Measurement of Waveplate Parameters over Entire Clear Aperture Based on Differential Frequency Modulation with Dual Photoelastic Modulators

Round 1

Reviewer 1 Report

Authors proposed a novel measurement method using dual differential-frequency photoelastic modulation to realize highly sensitive, accurate, fast, and repeatable measurement of wave plate parameters over an entire clear aperture. The proposed method exhibits high precision and speed and provides an effective quality inspection and calibration method for wave plate. The manuscript can be regarded as original with good presentation and need some revisions:

1.     You should remove numbers after Keywords.

2.     In introduction, the definition of AC and DC should be added.

3.     A space should be left between the value and its unit.

4.     You should move the discussion of the types of wave plates from Principle section to introduction.

5.     In page 3, “and n_o and n_e are the refractive indices of ordinary and extraordinary light” you should clear it to the reader.

6.     In page 10, “From the statistical results, the retardance value of the 1/4 wave plate is almost completely distributed between 134.5-137nm, and the fast-axis azimuth is around 83.33°; Furthermore, the retardance value of the 1/2 wave plate is generally distributed between 265.1nm and 269nm, and the fast-axis azimuth is 109.40°, except for a few numerical anomalies.” is very long sentence. You should divide it.

7.     Very much Grammatical and formatting corrections are needed throughout the review. For example:

·        Line 16, replace " modulation" with “modulations”

·        Line 41, replace " parameters " with “parameter”

·        Line 49, replace " produce" with “produced”

·        Line 177, replace " retardace" with “retardance”

·        Line 194, replace " an motorized " with “a motorized”

·        Line 257, replace " do not exceeding" with “do not exceed”

 

·        Line 288, replace " ratardance" with “retardance”

Author Response

We consider that your comments are quite valuable. Some corrections and additions are made as below:

1. Comment: You should remove numbers after Keywords.

Reply: We greatly appreciate your comments. According to this suggestion, we removed numbers after Keywords.

(Please refer to the revised version on lines 27-28) “Keywords: wave plate; photoelastic modulation; differential frequency modulation; fast-axis azimuth; retardance.” (line 27-28).

2. Comment: In introduction, the definition of AC and DC should be added.

Reply: According to this suggestion, we added the definition of AC and DC.

(Please refer to the revised version on lines 76-77, 83-84) “Polarization modulation methods realize the modulation of light intensity alternating current (AC) signals.”(lines 76-77). And, “A single PEM is used, and the direct current (DC), first, and second harmonic terms of the photoelastic modulation are measured to obtain the wave plate parameters.”(lines 83-84)

3. Comment: A space should be left between the value and its unit.

Reply: We have left a space between the value and its unit.

(Please refer to the revised version).

4. Comment: You should move the discussion of the types of wave plates from Principle section to introduction.

Reply: We are very appreciative for the reviewer’s professional examination and comments on our article. The types of wave plates from Principle section are moved to introduction section. And, the phase retardance ,, is expressed by following the Muller matrix of waveplate.

(Please refer to revised version on lines 33-42). “The incident light is decomposed into ordinary and extraordinary light, with vibration directions perpendicular to each other. The ordinary light travels with the same velocity in every direction through the wave plate, and the extraordinary light travels with a velocity that is dependent upon the propagation direction within the wave plate. The main axis of the ordinary light refractive index is usually defined as the fast-axis. After the two polar-ized light components pass through the wave plate, a phase retardance is introduced. A wave plate is used to change the polarization state. Wave plates typically include a 1/4 wave plate, and a 1/2 wave plate, and the phase retardance corresponds to 90° and 180°, respectively. They are mainly employed in polarization-generating devices and polariza-tion-analysis devices.”(lines 33-42) And, “where, is the phase retardance. It can be further expressed as ,where, is the wavelength of incident light, d is the thickness of the wave plate, andandare the refractive indices of ordinary and extraordinary light, respectively.  is the fast-axis azimuth. It can be observed from the above formula that the polarization characteristics of the wave plate are fully determined by the two parameters of phase retardance  and fast-axis azimuth . They must be strictly measured and calibrated, especially the parameters over the entire clear aperture. ” (lines 144-150)

5. Comment: In page 3, “and n_o and n_e are the refractive indices of ordinary and extraordinary light” you should clear it to the reader.

Reply: Ordinary and extraordinary light have been further expressed in detail.

(Please refer to revised version on lines 33-37). “The incident light is decomposed into ordinary and extraordinary light, with vibration directions perpendicular to each other. The ordinary light travels with the same velocity in every direction through the waveplate, and the extraordinary light trav

els with a velocity that is dependent upon the propagation direction within the waveplate.”(lines 33-37)

6. Comment: In page 10, “From the statistical results, the retardance value of the 1/4 wave plate is almost completely distributed between 134.5-137nm, and the fast-axis azimuth is around 83.33°; Furthermore, the retardance value of the 1/2 wave plate is generally distributed between 265.1nm and 269nm, and the fast-axis azimuth is 109.40°, except for a few numerical anomalies.” is very long sentence. You should divide it.

Reply: According to this suggestion, we have divided the long sentence.

(Please refer to revised version on lines 345-348). “From the statistical results excepting for numerical anomalies, the retardance value of the 1/4 wave plate is almost completely distributed between 134.5-137nm. The fast-axis azimuth is around 83.33°. Furthermore, the 1/2 wave plate retardance is generally distributed between 265.1nm and 269nm. The fast-axis azimuth is around 109.40°.”(lines 345-348)

7. Comment: Very much Grammatical and formatting corrections are needed throughout the review. For example:

• Line 16, replace " modulation" with “modulations”
• Line 41, replace " parameters " with “parameter”
• Line 49, replace " produce" with “produced”
• Line 177, replace " retardace" with “retardance”
• Line 194, replace " an motorized " with “a motorized”
• Line 257, replace " do not exceeding" with “do not exceed”
• Line 288, replace " ratardance" with “retardance”

Reply: we have revised the manuscript, and the grammatical and formatting errors are corrected.

(Please refer to revised version).

______________________________________________

 We have seriously considered all the issues and made correction according to all the reviewers’ comments. If there are any questions with the manuscript, please inform us and we wish further discussion. We hope that the revised manuscript will be suitable for publication in Applied Science.

Yours sincerely,

Dr. Kewu Li, Shuang Wang , et al.

Reviewer 2 Report

Authors reported an article entitled “Measurement of wave plate parameters over entire clear aperture based on differential frequency modulation with dual photoelastic modulators”. However, for publication, I recommend a minor revision. Specifically, check all the formula again and make everything reader-friendly.

 

Abstract Line 22:     “ ;” => “ .”  (Semicolon => Full stop/period)

Keywords: 1, 2, 3, 4, and 5 not needed

wave plate => waveplate (For consistency to Author’s previous publications)

Line 33:  MgF2=> magnesium fluoride (MgF₂)   [Check other places also!]

         Authors can mention more examples in addition to the three mentioned here.

         a certain thickness =>  a certain thickness (...) ; a typical range, input here!

Line 41: Many wave plate parameters measurement studies =>   Many waveplate parameter measurement studies

Line 90:  This is repletion to Line 33 (Please re-express it)

Figure 1.  FPGA => a field programmable gate array (FPGA) 

                 PEM1 and PEM2 =>  A detailed scheme (as an inset figure; size & specific material should be described here) may be useful for Reader-Friendly.

Line 149: Check the formula (e.g., the element "row 2 column 2" in the matrix), which is different from the cited reference. Check all the equations one-by-one.

Line 147 and Line 153: M_S and M_A should be clearly defined by a sentence also just like Lines 131 and 134.

Line 179: the AD sampling frequency through the FPGA=> the analog-to-digital (AD) sampling frequency through the FPGA   (Note: Basically, a full name should be introduced before mentioning its initial for reader-friendly.)

Line 217.  ADC => Analog-to-Digital Converter (ADC)

Figure 2 and Figure 3a. Check the figure legend (Green line in the greenish background is not good; maybe delete a greenish background)

Figure 4b. Light green should be a dark green for a color contrast (visibility).

Line 328: 94/(1+1+5+94+1)=92%.  è ????

Line 347: Semicolon => Full stop/period

Please polish your manuscript!

Author Response

We earnestly appreciate your comments and suggestions. Some corrections and additions are made as below:

1. Comment: Abstract Line 22:     “ ;” => “ .”  (Semicolon => Full stop/period)

Keywords: 1, 2, 3, 4, and 5 not needed

wave plate => waveplate (For consistency to Author’s previous publications).

Reply: We are very grateful for your comments and thoughtful suggestions. According to this suggestion, the punctuation mark is corrected. Numbers after keywords are removed. “wave plate” is rewritten as “waveplate” for consistency to author’s previous publications.

(Please refer to the revised version)

2. Comment: Line 33:  MgF2=> magnesium fluoride (MgF₂)   [Check other places also!]

         Authors can mention more examples in addition to the three mentioned here.

         a certain thickness =>  a certain thickness (...) ; a typical range, input here!.

Reply: We have revised the subscript. The calcite crystal is added. The typical thickness range is tens of microns.

(Please refer to the revised version on lines 32-33) “It is typically made of quartz crystal, calcite crystal, MgF₂ crystal, or polymers with tens of microns thickness.”(lines 32-33).

3. Comment: Line 41: Many wave plate parameters measurement studies => Many waveplate parameter measurement studies.

Reply: The grammatical and formatting errors are corrected.

(Please refer to revised version on lines 48). “Many waveplate parameter measurement studies have been conducted.”(lines 48)  

4. Comment: Line 90: This is repletion to Line 33 (Please re-express it).

Reply: According to this suggestion, the expression of wave plates in principle section are moved to introduction section.

(Please refer to the revised version on lines 32-42 ) “It is typically made of quartz crystal, calcite crystal, MgF₂ crystal, or polymers with tens of microns thickness. The incident light is decomposed into ordinary and extraordinary light, with vibration directions perpendicular to each other. The ordinary light travels with the same velocity in every direction through the waveplate, and the extraordinary light travels with a velocity that is dependent upon the propagation direction within the waveplate. The main axis of the ordinary light refractive index is usually defined as the fast-axis. After the two polarized light components pass through the waveplate, a phase retardance is introduced. A waveplate is used to change the polarization state. Waveplates typically include a 1/4 waveplate, and a 1/2 waveplate, and the phase retardance corresponds to 90° and 180°, respectively. They are mainly employed in polarization-generating devices and polarization-analysis devices.”(lines 32-42).

5. Comment: Figure 1.  FPGA => a field programmable gate array (FPGA) 

                 PEM1 and PEM2 =>  A detailed scheme (as an inset figure; size & specific material should be described here) may be useful for Reader-Friendly..

Reply: Thank you once again for your time and interest. The definitions of FPGA, ADC, and LC are added in the figure title. The detailed information including size and material of PEM1 and PEM2 is described in experiment section.

(Please refer to the revised version on lines 107-108, 200-204) “FPGA: field programmable gate array; LC: Inductance-capacitance circuit; AD: Analog-to-digital converter.”(lines 107-108). “PEM1 and PEM2 are both single-drive octagonal symmetrical PEMs developed by us, the piezoelectric driver is piezoelectric quartz crystal, and the optical crystal is fused quartz crystal. The fused silica crystal sizes of PEM1 and PEM2 are 60mm´60mm´16mm and 54.2mm´54.2mm´16mm, respectively. The resonant frequencies of the two PEMs are 44.912kHz and 49.953kHz, respectively.”(lines 200-204).

6. Comment: Line 149: Check the formula (e.g., the element "row 2 column 2" in the matrix), which is different from the cited reference. Check all the equations one-by-one.

Reply: According to this suggestion, we have checked all the equations one-by-one. Line149, the Equation (3)  can also be written as ,they are equal.

(Please refer to the revised version on lines 143)

7. Comment: Line 147 and Line 153: M_Sand M_Ashould be clearly defined by a sentence also just like Lines 131 and 134.

Reply: M_S and M_A are clearly defined.

(Please refer to revised version on lines 141-142, 151-152). “The polarization transfer characteristics of the waveplate can be described by the Muller matrix () as [1,12].”(lines 141-142)  “Furthermore, the transmission axis of the analyzer is set at 45°, and its Muller matrix () is ​​expressed as.”(lines 151-152)  

8. Comment: Line 179: the AD sampling frequency through the FPGA=> the analog-to-digital (AD) sampling frequency through the FPGA   (Note: Basically, a full name should be introduced before mentioning its initial for reader-friendly.)

Reply: Full name are introduced before mentioning its initial.

(Please refer to revised version on lines 175-177). “Digital phase-locking technology is used to control the analog-to-digital converter (ADC) sampling frequency through the field programmable gate array (FPGA).”(lines 175-177)  

9. Comment: Line 217.  ADC => Analog-to-Digital Converter (ADC)

Reply: Full name are introduced before mentioning its initial.

(Please refer to revised version on lines 175-177, 214-215).”Signal acquisition is implemented using a 12-bit high-precision analog-to-digital converter (ADC), ”(lines 214-215)

10. Comment: Figure 2 and Figure 3a. Check the figure legend (Green line in the greenish background is not good; maybe delete a greenish background)

Figure 4b. Light green should be a dark green for a color contrast (visibility).

Reply: Thank you once again for your suggestions, we have revised the Figure 2, Figure 3a, Figure 4b.

(Please refer to revised version Figure 2, Figure 3a, Figure 4b).

11. Comment: Line 328: 94/(1+1+5+94+1)=92%.  è ????

Line 347: Semicolon => Full stop/period

Reply: To make the expression clear, line 328 are revised. Line 347:The semicolon are rewritten as a full stop.

(Please refer to revised version on lines 325-327). “It can be seen from the measurement data that the retardance of the entire clear aperture of the waveplate is mainly distributed in the range of (158.4±0.5) nm. There are 94 data points, accounting for 92% of the total 102 data points.”(lines 325-327)

______________________________________________

We have seriously considered all the issues and made correction according to all the reviewers’ comments. If there are any questions with the manuscript, please inform us and we wish further discussion. We hope that the revised manuscript will be suitable for publication in Applied Science.

Yours sincerely,

Dr. Kewu Li,Shuang Wang, et al.