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Characteristics of non-diffractive beam generation related to concentration and propagation distance in highly random media
Optik - International Journal for Light and Electron Optics 202 (2020) 163628
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Original research article
Characteristics of non-diffractive beam generation related to concentration and propagation distance in highly random media
T
Alifu Xiafukaitia,*, Ziqi Pengb, Hiroaki Kuzea, Tatsuo Shiinac a b c
Center for Environmental Remote Sensing, Chiba University, 1-33 Yayoi-cho,Inage-ku,Chiba 263-8522, Japan Hunan University of Art and Science 3150, Dong Ting Road, Changde, 415500, PR China Graduate School of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
A R T IC LE I N F O
ABS TRA CT
Keywords: Annular beam Non-diffractive beam Light propagation Scattering Highly random media
Laser beam propagation in highly random media can potentially be applied to various optical studies, though the light penetration is often limited to the surface or skin regions of the targets. In free space, it is known that the use of a non-diffractive beam (Bessel beam) is useful for achieving a long-distance propagation by reducing the influence of diffraction. In our previous work [Z. Peng, and T. Shiina, Opt. Commun. 391, 94–99 (2017)], the generation and propagation of such a non-diffractive beam were studied in a scattering medium of colloidal suspension (diluted milk) up to the concentration of 1.2% using cell lengths between 10 and 30 cm. The transformation from an annular beam to a non-diffractive beam was observed using a detector with a narrow view angle of 5.5 mrad. In the present study, experimental results are reported for much higher concentrations using shorter cell lengths of 3 and 5 cm. It is found that a nondiffractive beam is generated as a central peak superposed on widely distributed intensity due to multiple scattering. The polarization property is preserved during the transformation from annular ring to central peak. At the propagation distance of 3 cm, the intensity of non-diffractive beam is maximized with a high media concentration of 22.0% which yields the scattering coefficient of 5 cm−1. Furthermore, it is found that the media concentration range that leads to the generation of the non-diffractive beam becomes wider for such shorter propagation distances.
1. Introduction Non-invasive and non-contact sensing technologies such as optical topography [1], optical coherence tomography (OCT) [2,3], and light detection and ranging (LIDAR) [4,5] are widely used in the fields of medical imaging [6,7], industry [8,9] and remote sensing [10,11]. These optical techniques have the advantages of providing high resolution data with low risk owing to the use of visible light rather than X-ray or ultrasound. In a highly dispersive media such as human tissue, the spread of a light beam occurs due to the influence of various optical processes including diffraction and scattering, leading to a finite length of the light propagation distance. As a result, the optical information available from a bulk sample of such random media is usually limited only to nearsurface portions [12–16]. Although near-infrared light exhibits relatively high transmittance when applied to the imaging of human tissue [17], its penetration depth is only a few millimeters from the skin surface [18]. In the case of cloud observation in optical remote sensing, light penetration is permitted only in the range of low optical depth [19]. Thus, it is desirable to improve light propagation distances in order to sense deeper portions of random media for studying media conditions such as uniformness and
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Corresponding author. E-mail address: [email protected] (A. Xiafukaiti).
https://doi.org/10.1016/j.ijleo.2019.163628 Received 29 July 2019; Accepted 13 October 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 202 (2020) 163628
A. Xiafukaiti, et al.
density variation. A non-diffractive beam was first proposed by Durnin et al. in 1978 [20,21] as a light beam having a transverse intensity distribution that can be modeled using a Bessel function. The beam profile remains unchanged even if it propagates over a long distance. In biological tissue characterization and laser scanning microscopy, for instance, an optical needle spot with an extended depth of field (DOF) has been used to simultaneously enhance the transverse resolution and significantly extend the field of view (FOV) [22–24]. Also, the self-reconstruction property of non-diffractive beams has been the focus of several scientific studies [25–27]. Propagation stability is ensured through the reconstruction of initial intensity distribution even when the beam encounters an obstacle. In optical sensing, the generation of a non-diffractive beam has been proposed by using an axicon prism and diffractive elements and other methods [28–31]. As such, the self-transform property of an annular beam has been recognized as one of the methods to generate non-diffractive beams [32,33] as manifested in the application to a micro-pulse lidar system [34]. It has been proven that as compared with a Gaussian beam, the propagation of an annular beam is more stable in a highly turbulent atmosphere [35]. In our previous study, a laboratory-based experiment was designed using an annular beam transmitted through a dense random media [36]. To realize a random media, we employed diluted milk with varying concentrations. Non-diffractive beams were successfully generated when the annular beam (40 mm diameter) propagated over a distance between 10 and 30 cm in the random media with 0.3–1.2% milk concentration [36]. Although these concentrations were much lower than those seen in human tissue or nimbostratus clouds, generation of non-diffractive beams was observed [37,38]. It was found that for increased media concentrations, shorter interaction lengths were required. The origin of these non-diffractive beams was considered to be the forward-scattering light that was generated when the annular beam propagated through the media. As an extension of these previous works, the present paper has the following two purposes. First, we study the property of non-diffractive beams when the random media has much higher concentrations close to the human tissue. When diluted with water at the concentration of about 30%, the milk suspension exhibits a scattering coefficient similar to that of human tissue [39]. Second, we examine the conditions of non-diffractive beam formation by varying the media concentration and interaction distance. Finally, we discuss how such a property can further be applied to optical sensing. 2. Experimental setup 2.1. Annular beam generation and optical cells Fig. 1(a) shows the experimental setup utilized for generating the annular beam. A diode-pumped, solid-state (DPSS) pulse laser (CryLas, FDSS532-Q1) produces laser pulses of 532 nm wavelength, with 4.6 kW peak power, 2 ns pulse width, and 10 kHz pulse repetition rate. A glass plate placed in front of the DPSS laser reflects part of the light toward a photodiode (PD), from which the trigger signal is obtained. Then, the laser intensity is adjusted by means of a neutral-density (ND) filter and a spatial filter, and a pair of Axicon prisms transforms the Gaussian beam to an annular beam. Each of the prisms has a diameter of 50.8 mm and an apex angle of 150°. The resulting annular beam has the same polarization as the incident Gaussian beam. The diameter of the annular beam can be changed by adjusting the distance between the two prisms. Typically, a shift of distance of 1 mm leads to the change in the annular beam diameter of 0.241 mm. The results described in the present paper are from the experiments in which the distance between the two axicon prisms was fixed at 170 mm, resulting in the annular ring diameter of 40 mm and ring width of 3 mm. As shown in Fig. 1(b), two short optical cells with thickness of 3 and 5 cm are used for evaluating the propagation property of the annular beam. In addition, longer cells with 10, 20, and 30 cm lengths are also used to study the conditions for generating the non-diffractive beams. 2.2. Optical property of random media Here, the suspension of particles with diameters of the order of 1 μm is employed to realize the random media that shows highly scattering property. In this study, processed milk (with milk fat 1.8% and casein 2.4%) is diluted with pure water to produce random media with various concentrations (0.1–30 %). Major scattering particles are milk fat and casein, though the scattering caused by fat particles is dominant. The absorption effect can be neglected because of the small absorption coefficient, e.g., 0.0066 cm−1 at 40% concentration [40]. Fig. 2 shows the scattering intensity distributions simulated using Mie scattering theory when the average particle sizes of milk fat and casein are assumed to be 1.0 and 0.1 μm, respectively. Each graph is normalized and represented in logarithmic scale. The scattering intensity is proportional to both the scattering cross-section and particle concentration. As indicated in this simulation result, the scattered light intensity of the fat particle is mostly in the forward direction with an anisotropic parameter, g, of 0.936. The casein particles, on the other hand, exhibit almost symmetric scattering in the forward and backward directions with a value of g close to zero, due to their smaller diameter (∼150 nm) [41]. Because of differences in size and scattering anisotropy, the contribution to the forward scattering by casein is sufficiently small as compared with that of milk fat. From the Brownian motion experiment conducted on the present sample, we have found that the average particle size of milk fat is around 1.1 μm (Fig. 3). 2.3. Detection system Because of the relatively high concentration employed in the present experiment, the incident laser beam is scattered in every direction from the optical cell, as indicated in Fig. 1(b). In order to detect only the forward scattering light, we employ a specially 2
Optik - International Journal for Light and Electron Optics 202 (2020) 163628
A. Xiafukaiti, et al.
Fig. 1. Experiment setup. (a) A pair of axicon prisms are used for the generation of annular beams; (b) pictures of optical cells with thickness of 3 and 5 cm illuminated by the annular beam of 40 mm diameter.
designed receiver unit, which consists of a lens with the focal length of 4.5 mm coupled to a multimode optical fiber with the core diameter of 50 μm. As a result, a narrow FOV angle of 5.5 mrad is attained. By moving this detector in a plane perpendicular to the laser beam transmission, the intensity distribution is measured across the diameter of the beam. The annular beam of p- or spolarization is transmitted through the random media, and the scattered light intensities of both p- and s-polarization are detected by placing a polarizing plate before the receiver unit. A photomultiplier tube (PMT, Hamamatsu, R-636) is used to detect weak signals. A high-speed sampling oscilloscope (Agilent, DCA-J 86100C, with a maximum sampling rate of 50 GHz) is used to record the signals. 3. Results and discussion 3.1. Generation of non-diffractive beam in high concentration random media Fig. 4 shows the intensity distribution of the forward scattering beam observed for (a) 5 cm and (b) 3 cm cells. Each curve is normalized at the position of 20 mm from the optical axis, corresponding to the size of the incident annular beam. In both Figs. 4(a) and (b), small peaks appear at the center with a diameter of around 6 mm for the highest concentrations of (a) 5.0% and (b) 22.0%, respectively. Although the intensity becomes much smaller, similar peak structures are seen also for the cases of reduced concentrations. As explained below, these central peaks are found to be non-diffractive beams resulting from the constructive 3
Optik - International Journal for Light and Electron Optics 202 (2020) 163628
A. Xiafukaiti, et al.
Fig. 2. Scattering intensity distributions (in logarithmic scale) of milk fat (left) and casein (right).
Fig. 3. Particle size distribution of processed milk.
interference of beams scattered in the forward direction. The broad signals below these narrow peaks, on the other hand, are ascribed to the multiple scattering. The high concentration of 22.0% yields the scattering coefficient of 5 cm−1, which is nearly equivalent to the value seen for human tissue. For concentrations beyond such an optimum value, the peak intensity decreases whereas the broad signal increases, as seen in both Fig. 4(a) and (b). The non-diffractive property of the central peak has been verified by measuring the intensity distribution after the cell. Fig. 5(a) and (b) shows the results observed for the 5 and 3 cm cells with 5.0% and 22.0% media concentration, respectively. The intensity distribution curves are those observed at stand-off distances of 0 (i.e., just behind the cell wall), 30, and 50 cm away from the cell. As seen in these figures, both the intensity and width of the central peak are mostly preserved even after the propagation distance of 50 cm in the air. After leaving the cell, the central part of the forward scattering light is propagated in a non-diffractive way, while the surrounding part due to multiple scattering showing divergent behavior. Fig. 6 shows the results of experiment in which the s-polarized annular beam is propagated in the random media with the milk concentration of 1.0%. Since originally the annular beam is p-polarized, the s-polarized incident beam is produced using a halfwavelength plate placed before the optical cell. Also, a polarizer is placed behind the cell to choose the detected polarization. From Fig. 6, it is apparent that the central peak is observed only for s-polarization, while for p-polarization, only the broad signal appears. This result is consistent with our previous results indicating that the non-diffractive beam is generated with the same polarization as the incident beam (p-polarization in the previous experiment) [38]. Usually, the light will not retain its polarization when multiple scattering is dominant in random media. In our experiment, however, the central peak is observed under appropriate conditions regarding the interaction length (i.e., cell length) and scattering property (media concentration), as manifested in Fig. 4. One of the important factors that make it possible to observe the central peak is the limited view angle (5.5 mrad) of the receiver. This ensures the observation of only the forward scattering beam after the media cell. Another factor is the number of scattering events that an injected photon experiences before forming the central peak. For example, a calculation based on the diffusion equation indicates that two to seven scattering events can take place in the optimal case of 5 cm cell length with 5.0% media concentration (Fig. 4(a)). Under this condition, the transport mean free path is about 0.7–2 cm. Too few events are considered 4
Optik - International Journal for Light and Electron Optics 202 (2020) 163628
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Fig. 4. Observed intensity distributions when the annular beam of 40 mm diameter is propagated in a column of colloidal suspension with the length of (a) 5 cm and (b) 3 cm. The dash-dotted lines indicate the range ( ± 3 mm around the center) that is used to distinguish the central peak from the broad signal.
Fig. 5. Intensity distributions observed at 0 (back of the cell), 30, and 50 cm positions downstream the cell: (a) 5 cm cell with the media concentration of 5.0% and (b) 3 cm cell with that of 22.0%. Note that in these graphs, the normalization at ± 20 mm is applied only to the 0 cm case so that the preservation of the central peak is seen clearly.
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Optik - International Journal for Light and Electron Optics 202 (2020) 163628
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Fig. 6. Signal shapes observed when the s- and p-polarized annular beams are propagated through the cell with concentration of 1.0%. It is noted that the central peak appears only for the s-polarization.
insufficient for the formation of the central beam starting from the annular beam having the diameter of 40 mm. Too many events, on the other hand, would hinder the propagation of the central peak generated inside the media. Also, the result shown in Fig. 6 indicates that only the forward scattering beam can retain its polarization after being scattered in the random media several times. This can be attributed presumably to the destructive interference among the s-polarized components. For evaluating the intensity of the central peak, we define the center intensity ratio, ri, as
Vp ri = ⎛ − 1⎞ × 100%, ⎝ Vs ⎠ ⎜
⎟
(1)
where Vp is the normalized intensity at the peak position and Vs is the average intensity at the position of ± 3 mm [36]. For example, for the case of 5.0% media concentration in Fig. 4(a), we have Vp = 1.166 and Vs = 1.142, resulting in the value of ri = 2.1%. As the media concentration, c, decreases (4.0%, 3.0%, and 2.0%), the value of ri also decreases (0.8%, 0.7%, and 0.5%, respectively). At the concentrations of c = 4.0% and 3.0%, side peaks (i.e., small rings) with smaller intensities appear, though such multiple-peak structure is not noticeable at c = 5.0%. At the smallest concentration of 2.0%, only a small central peak can be recognized above the broad signal. When the concentration is increased beyond 6.0%, only the broad signal appears, with no indication of the central peak. Fig. 4(b) shows the results observed with the propagation distance of 3 cm. In this case, it has been found that the central peak structure appears only when the media concentrations are higher than 16.0%. This suggests that for such a shorter propagation distance, the beams cannot effectively interfere to create non-diffractive beams in the forward direction unless the concentration becomes high. As a result, the highest central peak with ri = 2.4% is observed at a high media concentration of 22.0%. Fig. 7 shows how the cell length affects the media concentration at which the highest value of ri is observed. Additional experiments have been performed with longer cell lengths of 10, 20, and 30 cm to explore the relationship between media concentration and propagation distance. This result shows that the value of optimal media concentration sharply decreases with the propagation distance. This is ascribed to the fact that the forward scattering process is exponentially attenuated when the propagation distance becomes shorter. The present results shown in Figs. 4–7 are based on the experiments conducted with the input annular beam of 40 mm diameter. It is noted that by controlling the annular beam parameters such as the ring diameter and width, we can further manipulate the distance over which the non-diffractive beam can be generated. This feature is consistent with the present observation that the formation of the central peak is governed by the number of forward scattering events as the annular beam propagates through the highly scattering media.
Fig. 7. Influence of the propagation distance (cell length) on the optimum value of the media concentration at which the central peak (nondiffractive beam) is efficiently produced. 6
Optik - International Journal for Light and Electron Optics 202 (2020) 163628
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Fig. 8. Variation of the maximum center intensity ratio (ri) observed for different cell lengths between 3 and 30 cm. The horizontal axis is the media concentration. The curves indicate the ranges within which the generation of the central peak (non-diffractive beam) is observed. Each dot indicates the point at which the maximum value of ri is observed.
3.2. Variation of the maximum center intensity ratio with cell lengths Fig. 8 shows the variation of the maximum center intensity ratio (ri) with different concentrations when the propagation distance, L, is changed from 3 to 30 cm. The concentration at the peak intensity, cp, increases from 0.4% to 22% as the cell length decreases from L = 30 cm to 3 cm. For each propagation distance, the generation of non-diffracting beam is observed only within the region indicated by the dots. For the shortest propagation distance of 3 cm, the highest value of ri = 2.4% is observed, which is approximately 2.5 times higher than the value observed for L = 30 cm. This enhancement of the central peak intensity is ascribed to the stronger forward scattering in the random media having a higher concentration. For the regime of relatively longer propagation lengths (30, 20, and 10 cm), the increase in the value of maximum ri (0.8% to 1.8%) with the increase in media concentration (0.4% to 1.0%) is significant. For the regime with shorter propagation lengths (10, 5, and 3 cm), on the other hand, the increase in ri (1.8% to 2.4%) with the increase in the concentration (1.0% to 22.0%) is more limited. The change in the two regimes at the cell length of 10 cm (and hence, the concentration of 1.0%), is presumably explained by the more significant increase in multiple scattering for higher concentration. A simple extension of this result to near 100% media concentration range suggests the highest center intensity ratio of around 2.7%. Moreover, the concentration range, Δc, corresponding to the generation of non-diffractive beam for L = 3 cm (Δc = 7.0%) is approximately 14 times wider than that of L = 30 cm (Δc = 0.5%). It is noted that when Δc is normalized with cp, the value of Δc/cp is higher (Δc/cp = 1.25) for L = 30 cm than for L = 3 cm (Δc/cp = 0.32). 3.3. Relation between the media concentration ranges and beam transmittance Fig. 9 shows the observed relation between media concentration, c, and beam transmittance, Tb. The value of Tb is obtained from the transmittance experiment using the current detector system with a narrow FOV of 5.5 mrad. When the concentration is 0% (pure water), the measured transmittance is unity (100%). The transmittance linearly decreases in logscale until a certain value of media concentration, and afterwards, it decreases at a smaller rate with increasing concentration. In the region below the curve shown with (a) green solid line and above (c) blue solid line, the central peaks (non-diffractive beams) are generated. The red line indicates the curve representing the highest values of the center intensity ratio, ri. In the case of longer propagation distance (L > 10 cm), the nondiffractive beam is generated in the region of lower transmittance that changes drastically with concentration. For propagation distances shorter than 10 cm, on the other hand, the non-diffractive beam is generated in the region of relatively higher transmittance, which changes relatively slowly with the concentration. This is the reason why for shorter propagation distances such as 3 and 5 cm, the generation of non-diffractive beam is seen in a wider concentration range. Moreover, the range of transmittance between the curves (a) and (b) is mostly constant regardless of the value of media concentration. This indicates that the generation condition
Fig. 9. Relationship between the optical thickness (logarithm of beam transmittance) and media concentration, showing the generating range of non-diffractive beam. The area between curves (a) and (c) is the region where the non-diffractive beam can be generated, while curve (b) indicates the conditions at which the maximum intensity of non-diffractive beam is observed. 7
Optik - International Journal for Light and Electron Optics 202 (2020) 163628
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of the non-diffractive beam does not depend critically on the media concentration. 4. Conclusion We have described the generation of non-diffractive beams at media concentrations of 5.0% and 22.0%, much higher values as compared with our previous studies (up to ∼1.2%). The experimental results have shown that the central peak is generated when the annular beam interacts with the random media. The non-diffractive nature of the central peak has been confirmed by observing the beam propagation after leaving the cell. Also, the polarization of the incident annular beam is preserved for the central peak. In the present experiment, optical cells with shorter propagation distances (5 and 3 cm) have been employed. As a result, in comparison with the intensity of the broader signal due to multiple scattering, the values of center-peak intensity ratio, ri, of 2.1% and 2.4% are observed, respectively. At the shortest cell length of 3 cm, the media concentration that corresponds to the maximum value of ri is 22.0%. This high concentration of c = 22.0% yields the scattering coefficient of 5 cm−1, which is nearly equivalent to the value seen for human tissue. Experiments with different cell length of 3–30 cm have shown that the center-peak intensity ratio becomes higher for shorter distances due to the increase in the forward scattering intensity with higher media concentrations. Also, it has been found that the media concentration range that leads to the generation of the non-diffractive beam becomes wider at shorter propagation distances. The present results are based on the experiments using an annular beam with a ring diameter of 40 mm and ring width of 3 mm. By changing these ring parameters, further manipulation of the generation of non-diffractive beams becomes feasible. Such a capability will be exploited in a future work for controlling the generation and propagation of non-diffractive beams through different random media, and can be applied to various optical sensing purposes as a probe for testing the media concentration in medical field (human tissue pathology examination) and remote sensing (cloud and fog studies). Acknowledgements The authors wish to thank the Frontier Science Program of Chiba university and the ASAHI Glass Foundation, Japan for their financial supports. References [1] A. Maki, Y. Yamashita, Y. Ito, E. Watanabe, Y. Mayanagi, H. Koizumi, Spatial and temporal analysis of human motor activity using noninvasive NIR topography, Med. Phys. 22 (1995) 1997–2005, https://doi.org/10.1118/1.597496. [2] D. Huang, E.A. Swanson, C.P. Lin, J.S. Schuman, W.G. Stinson, W. Chang, M.R. Hee, T. Flotte, K. Gregory, C.A. Puliafito, J.G. Fujimoto, Optical coherence tomography, Science 254 (1991) 1178–1181, https://doi.org/10.1126/science.1957169. [3] A.F. Fercher, Optical coherence tomography, J. Biomed. Opt. 1 (1996) 157–173, https://doi.org/10.1117/12.231361. [4] R.T.H. Collis, Lidar: A new atmospheric probe, Q. J. R. Meteorol. Soc. 92 (1966) 220–230, https://doi.org/10.1002/qj.49709239205. [5] R.T.H. Collis, Lidar, Appl. Opt. 9 (1970) 1782–1788, https://doi.org/10.1364/AO.9.001782. [6] J.G. Fujimoto, M.E. Brezinski, G.J. Tearney, S.A. Boppart, B. Bouma, M.R. Hee, J.F. Southern, E.A. Swanson, Optical biopsy and imaging using optical coherence tomography, Nat. Med. 1 (1995) 970–972, https://doi.org/10.1038/nm0995-970. [7] H. Koizumi, T. Yamamoto, A. Maki, Y. Yamashita, H. Sato, H. Kawaguchi, N. Ichikawa, Optical topography: practical problems and new applications, Appl. Opt. 42 (2003) 3054–3062, https://doi.org/10.1364/AO.42.003054. [8] B. Bouma, G.J. Tearney, S.A. Boppart, M.R. Hee, M.E. Brezinski, J.G. Fujimoto, High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source, Opt. Lett. 20 (1995) 1486–1488, https://doi.org/10.1364/OL.20.001486. [9] X.C. De Lega, P. De Groot, Optical topography measurement of patterned wafers, AIP Conference Proceedings vol. 788, (2005), pp. 432–436, https://doi.org/10. 1063/1.2062999. [10] M.A. Lefsky, W.B. Cohen, G.G. Parker, D.J. Harding, Lidar remote sensing for ecosystem studies, Bioscience 52 (2002) 19–30, https://doi.org/10.1641/00063568(2002)052[0019:LRSFES]2.0.CO;2. [11] K. Lim, P. Treitz, M. Wulder, B. St-Onge, M. Flood, LiDAR remote sensing of forest structure, Prog. Phys. Geogr. 27 (2003) 88–106, https://doi.org/10.1191/ 0309133303pp360ra. [12] A. Ishimaru, Diffusion of light in turbid material, Appl. Opt. 28 (1989) 2210–2215, https://doi.org/10.1364/AO.28.002210. [13] D.J. Durian, D.A. Weitz, D.J. Pine, Multiple light-scattering probes of foam structure and dynamics, Science 252 (1991) 686–688, https://doi.org/10.1126/ science.252.5006.686. [14] A.N. Bogaturov, A.A.D. Canas, J.C. Dainty, A.S. Gurvich, V.A. Myakinin, C.J. Solomon, N.J. Wooder, Observation of the enhancement of coherence by backscattering through turbulence, Opt. Commun. 87 (1992) 1–4, https://doi.org/10.1016/0030-4018(92)90030-U. [15] E. Gershnik, E.N. Riba, Light propagation through multilayer atmospheric turbulence, Opt. Commun. 142 (1997) 99–105, https://doi.org/10.1117/12.281332. [16] W. Gao, Changes of polarization of light beams on propagation through tissue, Opt. Commun. 260 (2006) 749–754, https://doi.org/10.1016/j.optcom.2005.10. 064. [17] T. Vo-Dinh, Biomedical Photonics Handbook, 2nd ed., CRC Press, Boca Raton, 2014. [18] G.V.G. Baranoski, A. Krishnaswamy, Light and Skin Interactions: Simulations for Computer Graphics Applications, Morgan Kaufmann, 1st ed., Morgan Kaufmann, Burlington, 2010. [19] E.P. Zege, I.L. Katsev, I.N. Polonsky, Analytical solution to LIDAR return signals from clouds with regard to multiple scattering, Appl. Opt. 60 (1995) 345–353, https://doi.org/10.1007/BF01082270. [20] J. Durnin, J.J. Miceli Jr., J.H. Eberly, Diffraction-free beams, Phys. Rev. Lett. 58 (1987) 1499–1501, https://doi.org/10.1103/PhysRevLett.58.1499. [21] J. Durnin, Exact solutions for nondiffracting beams. I. The scalar theory, J. Opt. Soc. Am. A 4 (1987) 651–654, https://doi.org/10.1364/JOSAA.4.000651. [22] C.J.R. Sheppard, T. Wilson, Depth of field in scanning microscope, Opt. Lett. 3 (1978) 115–117, https://doi.org/10.1364/OL.3.000115. [23] J.-Y. Lu, J.F. Greenleaf, Ultrasonic nondiffracting transducer for medical imaging, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 37 (1990) 438–447, https://doi.org/10.1109/58.105250. [24] Z. Ding, H. Ren, Y. Zhao, J.S. Nelson, Z. Chen, High-resolution optical coherence tomography over a large depth range with an axicon lens, Opt. Lett. 27 (2002) 243–245, https://doi.org/10.1364/OL.27.000243. [25] Z. Bouchal, J. Wagner, M. Chlup, Self-reconstruction of a distorted nondiffracting beam, Opt. Commun. 151 (1998) 207–211, https://doi.org/10.1016/S00304018(98)00085-6. [26] S.H. Tao, X.C. Yuan, Self-reconstruction property of fractional Bessel beams, J. Opt. Soc. Am. A 21 (2004) 1192–1197, https://doi.org/10.1364/JOSAA.21. 001192.
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[27] F.O. Fahrbach, P. Simon, A. Rohrbach, Microscopy with self-reconstructing beams, Nat. Photonics 4 (2010) 780–785, https://doi.org/10.1038/nphoton.2010. 204. [28] J. Arlt, K. Dholakia, Generation of high-order Bessel beams by use of an axicon, Opt. Commun. 177 (2000) 297–301, https://doi.org/10.1016/S0030-4018(00) 00572-1. [29] W.-X. Cong, N.-X. Chen, B.-Y. Gu, Generation of nondiffracting beams by diffractive phase elements, J. Opt. Soc. Am. A 15 (1998) 2362–2364, https://doi.org/ 10.1364/JOSAA.15.002362. [30] T. Aruga, Generation of long-range nondiffracting narrow light beams, Appl. Opt. 36 (1997), https://doi.org/10.1364/AO.36.003762 3762-2768. [31] S.K. Tiwari, S.R. Mishra, S.P. Ram, H.S. Rawat, Generation of a Bessel beam of variable spot size, Appl. Opt. 51 (2012) 3718–3725, https://doi.org/10.1364/AO. 51.003718. [32] H. Eyyuboglu, Y. Yenice, Y. Baykal, Higher order annular gaussian laser beam propagation in free space, Opt. Eng. 45 (2006) 038002, , https://doi.org/10.1117/ 1.2181991. [33] M. Duocastella, C.B. Arnold, Bessel and annular beams for materials processing, Laser Photonics Rev. 6 (2012) 607–621, https://doi.org/10.1002/lpor. 201100031. [34] T. Shiina, K. Yoshida, M. Ito, Y. Okamura, In-line type micropulse lidar with an annular beam: experiment, Appl. Opt. 44 (2005) 7407–7413, https://doi.org/10. 1364/AO.44.007407. [35] T. Shiina, K.Yoshida M. Ito, Y. Okamura, Long-range propagation of annular beam for lidar application, Opt. Commun. 279 (2007) 159–167, https://doi.org/10. 1016/j.optcom.2007.07.029. [36] Z. Peng, T. Shiina, Generation control of a non-diffractive beam in random media by adjusting concentration, Opt. Commun. 391 (2017) 94–99, https://doi.org/ 10.1016/j.optcom.2017.01.020. [37] T. Shiina, Non-diffractive beam in random media, Opt. Commun. 398 (2017) 12–17, https://doi.org/10.1016/j.optcom.2017.04.028. [38] Z. Peng, T. Shiina, Analysis of a non-diffractive beam generated from an annular beam in random media, Opt. Commun. 42 (2017) 349–354, https://doi.org/10. 1016/j.optcom.2017.06.034. [39] T. Shiina, Y. Tsuge, T. Honda, Examination of propagation process of annular beam in random media, Proceedings SPIE 6585, Optical Sensing Technology and Applications (2007) 658524, https://doi.org/10.1117/12.723167. [40] D.A. Boas, Diffuse Photon Probes of Structural and Dynamical Properties of Turbid Media: Theory and Biomedical Applications, Ph.D. Dissertation, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pa, 1996https://repository.upenn.edu/dissertations/AAI9636132. [41] Y. Hasegawa, Y. Yamada, M. Tamura, Y. Nomura, Monte Carlo simulation of light transmission through living tissues, Appl. Opt. 30 (1991) 4515–4520, https:// doi.org/10.1364/AO.30.004515.
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Original research article
Characteristics of non-diffractive beam generation related to concentration and propagation distance in highly random media
T
Alifu Xiafukaitia,*, Ziqi Pengb, Hiroaki Kuzea, Tatsuo Shiinac a b c
Center for Environmental Remote Sensing, Chiba University, 1-33 Yayoi-cho,Inage-ku,Chiba 263-8522, Japan Hunan University of Art and Science 3150, Dong Ting Road, Changde, 415500, PR China Graduate School of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
A R T IC LE I N F O
ABS TRA CT
Keywords: Annular beam Non-diffractive beam Light propagation Scattering Highly random media
Laser beam propagation in highly random media can potentially be applied to various optical studies, though the light penetration is often limited to the surface or skin regions of the targets. In free space, it is known that the use of a non-diffractive beam (Bessel beam) is useful for achieving a long-distance propagation by reducing the influence of diffraction. In our previous work [Z. Peng, and T. Shiina, Opt. Commun. 391, 94–99 (2017)], the generation and propagation of such a non-diffractive beam were studied in a scattering medium of colloidal suspension (diluted milk) up to the concentration of 1.2% using cell lengths between 10 and 30 cm. The transformation from an annular beam to a non-diffractive beam was observed using a detector with a narrow view angle of 5.5 mrad. In the present study, experimental results are reported for much higher concentrations using shorter cell lengths of 3 and 5 cm. It is found that a nondiffractive beam is generated as a central peak superposed on widely distributed intensity due to multiple scattering. The polarization property is preserved during the transformation from annular ring to central peak. At the propagation distance of 3 cm, the intensity of non-diffractive beam is maximized with a high media concentration of 22.0% which yields the scattering coefficient of 5 cm−1. Furthermore, it is found that the media concentration range that leads to the generation of the non-diffractive beam becomes wider for such shorter propagation distances.
1. Introduction Non-invasive and non-contact sensing technologies such as optical topography [1], optical coherence tomography (OCT) [2,3], and light detection and ranging (LIDAR) [4,5] are widely used in the fields of medical imaging [6,7], industry [8,9] and remote sensing [10,11]. These optical techniques have the advantages of providing high resolution data with low risk owing to the use of visible light rather than X-ray or ultrasound. In a highly dispersive media such as human tissue, the spread of a light beam occurs due to the influence of various optical processes including diffraction and scattering, leading to a finite length of the light propagation distance. As a result, the optical information available from a bulk sample of such random media is usually limited only to nearsurface portions [12–16]. Although near-infrared light exhibits relatively high transmittance when applied to the imaging of human tissue [17], its penetration depth is only a few millimeters from the skin surface [18]. In the case of cloud observation in optical remote sensing, light penetration is permitted only in the range of low optical depth [19]. Thus, it is desirable to improve light propagation distances in order to sense deeper portions of random media for studying media conditions such as uniformness and
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Corresponding author. E-mail address: [email protected] (A. Xiafukaiti).
https://doi.org/10.1016/j.ijleo.2019.163628 Received 29 July 2019; Accepted 13 October 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 202 (2020) 163628
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density variation. A non-diffractive beam was first proposed by Durnin et al. in 1978 [20,21] as a light beam having a transverse intensity distribution that can be modeled using a Bessel function. The beam profile remains unchanged even if it propagates over a long distance. In biological tissue characterization and laser scanning microscopy, for instance, an optical needle spot with an extended depth of field (DOF) has been used to simultaneously enhance the transverse resolution and significantly extend the field of view (FOV) [22–24]. Also, the self-reconstruction property of non-diffractive beams has been the focus of several scientific studies [25–27]. Propagation stability is ensured through the reconstruction of initial intensity distribution even when the beam encounters an obstacle. In optical sensing, the generation of a non-diffractive beam has been proposed by using an axicon prism and diffractive elements and other methods [28–31]. As such, the self-transform property of an annular beam has been recognized as one of the methods to generate non-diffractive beams [32,33] as manifested in the application to a micro-pulse lidar system [34]. It has been proven that as compared with a Gaussian beam, the propagation of an annular beam is more stable in a highly turbulent atmosphere [35]. In our previous study, a laboratory-based experiment was designed using an annular beam transmitted through a dense random media [36]. To realize a random media, we employed diluted milk with varying concentrations. Non-diffractive beams were successfully generated when the annular beam (40 mm diameter) propagated over a distance between 10 and 30 cm in the random media with 0.3–1.2% milk concentration [36]. Although these concentrations were much lower than those seen in human tissue or nimbostratus clouds, generation of non-diffractive beams was observed [37,38]. It was found that for increased media concentrations, shorter interaction lengths were required. The origin of these non-diffractive beams was considered to be the forward-scattering light that was generated when the annular beam propagated through the media. As an extension of these previous works, the present paper has the following two purposes. First, we study the property of non-diffractive beams when the random media has much higher concentrations close to the human tissue. When diluted with water at the concentration of about 30%, the milk suspension exhibits a scattering coefficient similar to that of human tissue [39]. Second, we examine the conditions of non-diffractive beam formation by varying the media concentration and interaction distance. Finally, we discuss how such a property can further be applied to optical sensing. 2. Experimental setup 2.1. Annular beam generation and optical cells Fig. 1(a) shows the experimental setup utilized for generating the annular beam. A diode-pumped, solid-state (DPSS) pulse laser (CryLas, FDSS532-Q1) produces laser pulses of 532 nm wavelength, with 4.6 kW peak power, 2 ns pulse width, and 10 kHz pulse repetition rate. A glass plate placed in front of the DPSS laser reflects part of the light toward a photodiode (PD), from which the trigger signal is obtained. Then, the laser intensity is adjusted by means of a neutral-density (ND) filter and a spatial filter, and a pair of Axicon prisms transforms the Gaussian beam to an annular beam. Each of the prisms has a diameter of 50.8 mm and an apex angle of 150°. The resulting annular beam has the same polarization as the incident Gaussian beam. The diameter of the annular beam can be changed by adjusting the distance between the two prisms. Typically, a shift of distance of 1 mm leads to the change in the annular beam diameter of 0.241 mm. The results described in the present paper are from the experiments in which the distance between the two axicon prisms was fixed at 170 mm, resulting in the annular ring diameter of 40 mm and ring width of 3 mm. As shown in Fig. 1(b), two short optical cells with thickness of 3 and 5 cm are used for evaluating the propagation property of the annular beam. In addition, longer cells with 10, 20, and 30 cm lengths are also used to study the conditions for generating the non-diffractive beams. 2.2. Optical property of random media Here, the suspension of particles with diameters of the order of 1 μm is employed to realize the random media that shows highly scattering property. In this study, processed milk (with milk fat 1.8% and casein 2.4%) is diluted with pure water to produce random media with various concentrations (0.1–30 %). Major scattering particles are milk fat and casein, though the scattering caused by fat particles is dominant. The absorption effect can be neglected because of the small absorption coefficient, e.g., 0.0066 cm−1 at 40% concentration [40]. Fig. 2 shows the scattering intensity distributions simulated using Mie scattering theory when the average particle sizes of milk fat and casein are assumed to be 1.0 and 0.1 μm, respectively. Each graph is normalized and represented in logarithmic scale. The scattering intensity is proportional to both the scattering cross-section and particle concentration. As indicated in this simulation result, the scattered light intensity of the fat particle is mostly in the forward direction with an anisotropic parameter, g, of 0.936. The casein particles, on the other hand, exhibit almost symmetric scattering in the forward and backward directions with a value of g close to zero, due to their smaller diameter (∼150 nm) [41]. Because of differences in size and scattering anisotropy, the contribution to the forward scattering by casein is sufficiently small as compared with that of milk fat. From the Brownian motion experiment conducted on the present sample, we have found that the average particle size of milk fat is around 1.1 μm (Fig. 3). 2.3. Detection system Because of the relatively high concentration employed in the present experiment, the incident laser beam is scattered in every direction from the optical cell, as indicated in Fig. 1(b). In order to detect only the forward scattering light, we employ a specially 2
Optik - International Journal for Light and Electron Optics 202 (2020) 163628
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Fig. 1. Experiment setup. (a) A pair of axicon prisms are used for the generation of annular beams; (b) pictures of optical cells with thickness of 3 and 5 cm illuminated by the annular beam of 40 mm diameter.
designed receiver unit, which consists of a lens with the focal length of 4.5 mm coupled to a multimode optical fiber with the core diameter of 50 μm. As a result, a narrow FOV angle of 5.5 mrad is attained. By moving this detector in a plane perpendicular to the laser beam transmission, the intensity distribution is measured across the diameter of the beam. The annular beam of p- or spolarization is transmitted through the random media, and the scattered light intensities of both p- and s-polarization are detected by placing a polarizing plate before the receiver unit. A photomultiplier tube (PMT, Hamamatsu, R-636) is used to detect weak signals. A high-speed sampling oscilloscope (Agilent, DCA-J 86100C, with a maximum sampling rate of 50 GHz) is used to record the signals. 3. Results and discussion 3.1. Generation of non-diffractive beam in high concentration random media Fig. 4 shows the intensity distribution of the forward scattering beam observed for (a) 5 cm and (b) 3 cm cells. Each curve is normalized at the position of 20 mm from the optical axis, corresponding to the size of the incident annular beam. In both Figs. 4(a) and (b), small peaks appear at the center with a diameter of around 6 mm for the highest concentrations of (a) 5.0% and (b) 22.0%, respectively. Although the intensity becomes much smaller, similar peak structures are seen also for the cases of reduced concentrations. As explained below, these central peaks are found to be non-diffractive beams resulting from the constructive 3
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Fig. 2. Scattering intensity distributions (in logarithmic scale) of milk fat (left) and casein (right).
Fig. 3. Particle size distribution of processed milk.
interference of beams scattered in the forward direction. The broad signals below these narrow peaks, on the other hand, are ascribed to the multiple scattering. The high concentration of 22.0% yields the scattering coefficient of 5 cm−1, which is nearly equivalent to the value seen for human tissue. For concentrations beyond such an optimum value, the peak intensity decreases whereas the broad signal increases, as seen in both Fig. 4(a) and (b). The non-diffractive property of the central peak has been verified by measuring the intensity distribution after the cell. Fig. 5(a) and (b) shows the results observed for the 5 and 3 cm cells with 5.0% and 22.0% media concentration, respectively. The intensity distribution curves are those observed at stand-off distances of 0 (i.e., just behind the cell wall), 30, and 50 cm away from the cell. As seen in these figures, both the intensity and width of the central peak are mostly preserved even after the propagation distance of 50 cm in the air. After leaving the cell, the central part of the forward scattering light is propagated in a non-diffractive way, while the surrounding part due to multiple scattering showing divergent behavior. Fig. 6 shows the results of experiment in which the s-polarized annular beam is propagated in the random media with the milk concentration of 1.0%. Since originally the annular beam is p-polarized, the s-polarized incident beam is produced using a halfwavelength plate placed before the optical cell. Also, a polarizer is placed behind the cell to choose the detected polarization. From Fig. 6, it is apparent that the central peak is observed only for s-polarization, while for p-polarization, only the broad signal appears. This result is consistent with our previous results indicating that the non-diffractive beam is generated with the same polarization as the incident beam (p-polarization in the previous experiment) [38]. Usually, the light will not retain its polarization when multiple scattering is dominant in random media. In our experiment, however, the central peak is observed under appropriate conditions regarding the interaction length (i.e., cell length) and scattering property (media concentration), as manifested in Fig. 4. One of the important factors that make it possible to observe the central peak is the limited view angle (5.5 mrad) of the receiver. This ensures the observation of only the forward scattering beam after the media cell. Another factor is the number of scattering events that an injected photon experiences before forming the central peak. For example, a calculation based on the diffusion equation indicates that two to seven scattering events can take place in the optimal case of 5 cm cell length with 5.0% media concentration (Fig. 4(a)). Under this condition, the transport mean free path is about 0.7–2 cm. Too few events are considered 4
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Fig. 4. Observed intensity distributions when the annular beam of 40 mm diameter is propagated in a column of colloidal suspension with the length of (a) 5 cm and (b) 3 cm. The dash-dotted lines indicate the range ( ± 3 mm around the center) that is used to distinguish the central peak from the broad signal.
Fig. 5. Intensity distributions observed at 0 (back of the cell), 30, and 50 cm positions downstream the cell: (a) 5 cm cell with the media concentration of 5.0% and (b) 3 cm cell with that of 22.0%. Note that in these graphs, the normalization at ± 20 mm is applied only to the 0 cm case so that the preservation of the central peak is seen clearly.
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Fig. 6. Signal shapes observed when the s- and p-polarized annular beams are propagated through the cell with concentration of 1.0%. It is noted that the central peak appears only for the s-polarization.
insufficient for the formation of the central beam starting from the annular beam having the diameter of 40 mm. Too many events, on the other hand, would hinder the propagation of the central peak generated inside the media. Also, the result shown in Fig. 6 indicates that only the forward scattering beam can retain its polarization after being scattered in the random media several times. This can be attributed presumably to the destructive interference among the s-polarized components. For evaluating the intensity of the central peak, we define the center intensity ratio, ri, as
Vp ri = ⎛ − 1⎞ × 100%, ⎝ Vs ⎠ ⎜
⎟
(1)
where Vp is the normalized intensity at the peak position and Vs is the average intensity at the position of ± 3 mm [36]. For example, for the case of 5.0% media concentration in Fig. 4(a), we have Vp = 1.166 and Vs = 1.142, resulting in the value of ri = 2.1%. As the media concentration, c, decreases (4.0%, 3.0%, and 2.0%), the value of ri also decreases (0.8%, 0.7%, and 0.5%, respectively). At the concentrations of c = 4.0% and 3.0%, side peaks (i.e., small rings) with smaller intensities appear, though such multiple-peak structure is not noticeable at c = 5.0%. At the smallest concentration of 2.0%, only a small central peak can be recognized above the broad signal. When the concentration is increased beyond 6.0%, only the broad signal appears, with no indication of the central peak. Fig. 4(b) shows the results observed with the propagation distance of 3 cm. In this case, it has been found that the central peak structure appears only when the media concentrations are higher than 16.0%. This suggests that for such a shorter propagation distance, the beams cannot effectively interfere to create non-diffractive beams in the forward direction unless the concentration becomes high. As a result, the highest central peak with ri = 2.4% is observed at a high media concentration of 22.0%. Fig. 7 shows how the cell length affects the media concentration at which the highest value of ri is observed. Additional experiments have been performed with longer cell lengths of 10, 20, and 30 cm to explore the relationship between media concentration and propagation distance. This result shows that the value of optimal media concentration sharply decreases with the propagation distance. This is ascribed to the fact that the forward scattering process is exponentially attenuated when the propagation distance becomes shorter. The present results shown in Figs. 4–7 are based on the experiments conducted with the input annular beam of 40 mm diameter. It is noted that by controlling the annular beam parameters such as the ring diameter and width, we can further manipulate the distance over which the non-diffractive beam can be generated. This feature is consistent with the present observation that the formation of the central peak is governed by the number of forward scattering events as the annular beam propagates through the highly scattering media.
Fig. 7. Influence of the propagation distance (cell length) on the optimum value of the media concentration at which the central peak (nondiffractive beam) is efficiently produced. 6
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Fig. 8. Variation of the maximum center intensity ratio (ri) observed for different cell lengths between 3 and 30 cm. The horizontal axis is the media concentration. The curves indicate the ranges within which the generation of the central peak (non-diffractive beam) is observed. Each dot indicates the point at which the maximum value of ri is observed.
3.2. Variation of the maximum center intensity ratio with cell lengths Fig. 8 shows the variation of the maximum center intensity ratio (ri) with different concentrations when the propagation distance, L, is changed from 3 to 30 cm. The concentration at the peak intensity, cp, increases from 0.4% to 22% as the cell length decreases from L = 30 cm to 3 cm. For each propagation distance, the generation of non-diffracting beam is observed only within the region indicated by the dots. For the shortest propagation distance of 3 cm, the highest value of ri = 2.4% is observed, which is approximately 2.5 times higher than the value observed for L = 30 cm. This enhancement of the central peak intensity is ascribed to the stronger forward scattering in the random media having a higher concentration. For the regime of relatively longer propagation lengths (30, 20, and 10 cm), the increase in the value of maximum ri (0.8% to 1.8%) with the increase in media concentration (0.4% to 1.0%) is significant. For the regime with shorter propagation lengths (10, 5, and 3 cm), on the other hand, the increase in ri (1.8% to 2.4%) with the increase in the concentration (1.0% to 22.0%) is more limited. The change in the two regimes at the cell length of 10 cm (and hence, the concentration of 1.0%), is presumably explained by the more significant increase in multiple scattering for higher concentration. A simple extension of this result to near 100% media concentration range suggests the highest center intensity ratio of around 2.7%. Moreover, the concentration range, Δc, corresponding to the generation of non-diffractive beam for L = 3 cm (Δc = 7.0%) is approximately 14 times wider than that of L = 30 cm (Δc = 0.5%). It is noted that when Δc is normalized with cp, the value of Δc/cp is higher (Δc/cp = 1.25) for L = 30 cm than for L = 3 cm (Δc/cp = 0.32). 3.3. Relation between the media concentration ranges and beam transmittance Fig. 9 shows the observed relation between media concentration, c, and beam transmittance, Tb. The value of Tb is obtained from the transmittance experiment using the current detector system with a narrow FOV of 5.5 mrad. When the concentration is 0% (pure water), the measured transmittance is unity (100%). The transmittance linearly decreases in logscale until a certain value of media concentration, and afterwards, it decreases at a smaller rate with increasing concentration. In the region below the curve shown with (a) green solid line and above (c) blue solid line, the central peaks (non-diffractive beams) are generated. The red line indicates the curve representing the highest values of the center intensity ratio, ri. In the case of longer propagation distance (L > 10 cm), the nondiffractive beam is generated in the region of lower transmittance that changes drastically with concentration. For propagation distances shorter than 10 cm, on the other hand, the non-diffractive beam is generated in the region of relatively higher transmittance, which changes relatively slowly with the concentration. This is the reason why for shorter propagation distances such as 3 and 5 cm, the generation of non-diffractive beam is seen in a wider concentration range. Moreover, the range of transmittance between the curves (a) and (b) is mostly constant regardless of the value of media concentration. This indicates that the generation condition
Fig. 9. Relationship between the optical thickness (logarithm of beam transmittance) and media concentration, showing the generating range of non-diffractive beam. The area between curves (a) and (c) is the region where the non-diffractive beam can be generated, while curve (b) indicates the conditions at which the maximum intensity of non-diffractive beam is observed. 7
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of the non-diffractive beam does not depend critically on the media concentration. 4. Conclusion We have described the generation of non-diffractive beams at media concentrations of 5.0% and 22.0%, much higher values as compared with our previous studies (up to ∼1.2%). The experimental results have shown that the central peak is generated when the annular beam interacts with the random media. The non-diffractive nature of the central peak has been confirmed by observing the beam propagation after leaving the cell. Also, the polarization of the incident annular beam is preserved for the central peak. In the present experiment, optical cells with shorter propagation distances (5 and 3 cm) have been employed. As a result, in comparison with the intensity of the broader signal due to multiple scattering, the values of center-peak intensity ratio, ri, of 2.1% and 2.4% are observed, respectively. At the shortest cell length of 3 cm, the media concentration that corresponds to the maximum value of ri is 22.0%. This high concentration of c = 22.0% yields the scattering coefficient of 5 cm−1, which is nearly equivalent to the value seen for human tissue. Experiments with different cell length of 3–30 cm have shown that the center-peak intensity ratio becomes higher for shorter distances due to the increase in the forward scattering intensity with higher media concentrations. Also, it has been found that the media concentration range that leads to the generation of the non-diffractive beam becomes wider at shorter propagation distances. The present results are based on the experiments using an annular beam with a ring diameter of 40 mm and ring width of 3 mm. By changing these ring parameters, further manipulation of the generation of non-diffractive beams becomes feasible. Such a capability will be exploited in a future work for controlling the generation and propagation of non-diffractive beams through different random media, and can be applied to various optical sensing purposes as a probe for testing the media concentration in medical field (human tissue pathology examination) and remote sensing (cloud and fog studies). Acknowledgements The authors wish to thank the Frontier Science Program of Chiba university and the ASAHI Glass Foundation, Japan for their financial supports. References [1] A. Maki, Y. Yamashita, Y. Ito, E. Watanabe, Y. Mayanagi, H. Koizumi, Spatial and temporal analysis of human motor activity using noninvasive NIR topography, Med. Phys. 22 (1995) 1997–2005, https://doi.org/10.1118/1.597496. [2] D. Huang, E.A. Swanson, C.P. Lin, J.S. Schuman, W.G. Stinson, W. Chang, M.R. Hee, T. Flotte, K. Gregory, C.A. Puliafito, J.G. Fujimoto, Optical coherence tomography, Science 254 (1991) 1178–1181, https://doi.org/10.1126/science.1957169. [3] A.F. Fercher, Optical coherence tomography, J. Biomed. Opt. 1 (1996) 157–173, https://doi.org/10.1117/12.231361. [4] R.T.H. Collis, Lidar: A new atmospheric probe, Q. J. R. Meteorol. Soc. 92 (1966) 220–230, https://doi.org/10.1002/qj.49709239205. [5] R.T.H. Collis, Lidar, Appl. Opt. 9 (1970) 1782–1788, https://doi.org/10.1364/AO.9.001782. [6] J.G. Fujimoto, M.E. Brezinski, G.J. Tearney, S.A. Boppart, B. Bouma, M.R. Hee, J.F. Southern, E.A. Swanson, Optical biopsy and imaging using optical coherence tomography, Nat. Med. 1 (1995) 970–972, https://doi.org/10.1038/nm0995-970. [7] H. Koizumi, T. Yamamoto, A. Maki, Y. Yamashita, H. Sato, H. Kawaguchi, N. Ichikawa, Optical topography: practical problems and new applications, Appl. Opt. 42 (2003) 3054–3062, https://doi.org/10.1364/AO.42.003054. [8] B. Bouma, G.J. Tearney, S.A. Boppart, M.R. Hee, M.E. Brezinski, J.G. Fujimoto, High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source, Opt. Lett. 20 (1995) 1486–1488, https://doi.org/10.1364/OL.20.001486. [9] X.C. De Lega, P. De Groot, Optical topography measurement of patterned wafers, AIP Conference Proceedings vol. 788, (2005), pp. 432–436, https://doi.org/10. 1063/1.2062999. [10] M.A. Lefsky, W.B. Cohen, G.G. Parker, D.J. Harding, Lidar remote sensing for ecosystem studies, Bioscience 52 (2002) 19–30, https://doi.org/10.1641/00063568(2002)052[0019:LRSFES]2.0.CO;2. [11] K. Lim, P. Treitz, M. Wulder, B. St-Onge, M. Flood, LiDAR remote sensing of forest structure, Prog. Phys. Geogr. 27 (2003) 88–106, https://doi.org/10.1191/ 0309133303pp360ra. [12] A. Ishimaru, Diffusion of light in turbid material, Appl. Opt. 28 (1989) 2210–2215, https://doi.org/10.1364/AO.28.002210. [13] D.J. Durian, D.A. Weitz, D.J. Pine, Multiple light-scattering probes of foam structure and dynamics, Science 252 (1991) 686–688, https://doi.org/10.1126/ science.252.5006.686. [14] A.N. Bogaturov, A.A.D. Canas, J.C. Dainty, A.S. Gurvich, V.A. Myakinin, C.J. Solomon, N.J. Wooder, Observation of the enhancement of coherence by backscattering through turbulence, Opt. Commun. 87 (1992) 1–4, https://doi.org/10.1016/0030-4018(92)90030-U. [15] E. Gershnik, E.N. Riba, Light propagation through multilayer atmospheric turbulence, Opt. Commun. 142 (1997) 99–105, https://doi.org/10.1117/12.281332. [16] W. Gao, Changes of polarization of light beams on propagation through tissue, Opt. Commun. 260 (2006) 749–754, https://doi.org/10.1016/j.optcom.2005.10. 064. [17] T. Vo-Dinh, Biomedical Photonics Handbook, 2nd ed., CRC Press, Boca Raton, 2014. [18] G.V.G. Baranoski, A. Krishnaswamy, Light and Skin Interactions: Simulations for Computer Graphics Applications, Morgan Kaufmann, 1st ed., Morgan Kaufmann, Burlington, 2010. [19] E.P. Zege, I.L. Katsev, I.N. Polonsky, Analytical solution to LIDAR return signals from clouds with regard to multiple scattering, Appl. Opt. 60 (1995) 345–353, https://doi.org/10.1007/BF01082270. [20] J. Durnin, J.J. Miceli Jr., J.H. Eberly, Diffraction-free beams, Phys. Rev. Lett. 58 (1987) 1499–1501, https://doi.org/10.1103/PhysRevLett.58.1499. [21] J. Durnin, Exact solutions for nondiffracting beams. I. The scalar theory, J. Opt. Soc. Am. A 4 (1987) 651–654, https://doi.org/10.1364/JOSAA.4.000651. [22] C.J.R. Sheppard, T. Wilson, Depth of field in scanning microscope, Opt. Lett. 3 (1978) 115–117, https://doi.org/10.1364/OL.3.000115. [23] J.-Y. Lu, J.F. Greenleaf, Ultrasonic nondiffracting transducer for medical imaging, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 37 (1990) 438–447, https://doi.org/10.1109/58.105250. [24] Z. Ding, H. Ren, Y. Zhao, J.S. Nelson, Z. Chen, High-resolution optical coherence tomography over a large depth range with an axicon lens, Opt. Lett. 27 (2002) 243–245, https://doi.org/10.1364/OL.27.000243. [25] Z. Bouchal, J. Wagner, M. Chlup, Self-reconstruction of a distorted nondiffracting beam, Opt. Commun. 151 (1998) 207–211, https://doi.org/10.1016/S00304018(98)00085-6. [26] S.H. Tao, X.C. Yuan, Self-reconstruction property of fractional Bessel beams, J. Opt. Soc. Am. A 21 (2004) 1192–1197, https://doi.org/10.1364/JOSAA.21. 001192.
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Optik - International Journal for Light and Electron Optics 202 (2020) 163628
A. Xiafukaiti, et al.
[27] F.O. Fahrbach, P. Simon, A. Rohrbach, Microscopy with self-reconstructing beams, Nat. Photonics 4 (2010) 780–785, https://doi.org/10.1038/nphoton.2010. 204. [28] J. Arlt, K. Dholakia, Generation of high-order Bessel beams by use of an axicon, Opt. Commun. 177 (2000) 297–301, https://doi.org/10.1016/S0030-4018(00) 00572-1. [29] W.-X. Cong, N.-X. Chen, B.-Y. Gu, Generation of nondiffracting beams by diffractive phase elements, J. Opt. Soc. Am. A 15 (1998) 2362–2364, https://doi.org/ 10.1364/JOSAA.15.002362. [30] T. Aruga, Generation of long-range nondiffracting narrow light beams, Appl. Opt. 36 (1997), https://doi.org/10.1364/AO.36.003762 3762-2768. [31] S.K. Tiwari, S.R. Mishra, S.P. Ram, H.S. Rawat, Generation of a Bessel beam of variable spot size, Appl. Opt. 51 (2012) 3718–3725, https://doi.org/10.1364/AO. 51.003718. [32] H. Eyyuboglu, Y. Yenice, Y. Baykal, Higher order annular gaussian laser beam propagation in free space, Opt. Eng. 45 (2006) 038002, , https://doi.org/10.1117/ 1.2181991. [33] M. Duocastella, C.B. Arnold, Bessel and annular beams for materials processing, Laser Photonics Rev. 6 (2012) 607–621, https://doi.org/10.1002/lpor. 201100031. [34] T. Shiina, K. Yoshida, M. Ito, Y. Okamura, In-line type micropulse lidar with an annular beam: experiment, Appl. Opt. 44 (2005) 7407–7413, https://doi.org/10. 1364/AO.44.007407. [35] T. Shiina, K.Yoshida M. Ito, Y. Okamura, Long-range propagation of annular beam for lidar application, Opt. Commun. 279 (2007) 159–167, https://doi.org/10. 1016/j.optcom.2007.07.029. [36] Z. Peng, T. Shiina, Generation control of a non-diffractive beam in random media by adjusting concentration, Opt. Commun. 391 (2017) 94–99, https://doi.org/ 10.1016/j.optcom.2017.01.020. [37] T. Shiina, Non-diffractive beam in random media, Opt. Commun. 398 (2017) 12–17, https://doi.org/10.1016/j.optcom.2017.04.028. [38] Z. Peng, T. Shiina, Analysis of a non-diffractive beam generated from an annular beam in random media, Opt. Commun. 42 (2017) 349–354, https://doi.org/10. 1016/j.optcom.2017.06.034. [39] T. Shiina, Y. Tsuge, T. Honda, Examination of propagation process of annular beam in random media, Proceedings SPIE 6585, Optical Sensing Technology and Applications (2007) 658524, https://doi.org/10.1117/12.723167. [40] D.A. Boas, Diffuse Photon Probes of Structural and Dynamical Properties of Turbid Media: Theory and Biomedical Applications, Ph.D. Dissertation, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pa, 1996https://repository.upenn.edu/dissertations/AAI9636132. [41] Y. Hasegawa, Y. Yamada, M. Tamura, Y. Nomura, Monte Carlo simulation of light transmission through living tissues, Appl. Opt. 30 (1991) 4515–4520, https:// doi.org/10.1364/AO.30.004515.
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