Simple Estimate of the Impact of M² and Strehl Ratio on the Effective Focusable Spot Size

Round 1

Reviewer 1 Report

This is a theoretical study on the influence of M2 and Strehl Ratio on the effective focusable spot size. The qualitative and quantitative estimation of the interplay of M2 and SR on the effectively focusable spot size is presented. In my opinion, the manuscript is suitable for publication in Optics however some issues should be resolved:

1) The introduction section is insufficient. Adding some real examples of experimental works where the results of the manuscript can be applied will improve the quality of the work.

2) There are problems (lines 96, 170, 209, etc.) with references in the manuscript. Please check it. 

3) I recommend numerating the equations used in the manuscript for better clarity for the reader.

4) Some typos should be cleaned from the text, e.g. line 113 ("M2 values of 1251 or below"), line 290 ("assumptions; could explain")/

5) The software used for calculations should be indicated in Methods section. The used algorithms can be provided in Supplementary section.

Author Response

This is a theoretical study on the influence of M2 and Strehl Ratio on the effective focusable spot size. The qualitative and quantitative estimation of the interplay of M2 and SR on the effectively focusable spot size is presented. In my opinion, the manuscript is suitable for publication in Optics however some issues should be resolved:

• Thank you for your positive overall score

1) The introduction section is insufficient. Adding some real examples of experimental works where the results of the manuscript can be applied will improve the quality of the work.

• Thank you for your suggestion. We have now presented some works also at the introduction, and subsequently discussed them in the discussion.
  • Uwe Urmoneit, Adam Hotz, Thomas Fröhlich, Hans-Joachim Krauß, Influence of Laser Beam Diameter on the Resistance of Laser Protection Filters to Laser Radiation, Physics Procedia, Volume 56, 2014, Pages 1377-1383, ISSN 1875-3892, https://0-doi-org.brum.beds.ac.uk/10.1016/j.phpro.2014.08.066.
  • Siegman, A. E. (October 1997). "How to (Maybe) Measure Laser Beam Quality". Tutorial presentation at the Optical Society of America Annual Meeting, Long Beach, California
  • Mahajan, Virendra (1983), "Strehl ratio for primary aberrations in terms of their aberration variance", J. Opt. Soc. Am., 73 (6): 860–861, doi:10.1364/JOSA.73.000860
  • Ross & Latham, Appropriate measures and consistent standard for high energy laser beam quality, Journal of Directed Energy, 2, Summer 2006 pages, pp. 22-58.
  • Jürgen Eichler, Lothar Dünkel, Bernd Eppich: Die Strahlqualität von Lasern – Wie bestimmt man Beugungsmaßzahl und Strahldurchmesser in der Praxis? In: Laser Technik Journal. Band 1, Nr. 2, Oktober 2004, S. 63–66, doi:10.1002/latj.200790019
  • Strehl, K. 1895, Aplanatische und fehlerhafte Abbildung im Fernrohr, Zeitschrift für Instrumentenkunde 15 (Oct.), 362-370.
  • Sacek, Vladimir (July 14, 2006), "6.5. Strehl ratio", Notes on amateur telescope optics, https://www.telescope-optics.net/Strehl.htm
  • Samuel Arba-Mosquera, Pascal Naubereit, Simas Sobutas, and Shwetabh Verma, "Analytical optimization of the cutting efficiency for generic cavitation bubbles," Biomed. Opt. Express 12, 3819-3835 (2021)
  • Arba-Mosquera, Samuel, Krüger, Luise, Naubereit, Pascal, Sobutas, Simas, Verma, Shwetabh, Zheleznyak, Len and Knox, Wayne H.. "Analytical optimization of the laser induced refractive index change (LIRIC) process: maximizing LIRIC without reaching the damage threshold" Advanced Optical Technologies, vol. 10, no. 6, 2021, pp. 363-373. https://0-doi-org.brum.beds.ac.uk/10.1515/aot-2021-0052
  • H. Griessmann, A. C. Martinez-Becerril, and J. S. Lundeen, "A method to determine the M2 beam quality from the electric field in a single plane," Opt. Continuum 2, 1833-1848 (2023)

2) There are problems (lines 96, 170, 209, etc.) with references in the manuscript. Please check it. 

• Thank you. This has been fixed now

3) I recommend numerating the equations used in the manuscript for better clarity for the reader.

• Thank you. This has been fixed now

4) Some typos should be cleaned from the text, e.g. line 113 ("M2 values of 1251 or below"), line 290 ("assumptions; could explain")/

• Thank you. This has been fixed now

5) The software used for calculations should be indicated in Methods section. The used algorithms can be provided in Supplementary section.

• Calculations have been made by “pen and paper”, and plots have been simply generated using Microsoft Excel

Reviewer 2 Report

The manuscript entitled " Simple estimate of the impact of M2 and Strehl Ratio on the effective focusable spot size Estimate of the impact of M2 and Strehl Ratio on the spot size in focus " is interesting but should be carefully revised as it is not clearly presented.

1.      The idea of investigation is not clear. What is the novelty of the manuscript?

2.      The scientific background should be more detailed in the field of art.

3.      The formulas are difficult to read, I recommend using the equation editor

4.      no use of superscripts 𝑀2>2, l.139

5.      “The RMS to SR approximation holds valid for SR as low as ~0.3,Error! Bookmark not defined. and yet, as mentioned before, SR >0.8 is considered reasonably diffraction limited.Error! Book  mark not defined”. l. 186

6.      Conclusions doesn’t contain any results.

7.      What is the application of presented results?

Author Response

The manuscript entitled " Simple estimate of the impact of M2 and Strehl Ratio on the effective focusable spot size Estimate of the impact of M2 and Strehl Ratio on the spot size in focus " is interesting but should be carefully revised as it is not clearly presented.

• Thank you for your overall positive score

1. The idea of investigation is not clear. What is the novelty of the manuscript?

• Thank you. This has been now added to the introduction
  • The novelty of this manuscript is providing analytical (yet simple) close-form equations to account for M2 and SR effects in photochemical and laser-tissue interaction models.

2. The scientific background should be more detailed in the field of art.

• Thank you. This has been now added to the introduction
  • M2 is a heuristic parameter of the laser beam related to the spot size in focus;6 whereas the SR is a measure of the quality of optical image formation, originally pro-posed by Karl Strehl.7 The SR is frequently defined as the ratio of the peak aberrated image intensity from a point source compared to the maximum attainable intensity using an ideal optical system limited only by diffraction over the system's aperture.8  Usually M2 values of 1.25 or below are considered excellent (and non-rigorously as „close to the diffraction-limit“).9  Similarly optical systems with SR values of 0.8 or better are con-sidered excellent (and non-rigorously as „close to the diffraction-limit“).7
  • It has been previously shown that M2 and SR affects different laser tissue interaction processes including laser induced optical breakdown (LIOB)10 and laser induced refrac-tive index change (LIRIC).11

3. The formulas are difficult to read, I recommend using the equation editor

• Thank you. This has been fixed now

4. no use of superscripts ?2>2, l.139

• Thank you. This has been fixed now

5. “The RMS to SR approximation holds valid for SR as low as ~0.3,Error! Bookmark not defined. and yet, as mentioned before, SR >0.8 is considered reasonably diffraction limited.Error! Book  mark not defined”. l. 186

• Thank you. This has been fixed now

6. Conclusions doesn’t contain any results.

• Thank you. This has been fixed now
  • Adding M2 and SR as parameters into photochemical models to consciously deviate from the diffraction-limited assumptions; could explain the empirical findings ob-served/determined with real world experiences, in particular using commercially availa-ble systems. This work provides analytical (yet simple) close-form equations to account for M2 and SR effects in photochemical and laser-tissue interaction models.

7. What is the application of presented results?

• Thank you. This has been fixed now
  • Adding M2 and SR as parameters into photochemical models to consciously deviate from the diffraction-limited assumptions; could explain the empirical findings ob-served/determined with real world experiences, in particular using commercially availa-ble systems. This work provides analytical (yet simple) close-form equations to account for M2 and SR effects in photochemical and laser-tissue interaction models.

Reviewer 3 Report

Review of the manuscript entitled ‘Simple estimate of the impact of M2 and Strehl Ratio on the effective focusable spot size Estimate of the impact of M2 and Strehl Ratio on the spot size in focus’

Authors describe a simple method to determine the impact of M2 and SR on the effective focusable spot size avoiding complex propagations of the beam wavefront is proposed. The model is based upon previous models and the definition of M2 and SR in a simple manner.

The study is interesting and deserves to be accepted. However, the manuscript can be improved.

- Simple picture presenting the different parameters (M2, SR, NA) will help the reader.

- The formula must be edited with a formula editor and not written on a line.

- In the introduction authors must present why the study is done,

- A tab summing up all the results must be inserted.

Author Response

Review of the manuscript entitled ‘Simple estimate of the impact of M2 and Strehl Ratio on the effective focusable spot size Estimate of the impact of M2 and Strehl Ratio on the spot size in focus’

Authors describe a simple method to determine the impact of M2 and SR on the effective focusable spot size avoiding complex propagations of the beam wavefront is proposed. The model is based upon previous models and the definition of M2 and SR in a simple manner.

The study is interesting and deserves to be accepted. However, the manuscript can be improved.

• Thank you for your overall positive scores

- Simple picture presenting the different parameters (M2, SR, NA) will help the reader.

• Thank you. We think M², SR, and NA shall be so commonplace entities that it shall suffice with the provided references

- The formula must be edited with a formula editor and not written on a line.

• Thank you. This has been fixed now

- In the introduction authors must present why the study is done,

• Thank you. This has been now added to the introduction
  • M2 is a heuristic parameter of the laser beam related to the spot size in focus;6 whereas the SR is a measure of the quality of optical image formation, originally pro-posed by Karl Strehl.7 The SR is frequently defined as the ratio of the peak aberrated image intensity from a point source compared to the maximum attainable intensity using an ideal optical system limited only by diffraction over the system's aperture.8  Usually M2 values of 1.25 or below are considered excellent (and non-rigorously as „close to the diffraction-limit“).9  Similarly optical systems with SR values of 0.8 or better are con-sidered excellent (and non-rigorously as „close to the diffraction-limit“).7
  • It has been previously shown that M2 and SR affects different laser tissue interaction processes including laser induced optical breakdown (LIOB)10 and laser induced refrac-tive index change (LIRIC).11
  • The novelty of this manuscript is providing analytical (yet simple) close-form equations to account for M2 and SR effects in photochemical and laser-tissue interaction models.

- A tab summing up all the results must be inserted.

• Thank you. This has been fixed now

Round 2

Reviewer 1 Report

Authors responded to all my concerns and now the manuscript can be accepted in present form.  

Reviewer 2 Report

The manuscript entitled " Simple estimate of the impact of M2 and Strehl Ratio on the effective focusable spot size Estimate of the impact of M2 and Strehl Ratio on the spot size in focus " can be publish in the present form.