Experimental Validation of Designs for Permeable Diffractive Lenses Based on Photon Sieves for the Sensing of Running Fluids
, Angela Soria-Garcia 2, Joaquin Andres-Porras 2, Jesus del Hoyo 2, Mahmoud H. Elshorbagy 1,3, Luis Miguel Sanchez-Brea 2 and Javier Alda 1,*
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis contribution reports the experimental validation of several designs of photon sieves having focusing capabilities. These permeable optical elements have been implemented with a spatial light modulator working in pure-amplitude mode. The focal region has been scanned using a traveling stage holding a camera. Using this experimental setup, the authors have characterized the focal region of the photon sieves and we have determined some parameters of interest, as the depth of focus and the transverse extent of the focal region.
Here are some comments for revision.
1, The authors used pure amplitude mode spatial light modulator, which can be replaced by phase only spatial light modulators. Can the authors comment on this point?
2, The fitting function in Eq. (3) was chosen as the Gaussian function, can the authors comment on the reason for this?
Author Response
[See attached file containing a copy of this reply with better formatting]
This contribution reports the experimental validation of several designs of photon sieves having focusing capabilities. These permeable optical elements have been implemented with a spatial light modulator working in pure-amplitude mode. The focal region has been scanned using a traveling stage holding a camera. Using this experimental setup, the authors have characterized the focal region of the photon sieves and we have determined some parameters of interest, as the depth of focus and the transverse extent of the focal region.
Here are some comments for revision.
1, The authors used pure amplitude mode spatial light modulator, which can be replaced by phase only spatial light modulators. Can the authors comment on this point?
The reason to have the spatial light modulator working in amplitude mode is linked to the need to reproduce, as faithfully as possible, the binary amplitude masks of the photon sieves under analysis. If the SLM were set to work in phase only mode, it would not mimic the situation of a real photon sieve. This amplitude mode is set by adjusting the polarizing elements in the experimental setup.
2, The fitting function in Eq. (3) was chosen as the Gaussian function, can the authors comment on the reason for this?
There are two main reasons why the Gaussian fitting was applied to our case. The first one is the use of a TEM00 Gaussian mode illumination along the optical train. It is true that the SLM is filled, as homogeneously as possible by the light beam, but the Gaussian distribution is still there. The second reason is linked with the capability of using the classical parameterization of laser beams through the values of the Gaussian width evolution, the divergence, and the quality factor M2, that have been used for a proper comparison among masks.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper provides a scheme for measuring the refractive index of a fluid, and establishes a design model for permeable optical elements, which I think is a interdisciplinary fusion of optics and running fluid. The work is very detailed, with strong data support, it is recommended to publish.
Author Response
This paper provides a scheme for measuring the refractive index of a fluid, and establishes a design model for permeable optical elements, which I think is a interdisciplinary fusion of optics and running fluid. The work is very detailed, with strong data support, it is recommended to publish
We really appreciate the kind comments of the referee. They help us to maintain our research activity at the highest possible level.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsNotes to the manuscript
“Experimental validation of designs for permeable diffractive lenses based on Photon Sieves for the sensing of running fluids.”
The authors report the experimental validation of several designs of photon sieves having focusing capabilities. Among the various properties of such lenses, one clearly distinguishes them from other optical elements: they transmit not only radiation, but also matter in liquid and gaseous states. This property is very important in a number of cases, for example, in the method described in the article for measuring the refractive index of a liquid; which allows one to put up with the deterioration of the characteristics of the formed beam. There are several methods for constructing the photon sieve. The authors compared them and concluded that one of the designs, labeled as Ring-by-Ring method, behaves in a quite balanced manner and becomes a preferred choice. Note that the experiments were not conducted on permeable diffractive lenses made of the material, but on their implementations with a spatial light modulator. This significantly simplifies the trial experiments conducted before using the optical element in the finished device.
The text of the article is well written, no errors were found, except for a few typos. There is only one wish: in item 3.1. add a drawing showing the relative positions of the radiation source, permeable lens, liquid and receiver.
Also it should be noted that for the application of the lenses under consideration planned by the authors - refractometric sensing - it is important to have a short DOF. Therefore, it is desirable that the authors add to the text of the manuscript a discussion of the issue of how the DOF could be reduced. Probably, one of the ways is to enhance focusing (increase the numerical aperture). However, there may be restrictions on the manufacture of lenses. In addition, it is known that even with sharp focusing, the longitudinal size of the focal spot is always larger than the transverse one [https://doi.org/10.1002/jms.4914]. Therefore, various possibilities associated with interference effects, as well as additional apodization, can be considered [https://doi.org/10.1364/JOSAA.18.000036; http://dx.doi.org/10.1364/JOSAA.30.002029; https://doi.org/10.1364/OPTICA.2.000812].
Other notes.
Page 2, Lines 34-36. It is possible that the reference [15] is wrong: Line 34 says “interesting niche is X-ray optics”, and the heading [15] is “Terahertz Sieves”.
Page 4, Line 134. “the pure-amplitud mode” replace by “the pure-amplitude mode”.
Page 9, Eq. (7) and Line 247. Different designations of the denominator in the formula and in the text.
Page 13, Line 359. “why with have analized this case” replace by “why we have analized this case”.
Page 14, Line 398. “the permability” replace by “the permeability”.
Author Response
[See attached file for a better formatted version of this reply, including figures]
The authors report the experimental validation of several designs of photon sieves having focusing capabilities. Among the various properties of such lenses, one clearly distinguishes them from other optical elements: they transmit not only radiation, but also matter in liquid and gaseous states. This property is very important in a number of cases, for example, in the method described in the article for measuring the refractive index of a liquid; which allows one to put up with the deterioration of the characteristics of the formed beam. There are several methods for constructing the photon sieve. The authors compared them and concluded that one of the designs, labeled as Ring-by-Ring method, behaves in a quite balanced manner and becomes a preferred choice. Note that the experiments were not conducted on permeable diffractive lenses made of the material, but on their implementations with a spatial light modulator. This significantly simplifies the trial experiments conducted before using the optical element in the finished device.
The text of the article is well written, no errors were found, except for a few typos. There is only one wish: in item 3.1. add a drawing showing the relative positions of the radiation source, permeable lens, liquid and receiver.
Also it should be noted that for the application of the lenses under consideration planned by the authors - refractometric sensing - it is important to have a short DOF. Therefore, it is desirable that the authors add to the text of the manuscript a discussion of the issue of how the DOF could be reduced. Probably, one of the ways is to enhance focusing (increase the numerical aperture). However, there may be restrictions on the manufacture of lenses. In addition, it is known that even with sharp focusing, the longitudinal size of the focal spot is always larger than the transverse one [https://doi.org/10.1002/jms.4914]. Therefore, various possibilities associated with interference effects, as well as additional apodization, can be considered [https://doi.org/10.1364/JOSAA.18.000036; http://dx.doi.org/10.1364/JOSAA.30.002029; https://doi.org/10.1364/OPTICA.2.000812].
After revising Sec. 3.1, we agree with the referee about the need of a graph showing the experimental setup that may help to better understand how the system works for refractometric sensor. The new figure 8 and the caption has been modified as follows.
| Figure 8. (a) Normalized responsivity, R(n), for the integrated signal of a detector with 50 mm in diameter and located at z=f'(n=1.333) = 133.3 mm. (b) Variation of the normalized responsivity with respect to the index of refraction, dR/dn. The module of this derivative can be considered as the normalized sensitivity, SB, for the normalized responsivity, R(n), as defined in Eq. (9). This calculation has been done for the RbR mask. The colored band around the value of n represents the dynamic range considering that SB is larger than 0.9 the maximum value of SB. The presence of two dynamic range reveals the capability of the sensor to explore two different regions with the same configuration. (c) Optical setup where a collimated beam, after crossing through the photon sieve, focus the light on a detector located at a distance z = 133.3 mm, that remain fixed when varying n. |
We thank to the reviewer for his/her suggestions about the relation between the beam waist and the DOF that is presented in Ref. https://doi.org/10.1002/jms.4914. As a matter of fact, we have added this reference to the bibliography in our revised version. The change in the manuscript is as follows:
… For this purpose, we have evaluated the Depth Of Focus (DOF) and the beamwidth transversal size. For a laser beam, it has been shown that, when the DOF is defined in terms of the Rayleigh range, there exist an analytical relation between the transversal and longitudinal extent of the waist [R1]. Following the laser beam propagation model, we have also calculated the beam quality factor, M2. Other geometrical parameters of the propagation and the mask, as the beam’s ellipticity, and the device’s permeability, are also evaluated. This last quantity…
[R1] Joignant AN, Xi Y, Muddiman DC. Impact of wavelength and spot size on laser depth of focus: Considerations for mass spectrometry imaging of non-flat samples. J Mass Spectrom. 2023; 58(5):e4914. doi:10.1002/jms.4914
With respect to the use of interference effects and phase effects, as those described in the references given by the referee, we think that their application to the case of photon sieves working with running fluids could be difficult, as these techniques require a tight control of the phase distribution.
The referee is right when pointing out the discussion about the Depth of Focus (DOF). The refractometric example given in the manuscript would benefit from a shorter DOF and, as the referee describes, an easy solution would be to increase the transversal size of the photon sieve. However, this strategy could be limited by fabrication constrains. In any case, the proposed masks already consider these limitations and could be easily prepared for a larger aperture. However, the drilling of several thousands of circular holes could also compromise the practical realization of the photon sieves. To overcome the limitation of a successive mechanization of the individual circular apertures, some other techniques, as chemical etching may overcome this issue by generating all the holes simultaneously. Also, if the sensing strategy is based on the functionalization of the remaining surface of the photon sieve, the use of a short DOF is not so important, as a longer focal region would help to work with optomechanical system with larger tolerances. This discussion has been added to the manuscript in two locations (in Section 2.1, and in the discussion of the DOF values in section 3):
… aperture, that we have set in the interval [16, 180] mm. The time to fabricate many holes may compromise the accuracy in the location and shape of them. To overcome this issue, some other manufacturing techniques, as chemical attack, or etching, can be applied to generate all the holes simultaneously, as it has been demonstrated for a variety of substrates and applications [R2, R3, R4, R5]. This could be of importance for the fabrication of wide aperture photon sieves involving many Fresnel zones.
[R2] Kang, E. K.; Lee, Y. W.; Ravindran, S.; Lee, J. K.; Choi, H. J.; Ju, G. W.; Min, J. W.; Song, Y. M.; Sohn, I.-B. & Lee, Y. T.
4 channel x 10 Gb/s bidirectional optical subassembly using silicon optical bench with precise passive optical alignment, Opt. Express 2016, 24, 10777-10785
[R3] Chen, S.-T. & Luo, T.-S. Fabrication of micro-hole arrays using precision filled wax metal deposition, Journal of Materials Processing Technology, 2010, 210, 504-509
[R4] Chen, S.; Zhang, L.; Zhao, Y.; Ke, M.; Li, B.; Chen, L. & Cai, S.
A perforated microhole-based microfluidic device for improving sprouting angiogenesis in vitro Biomicrofluidics, 2017, 11, 054111
[R5] Jia, P.; Zhou, S.; Cai, X.; Guo, Q.; Niu, H.; Ning, W.; Sun, Y. & Zhang, D. High-fidelity synthesis of microhole templates with low-surface-energy-enabled self-releasing photolithography, RSC Adv., 2024, 14, 12125-12130
As we have seen, the DOF values (see Figure 4) are essential to understand where to place a detector in the focal region along the z-axis. In Sec. 3.1 we present a refractometric sensor with a performance that increases when the DOF is shorter. However, shortening this parameter is typically done by increasing the transversal size of the PS, which is mostly limited by the fabrication constrains. At the same time, some other sensing approaches, based on the functionalization of the PS surface (when it works in reflective mode), may benefit from a larger DOF, as it allows larger tolerances in the optomechanical design. When comparing…
Other notes.
Page 2, Lines 34-36. It is possible that the reference [15] is wrong: Line 34 says “interesting niche is X-ray optics”, and the heading [15] is “Terahertz Sieves”.
We have checked this issue and corrected properly in the revised version. We have removed the Terahertz referenced and placed in a dedicated sentence after the discussion made for the X-ray applications. This new placement, along with some other modifications in the bibliography, has changed the reference numbers in the revised version.
Page 4, Line 134. “the pure-amplitud mode” replace by “the pure-amplitude mode”.
We thank the reviewer for his/her detailed reading of the manuscript. We have corrected this misspelling, and we have made a full revision of the style and grammar of the whole manuscript.
Page 9, Eq. (7) and Line 247. Different designations of the denominator in the formula and in the text.
Thanks a lot for checking this. We have revised this inconsistence between the equation and the text. We are sorry for this error.
Page 13, Line 359. “why with have analized this case” replace by “why we have analized this case”.
We have corrected this error to improve the reading of the manuscript.
Page 14, Line 398. “the permability” replace by “the permeability
This misprint has been corrected. We are sorry for having this (and some other spelling mistakes) in our original submission.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsAll comments are collected in the attached file.
Comments for author File: Comments.pdf
Author Response
[Please check the attached file for a better formatted version of this reply, including figures relevant to our reply]
The authors implemented several photon sieve masks in an optical bench to obtain their optical performance. The photon sieves have been implemented using a spatial light modulator working in pure-amplitude mode. As a practical example, the capabilities of photon sieves as refractometricsensors for running fluids has been computationally evaluated for one type of a photon sieve mask. The results are interesting, although the experimental results are only given for simulation at SLM.
The authors should take into account some comments:
1) page 9, line 247: formula (7) uses Acirc, which is not described, but AFZP is described below;
We thank to the reviewer for his/her attention to these details. We have corrected this issue to improve the self-consistence of the manuscript.
2) Table 1 shows theoretical DOF=5.3 mm for FZP (the smallest of those considered), but the experimental value was significantly larger (10.4 mm). This is a very strange result, check it out. Moreover, the pictures in Fig. 7k,l show that DOF for FZP is the smallest of those considered.
When comparing the experimental and simulated results for the FZP we were also paying attention to the large departure in the DOF values. The results from the simulation make sense very much, but the experimental values show the type of discrepancies outlined by the referee. Our best explanation for this issue is the presence of residual astigmatism at the SLM and some inhomogeneities in the illumination. This has been revealed in the form of a non-negligible pedestal in the irradiance map around the focal point in the case of FZP.
To properly address this referee’s comment, we are presenting in this reply some plots that may support our guessing about the observed discrepancies. In Fig. R1 we show the axial maximum irradiance obtained for the FZP mask (experimental and simulated), along with the graphical representation of the DOF. Also, we have included the transversal irradiance maps obtained experimentally, and from simulations. The axial distribution, represented in a similar form as Fig. 4 of our manuscript, shows the presence of a pedestal in the experimental case. This pedestal needs to be considered to have a sound definition of the DOF as the FWHM of this evolution, as discussed in the manuscript when analyzing Fig. 4. On the other hand, the irradiance maps obtained in the experiment reveals the presence of a residual astigmatism. Both the pedestal and astigmatism does not appear in the simulated results. As far as the FZP is not a truly photon sieve, we think that a discussion of this discrepancy between experiment and simulation is not a main objective of this contribution, and we have decided not to include in the manuscript.
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Figure R1: Analysis of the FZP mask. Top: Evolution of the Imax values obtained along the propagating axis for the FZP mask. The experimental values are plotted in blue, and the simulated results are plotted in orange. Bottom: Irradiance maps at different z planes for the experimental measurement and simulated results (the colormap and range is the same for all the maps). |
With respect to Figs. 7k,l, we can see that the transversal size is the smallest of all the maps in this figure. This complies with the values presented in Table 7 for the transversal size w0,x and w0,y (both for the experimental and the simulated case). However, due to the definition of the DOF, in terms of the FWHM, this last parameter is affected by the existence of a pedestal in irradiance.
3) It is necessary to describe in more detail and possibly illustrate how the value of the responsivity of the optoelectronic detection system R(n) and the change in the focus position f(n) are related.
The value of R is obtained by integrating the irradiance distribution on a circle that can be related to the size of the detector. In our case we have consider a diameter of 50 mm. The value of this integrated irradiance has been normalized to have it applicable to any type of optoelectronic transduction. As expected, the maximum normalized R happens at the focal position, that also depends on the index of refraction through Eq. (11). The case represented in Fig. 8 correspond to a photon sieve of f’=100 mm in vacuum, which moves its focal point to f’=133 mm for an index of refraction of n=1.33. As expected, the maximum signal is obtained at the distance z=133 mm. If we don’t move the detector, the irradiance changes with the index of refraction and shows two regions of interest, where the change in irradiance when varying the index of refraction is larger. One of them is located at n=1.27, and the other at n=1.38. Around these values, the irradiance varies with high linearity, allowing the definition of two index region where the refractometric sensor perform the best. This explanation is illustrated by Fig. 8a, and 8b. The addition of Fig. 8.c in the revised version helps to understand the experimental setup.
As suggested by the reviewer, we have modified the explanation given in Sec. 3.1 to better describe the operation of the sensor.
…Practically, we have evaluated how much irradiance falls within a light detector apertured with a 50 mm diameter pinhole and located at the focal plane of the PS. Using “Diffractio", this integrated irradiance on the detector is obtained in terms of the index of refraction. This focal plane is selected for a reference value of the index of refraction, which in our case is n=1.333. Figure 8a shows the normalized signal in terms of the index of refraction for the RbR mask, R(n), when the detector is located at f’(n = 1.333) = 133.3 mm. The distance between the PS and the detector is fixed when varying the index of refraction. As, expected, this plot has a maximum equal to 1 when n = 1.333. For a refractometric sensor based on optoelectronic signals [33], we calculated the normalized sensitivity defined in Eq. (9). This parameter is represented in Fig. 8b, having local maximum of SB,max = 7.86 RIU-1 at n = 1.27, and a local minimum of SB,min = 7.77 RIU-1 at n = 1.38. These values of the index of refraction are those where the change in intensity is larger. Around these values of the index of refraction, we can define a dynamic range where the linearity of the signal is almost preserved. If we assume a variation…
… once the geometry is set. This means that, as shown in Fig. 8c, the distance between the PS and the detector remains fixed and allows the operation of the sensor in two dynamic ranges (see colored bands in Fig. 8) with quite similar sensitivities. These ranges are around two values of the index of refraction: nsensmax and nsensmin, as shown in Fig. 8a. These locations do not coincide with the maximum responsivity, R, that happens for an an index n=1.333 in the given example. For refractometric sensors based on plasmonic resonances, if we need to monitor another medium, …
4) In addition, it is necessary to discuss in more detail what characteristics of the considered lenses are most important for increasing the sensitivity of the proposed approach as a refractometric sensor - DOF, FWHM, M2,Aps? It is known that binary lenses have additional local foci [Subharmonic focal-length intensities formed by Fresnel lenses, Appl. Opt. 33, 8194–8196 (1994); Local foci of a parabolic binary diffraction lens, Applied Optics, 54(18), 5680-5685 (2015)]. Does it make sense to use them for additional measurement accuracy?
The discussion about what is the most important parameter in the characterization of the focal region is strongly dependent on the application. For example, for the type of sensing device described in section 3.1, the DOF is likely the most interesting one. However, if the running flux of fluid is large, maybe a larger permeability is preferable. Even more, if the photon sieves were intended for image-forming, some other parameters, as the Strehl ratio or the MTF, should be monitored. Then, our choice of the RbR mask among the other is mainly based on its balanced values in the studied parameters. This type of discussion is made in the two paragraphs before the beginning of Section 3.1, where we justify our selection of the RbR mask.
The presence of additional foci is not of importance for the refractometric sensor that we are analyzing in this paper. Figure R2 shows the presence of these additional foci where we can see how the 3rd order foci is far away from the first one (it is actually located at f’/3) and do not disturb the irradiance around it for a limited range in variation of the index of refraction. This figure corresponds to Fig. 1 in our referenced paper https://doi.org/10.1016/j.ijleo.2025.172342
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Figure R2: Top: Relative encircled energy with respect to the total energy entering the aperture of the FZP, as a function of the location at the propagation axis, z. The arrows and the m label represent the location of the higher-order foci, located at a distance z=f’/m, where m is an odd number. Bottom: Focal region of the irradiance map at each foci represented in the top plot. The range in the colormap is the same for all the maps and has been normalized to present the full range when z=f’, case #1. The percentage values replicate the relative encircled energy presented in the top figure. |
5) page 6, line 192: instead of “nomimal” should be “nominal”;
This error has been corrected in the revised version of the manuscript.
Author Response File: Author Response.pdf
Round 2
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors have mostly taken my comments into account.
