limit of the nanopositioning stage, the dead path of the 3DOFLM system, which was a distance between the MMI kit and the null point of the measurement position, was designed to be 36 mm. Therefore, the error due to the dead path can be negligible [27].” (Lines 198-201) “27 Samir, M. Introduction to precision machine design and error assessment. Boca Raton: CRC Press, 2013.” (Lines 427-428) In the Figure 6 on page 7 the noise for one angle seems to be correlated to the inverse of the other angle. A discussion of this should be in the text indicating possible causes such as intensity variations of ground noise etc. Thank you for your kind suggestions. We are sorry for not discussing the noise clearly. In the revised version, we have added the below description. “It should be noted that although the laser beams for measuring the pitch and yaw angle errors were from an identical laser diode, due to the nonuniformity of the output intensity distribution of the laser diode, the stability in pitch and yaw angle errors measurements were not similar but inversely correlated in figure 6. The reason for the larger pitch variation could be due to the mechanical vibration.” (Lines 217-222) In the text below "Jones vector should be "Jones Calculus" or "Jones Matrices Math" 150 interference. Analyzed by the Jones vector, the intensity of each photodetector can be expressed as We are sorry for this careless mistake. “Jones vector” has been replaced by “Jones matrix”. (Line 151) A note concerning the below statement that it is easier to get the deviation of the angles than it is to determine the actual value of the angle. 181 calculated if the +1st order diffraction angle can be measured at known incident angle and grating Thank you for your kind suggestions. As pointed out by the reviewer, it is easier to obtain the drift of +1st order diffraction angle than it is to determine the actual value of +1st order diffraction angle. The sentence in Line 181 “calculated if the +1st order diffraction angle can be measured at known incident angle and grating” was to explain how to calculate the laser wavelength based on the law of grating equation (eq. (8)). Same as the answer to the first comment, this nominal incident angle could be calibrated by using a reference measuring system, i.e. the NMM-1. Then the deviation of this angle could be measured by the developed 3DOFLM system. Is the 0,25 mm correct below? Seems small. 207 high precision QPD (OSI Co., USA, model SPOT-4DMI) with an active area of 0.25 mm, an element 208 We are sorry for this careless mistake. “High precision QPD (OSI Co., USA, model SPOT-4DMI) with an active area of 0.25 mm” has been replaced by “high precision QPD (OSI Co., USA, model SPOT-4DMI) with an active area of 0.25 mm per element”. (Line 212)

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors describe the development of a compact laser measurement system which enables real-time wavelength measurement and correction.

The paper is well structured, but contains several spelling and grammar errors against the English language which makes some sections difficult to read.

Before the paper can be accepted for publication, the authors should address the following comments:

1)      Check the grammar, spelling and punctuation marks of the text. Some examples:
Line 33: “…planar stages suffer from the Abbe error”
Line 36: “THEIR travel accuracy, …”
Line 42: “…are regarded AS more stable…”
Line 45: rephrase “would meet inherent Abbe error”
Line 53: “…stage by THE author’s group…”
Line 54: “…size, it suffers from low stability”
Line 78-80: rephrase. “in which” doesn’t make sense and it should be “…with a certain optical path difference can be employed…”
Line 83 what is meant with “feasibilities” of optical fiber…?
Line 84: “…of this kind OF wavelength measurement…”
Line 85: “predestinates it to BE applied in different kinds…”
and many, many more

2)      Line 33: include a reference or a brief explanation of the “Abbe error”

3)      Line 74: I would specify “when an optical path difference between a reference path and a measurement path is generated”

4)      Line 87: why is a CCD not able to provide sufficient resolution? Is that also the case for high-end CCDs with e.g. 42 megapixel resolution?

5)      Line 90 “based on the spectrometry principle” needs some explanation

6)      Figure 1: I would rotate QWP3 by 90 degrees such that it is clearer that it corresponds to the horizontal element

7)      Section 2.1: I would already here mention the laser wavelength and specify if there are requirements about the polarization of the laser diode (should it be linearly polarized?)

8)      Eqs 2-5: is the path difference Δz really along the z-axis? From the figure, it would seem to me that the mirror 3 is moving along the Y-axis.

9)      Check the axes definition in this figure. It looks as if X and Y have been reversed in comparison to Fig. 1

10)   Line 179: It would be nice if you could include the theta_i and theta_d angles on a drawing

11)   Line 182-183: it is an incidence angle rather than an incident angle

12)   Line 196: indicate the U-shaped holder in Fig 5

13)   Figure 5: add a scale bar to give an idea about the total dimensions of the system.
Is 80mm x 90mm x 20mm compact enough for integration into nanopositioning stages? Is there room for further miniaturization of the system?

14)   Line 213: “It is quite satisfactory” à by which standard?/compared to what? Is there room for further improvement? If so, how?

15)   Line 228: “was acceptable for use”: same comment as above

16)   Figure 8: switch position of (a) and (b). In Fig. 7 the pitch is in the left figure whereas in the current Fig. 8 it is in the right figure.
In addition, the residuals for the pitch seem to be larger than for the yaw. Is there a reason for that?

17)   Fig. 9: I would consider using the same scale for the X and the Y axis

18)   Line 248: remove “Since”

19)   Line 257: “was small enough” à compared to what?

20)   Fig 11 caption: “…error of the COMMERCIAL nanopositioning…”

21)   Line 264: “…for five measurements was estimated…”

22)   Line 270: “of five measurements”

23)   Line 273: should be 20mm

24)   Fig 13: include the equation and R^2 value for the fitted curve

25)   Line 280: why was a 1um pitch selected?

26)   Line 284: check the number of significant digits in 0.0037452nm

27)   Line 291: “was acceptable for use” à see previous comments

28)   Table 1: check number of significant digits (especially of the last line)

29)   Line 309: “of five measurements”

30)   Line 318: “…3DOFLM system. The improvement…”

31)   Line 326: “was experimented” makes it sound as if the authors did that

32)   Line 330: I think the accuracy of +/- 65nm without wavelength correction is a bit underestimated if I look at Fig. 12(a). I would say it is closer to +/- 45nm except for one outlier.

Do the authors think they could further improve the +/-25nm accuracy they achieved? Could the same accuracy be achieved when further miniaturization would be pursued? Or is the system now compact enough for practical deployment?
It would help if the reader would also have an indication of the size of the commercial tools with which the performance has been benchmarked.

Author Response

Response to the comments from the Reviewer 2 We appreciate very much for your kind and beneficial comments as well as suggestions to our manuscript. The manuscript has been revised point by point according to your advices. We would like to sincerely respond to your comments as follows: The authors describe the development of a compact laser measurement system which enables real-time wavelength measurement and correction. The paper is well structured, but contains several spelling and grammar errors against the English language which makes some sections difficult to read. Before the paper can be accepted for publication, the authors should address the following comments: Thank the reviewer very much for his kind comment on our paper. The paper has been further improved based on the suggestions from the reviewer. 1) Check the grammar, spelling and punctuation marks of the text. Some examples: Line 33: “…planar stages suffer from the Abbe error”---It has been corrected. (Line 33) Line 36: “THEIR travel accuracy, …”---It has been corrected. (Line 36) Line 42: “…are regarded AS more stable…”---It has been corrected. (Line 42) Line 45: rephrase “would meet inherent Abbe error” The sentence “using linear grating encoder as the feedback sensor would meet inherent Abbe error if the grating axis cannot be in line with the moving axis” has been replaced by “…due to the geometric design of linear encoders, it is difficult to follow the Abbe principle when being installed into the coplanar stage as the feedback sensor.” (Lines 44-45) The corresponding reference has been changed as follows: “10 Otsuka, J.; Ichikawa, S.; Masuda, T.; Suzuki, K. Development of a small ultraprecision positioning device with 5 nm resolution. Meas. Sci. Technol. 2005, 16, 2186-2192.” (Lines 390-391) Line 53: “…stage by THE author’s group…”---It has been corrected. (Line 54) Line 54: “…size, it suffers from low stability” ---It has been corrected. (Lines 54-55) Line 78-80: rephrase. “in which” doesn’t make sense and it should be “…with a certain optical path difference can be employed…” “Optical beating methods with high measurement accuracy, in which an optical system with a certain optical path different, can be employed to measure the laser wavelength” has been replaced by “Optical beating methods with a certain optical path different can be employed to make a high accurate measurement of the laser wavelength”. (Lines 78-80) Line 83 what is meant with “feasibilities” of optical fiber…? “…feasibilities of optical fiber” has been replaced by “…specialties of optical fiber”. (Line 83) Line 84: “…of this kind OF wavelength measurement…”---It has been corrected. (Line 84) Line 85: “predestinates it to BE applied in different kinds…”---It has been corrected. (Line 85) and many, many more We are sorry for these careless mistakes. All the above mistakes have been corrected in the revised manuscript. 2) Line 33: include a reference or a brief explanation of the “Abbe error” Thank you for your kind suggestions. A brief explanation of the Abbe error has been added in the revised manuscript. “… Abbe error, because the reference axis cannot be in line with the functional axis in the working space…” (Lines 33-34) 3) Line 74: I would specify “when an optical path difference between a reference path and a measurement path is generated” Thank you for your kind suggestions. The description has been added in the revised manuscript. (Lines 74-75) 4) Line 87: why is a CCD not able to provide sufficient resolution? Is that also the case for high-end CCDs with e.g. 42 megapixel resolution? Thank you for your kind suggestions. As pointed out by the reviewer, there are some high-end CCDs with 42 megapixel resolution. However, the cost of those are extremely expensive and its resolution and response rate are no better than the QPD, so that the high-end CCDs was not employed for wavelength measurement. 5) Line 90 “based on the spectrometry principle” needs some explanation Thank you for your kind suggestions. “…based on the spectrometry principle” have been replaced by “…based on the grating diffraction principle and the autocollimation principle”. (Lines 19-20, 90, 174-175) 6) Figure 1: I would rotate QWP3 by 90 degrees such that it is clearer that it corresponds to the horizontal element Thank you for your kind suggestions. QWP3 and QWP1 have been rotated by 90 degrees. Please refer to figure 1. 7) Section 2.1: I would already here mention the laser wavelength and specify if there are requirements about the polarization of the laser diode (should it be linearly polarized?) Thank you for your kind suggestions. As shown in figure 1, in the developed 3DOFLM system the polarization of the laser diode is mainly for the Michelson interferometer. The extracted beams for wavelength correction kit and autocollimation kit are all circularly polarized, although these two kits do not need polarizing beams because only the angle change of the beam is considered. May be the suggestion is right. The output beam may have stronger intensity (or higher efficiency) if the incidence beam is linearly polarized. We will investigate this effect in the future works. Thank you very much. 8) Eqs 2-5: is the path difference Δz really along the z-axis? From the figure, it would seem to me that the mirror 3 is moving along the Y-axis. Thank you for your kind suggestions. Δz is a symbol of the optical path difference of the two reflected beams. We did not consider the direction of this symbol in previous manuscript. Δz has been replaced by Δy. (Line 157) Please refer to eqs. (2)-(6). 9) Check the axes definition in this figure. It looks as if X and Y have been reversed in comparison to Fig. 1 Thank you for your kind suggestions. We have checked the figure 1, the definition of axes in the figure is based on the Right-hand rule. Please refer to figure 1. 10) Line 179: It would be nice if you could include the theta_i and theta_d angles on a drawing Thank you for your kind suggestions. θi and θd have been plotted in figure 4. Please refer to figure 4. 11) Line 182-183: it is an incidence angle rather than an incident angle Thank you for your kind suggestions. The “incident angle” has been replaced by “incidence angle” throughout the text. (Lines 180, 182, 184-185) 12) Line 196: indicate the U-shaped holder in Fig 5 Thank you for your kind suggestions. The indication of the U-shaped holder has been plotted in figure 5. Please refer to figure 5. 13) Figure 5: add a scale bar to give an idea about the total dimensions of the system. Is 80mm x 90mm x 20mm compact enough for integration into nanopositioning stages? Is there room for further miniaturization of the system? Thank you for your kind suggestions. A scale bar has been plotted in figure 5. Please refer to figure 5. The size of 3DOFLM system (80 mm (X) × 90 mm (Y) × 20 mm (Z)) is enough for the current nanopositioning stage, in which the space for mounting the displacement feedback sensor is 150 mm (X) × 100 mm (Y). Yes, it still has room for further miniaturization of the 3DOFLM system by reducing the space between elements and designing a small size angle mirror mount, which will be introduced in our future works. 14) Line 213: “It is quite satisfactory” à by which standard?/compared to what? Is there room for further improvement? If so, how? Thank you for your kind suggestions. “It is quite satisfactory” has been replaced by “It can be seen that the developed miniature autocollimator kit satisfied stability for angular error measurement with sub-arcsecond precision.” (Lines 221-222) Yes, the stability of the laser beam can be further improvement by using a laser beam drift feedback compensation method, which was proposed by our group. This method will be used in the 3DOFLM system to compensate the error caused by laser drift in our future works. 15) Line 228: “was acceptable for use”: same comment as above Thank you for your kind suggestions. “…was acceptable for use” has been replaced by “…was acceptable for sub-arcsecond precision angular error measurement.” (Line 237) 16) Figure 8: switch position of (a) and (b). In Fig. 7 the pitch is in the left figure whereas in the current Fig. 8 it is in the right figure. In addition, the residuals for the pitch seem to be larger than for the yaw. Is there a reason for that? Thank you for your kind suggestions. The positions of figures 8(a) and 8(b) have been switched. Please refer to figure 5. The reason for the larger pitch variation could be due to the mechanic vibration, as shown in figure 6. This expression has been added in the revised manuscript. (Lines 220-221) 17) Fig. 9: I would consider using the same scale for the X and the Y axis Thank you for your kind suggestions. The scale for the X- and Y-axes of figure 9 has been change to the same in the revised manuscript. Please refer to figure 9. 18) Line 248: remove “Since” Thank you for your kind suggestions. The mistake has been corrected in the revised manuscript. (Line 257) 19) Line 257: “was small enough” à compared to what? Thank you for your kind suggestions. “…was small enough” has been replaced by “…was small enough compared to the displacement of NMM-1”. (Line 266) 20) Fig 11 caption: “…error of the COMMERCIAL nanopositioning…” Thank you for your kind suggestions. The mistake has been corrected in the revised manuscript. Please refer to figure 11 caption. 21) Line 264: “…for five measurements was estimated…” 22) Line 270: “of five measurements” 29) Line 309: “of five measurements” Thank you for your kind suggestions. The mistakes have been corrected in the revised manuscript. (Lines 274, 279, 328) 23) Line 273: should be 20mm Thank you for your kind suggestions. We are sorry for not making it clear in our previous version. 20 mm is the measurement distance in the comparison experiment and 2 mm is the step interval. In the revised version, we have added the description on this. “…kit with a step interval of 2 mm in the measurement distance of 20 mm.” (Line 282) 24) Fig 13: include the equation and R^2 value for the fitted curve Thank you for your kind suggestions. The equation and R2 value for the fitted curve have been added in figure 13. Please refer to figure 13. 25) Line 280: why was a 1um pitch selected? Taking into consideration the size of the wavelength corrector kit, which is significantly determined by the size of +1st order diffraction angle and optical components, the grating pitch is selected to 1 μm based on eq. (8). This grating can be purchased from Edmund Optics. 26) Line 284: check the number of significant digits in 0.0037452nm Thank you for your kind suggestions. “0.0037452nm” has been replaced by “0.0037 nm”. (Line 293) 27) Line 291: “was acceptable for use” à see previous comments Thank you for your kind suggestions. “…was acceptable for use” has been replaced by “…was acceptable for sub-arcsecond precision angular error measurement.” (Lines 298-299) 28) Table 1: check number of significant digits (especially of the last line) Thank you for your kind suggestions. The number of significant digits in table 1 has been corrected in the revised manuscript. Please refer to table 1. 30) Line 318: “…3DOFLM system. The improvement…” Thank you for your kind suggestions. The mistake has been corrected in the revised manuscript. (Line 336) 31) Line 326: “was experimented” makes it sound as if the authors did that Thank you for your kind suggestions. “…was experimented” has been replaced to “…was adapted to”. (Line 343) 32) Line 330: I think the accuracy of +/- 65nm without wavelength correction is a bit underestimated if I look at Fig. 12(a). I would say it is closer to +/- 45nm except for one outlier. Do the authors think they could further improve the +/-25nm accuracy they achieved? Could the same accuracy be achieved when further miniaturization would be pursued? Or is the system now compact enough for practical deployment? It would help if the reader would also have an indication of the size of the commercial tools with which the performance has been benchmarked. Thank you for your kind suggestions. As pointed out by the reviewer, the displacement residuals between the 3DOFLM system and the NMM-1 in figure 12(a) was a bit underestimated. “±65 nm” has been replaced by “± 45 nm” in the revised manuscript. (Lines 273, 350) Yes, we can further improve the ± 25 nm accuracy by considered the influences of linearity error of Lissagous circle, incident beam angle and its drift, and thermal deformation of grating pitch on the wavelength measurement accuracy, which will be carried out in our future works. The size of 3DOFLM system now (80 mm (X) × 90 mm (Y) × 20 mm (Z)) is enough for the current version nanopositioning stage, in which the space for mounting the displacement feedback sensor is 150 mm (X) × 100 mm (Y). It still has room for further miniaturization of the 3DOFLM system by reducing the space between optical components and designing a small size angle mirror mount. The miniaturization of the measurement system will not influence the accuracy.

Author Response File: Author Response.pdf

Round  2

Reviewer 2 Report

The authors have satisfactorily addressed all my comments and have significantly improved the readability of the manuscript. It is now suitable for publication.