Numerical Analysis of Optical Trapping Force Affected by Lens Misalignments

Round 1

Reviewer 1 Report

This manuscript explores detrimental effects of imperfect experimental alignment of the trapping lens on optical trapping of microparticles in optical levitation experiments. The authors numerically explore two significant sources of imperfection: off-axis alignment of the laser beam and tilt of the trapping lens. From the experimental point of view, both effects are important in real life. The modelling, results and their evaluation are presented well. I have some general comments about the manuscript, which might help with the manuscript readability. In general, I recommend the manuscript for publication after these minor revisions.

1. Line 12 in the abstract: "to analyze the influence of off-axis and tilt of lens..": "off-axis" what? I presume the authors forgot to write "placement" or another word there.

2. The authors use "geometric optics" and "geometrical optics" inconsistently. It should be "geometrical optics".

3. Line 32: The authors claim that the "..theory of calculating the optical trapping force is constantly improving...". As the authors state later in the text, there are three different calculation methods based on the particle size in comparison with the laser wavelength: Rayleigh, Lorentz-Mie (which in principle is correct for every size) and ray optics. I wouldn't call any extensions a new theory or improvements of theory, because you are only changing the model of the trapping light and not the method of calculation. If the authors agree with this statement, I would ask them to change the claim in the sentence. If not, please provide me with a counter-argument.

4. The authors only sporadically mention that the laser is circularly polarized, which is required for the calculation method that they provide later in the text. However, tightly focused, linearly polarized Gaussian beams also result in elliptical cross-sections in the focal plane, which would provide different x and y frequencies as well. The authors should provide a clear argument earlier in the text -- say around line 53 where you mention the different frequencies -- that this is not what you are looking into because of the circularly polarized light. By the way, which of the two (lens placement imperfection or light polarization) is the reason mentioned in reference [12], which you cite in lines 53-54?

5. The authors should also mention the waist in the focal plane.

Author Response

Reviewer‘s comments：

This manuscript explores detrimental effects of imperfect experimental alignment of the trapping lens on optical trapping of microparticles in optical levitation experiments. The authors numerically explore two significant sources of imperfection: off-axis alignment of the laser beam and tilt of the trapping lens. From the experimental point of view, both effects are important in real life. The modelling, results and their evaluation are presented well. I have some general comments about the manuscript, which might help with the manuscript readability. In general, I recommend the manuscript for publication after these minor revisions.

 

Comments:

1. Line 12 in the abstract: "to analyze the influence of off-axis and tilt of lens..": "off-axis" what? I presume the authors forgot to write "placement" or another word there.

Response: Thank you for pointing out this. It is indeed our mistake to forget to write “placement” and we have corrected this error in revised manuscript.

 

1. The authors use "geometric optics" and "geometrical optics" inconsistently. It should be "geometrical optics".

Response: Thanks for this advice, we have corrected the expression in accordance with your comment.

 

1. Line 32: The authors claim that the "..theory of calculating the optical trapping force is constantly improving...". As the authors state later in the text, there are three different calculation methods based on the particle size in comparison with the laser wavelength: Rayleigh, Lorentz-Mie (which in principle is correct for every size) and ray optics. I wouldn't call any extensions a new theory or improvements of theory, because you are only changing the model of the trapping light and not the method of calculation. If the authors agree with this statement, I would ask them to change the claim in the sentence. If not, please provide me with a counter-argument.

Response: Thanks for this advice, we have removed the claim and emphasized in the text that our work focuses on a new application of geometrical optics rather than an improvement of the theory.

 

1. The authors only sporadically mention that the laser is circularly polarized, which is required for the calculation method that they provide later in the text. However, tightly focused, linearly polarized Gaussian beams also result in elliptical cross-sections in the focal plane, which would provide different x and y frequencies as well. The authors should provide a clear argument earlier in the text -- say around line 53 where you mention the different frequencies -- that this is not what you are looking into because of the circularly polarized light. By the way, which of the two (lens placement imperfection or light polarization) is the reason mentioned in reference [12], which you cite in lines 53-54?

Response: Thanks for your suggestion. To be more precise, we have replaced the sentence in line 53 with “Specifically, even without considering the polarization state of the trapping light, some unexpected phenomena such as the detection coupling within axes [26] and difference of x, y-axes resonant frequencies [12] may occur due to misalignment of the lens, so the influence of lens mounting on experiments is worth discussing.” In addition, we mention the reference [12] only to show the existence of resonant frequency asymmetry in the experiment, however, the exact cause of this phenomenon was not determined.

 

1. The authors should also mention the waist in the focal plane.

Response: Thanks for your suggestion. We have added this parameter to the simulation parameters section.

 

 

Revision:

1. off-axis placement (Line 12)
2. geometrical optics (Line 11, Line 12, Line 109, )
3. There are currently three different calculation methods based on the particle size in comparison with the laser wavelength. (Line 32-33)
4. Specifically, even without considering the polarization state of the trapping light, some unexpected phenomena such as the detection coupling within axes [26] and difference of x, y-axes resonant frequencies [12] may occur due to misalignment of the lens, so the influence of lens mounting on experiments is worth discussing. (Line 51-55)
5. And the waist radius in the focal plane is 1.99 μm. (Line 156-157)

Reviewer 2 Report

The work by Zhang et al. analyzed the effect of lens misalignments on optical force in the geometrical optics regime. As pointed out in the article, there were two kinds of lens misalignments, i.e., off-axis misalignment and tilting misalignment, the latter of which was thought to have a greater impact on optical trapping. Therefore, the simulation results provide guidance to reduce lens misalignments for more accurate optical trapping. Nevertheless, there are still some points needed to be considered:

1. Why is the numerical aperture set to 0.25 but not a higher value? Optical trapping usually requires an objective lens with a high numerical aperture for larger optical gradient force.
2.  If the numerical aperture of the lens is different, are the conclusions on the effect of the two lens misalignments the same as stated in the article?

      

Author Response

Reviewer's comments:

The work by Zhang et al. analyzed the effect of lens misalignments on optical force in the geometrical optics regime. As pointed out in the article, there were two kinds of lens misalignments, i.e., off-axis misalignment and tilting misalignment, the latter of which was thought to have a greater impact on optical trapping. Therefore, the simulation results provide guidance to reduce lens misalignments for more accurate optical trapping. Nevertheless, there are still some points needed to be considered:

 

Comments:

1. Why is the numerical aperture set to 0.25 but not a higher value? Optical trapping usually requires an objective lens with a high numerical aperture for larger optical gradient force.

Response: This advice is valuable. This numerical aperture was chosen because we wanted the simulation results to serve for our experimental setup, which is single-beam vertical vacuum optical trap. In this experimental setup, the gravity of the microsphere and the vertical optical scattering force balance each other, so a high numerical aperture is not required. Furthermore, a high numerical aperture usually results in low signal-to-noise ratio, so we will use low numerical aperture lens whenever possible.

 

1. If the numerical aperture of the lens is different, are the conclusions on the effect of the two lens misalignments the same as stated in the article?

Response: That’s a good question. In fact, we have tried to simulate with different numerical apertures, but the results obtained are more or less the same. Because in our experiments, we generally need to keep the microsphere at a certain distance from the focal point of the lens to get better axial force-displacement linearity. Therefore, not all light rays are incident on the microsphere, so the effect of changing the numerical aperture on optical trap is very limited.

 

Round 2

Reviewer 2 Report

All my questions have been addressed. I recommend this paper for publication.