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Abstract
The average intensity, as well as the intensity-intensity correlation at one and two points of the He-Ne laser beam passing in the monostatic double-passage (21 meter long in single pass) atmospheric channel with a retro-reflector are measured experimentally. The non-classic turbulence is generated in two different ways: by means of a 1.8-meter long turbulent chamber with 3D distributed non-classic turbulence and a localized hot air jet-stream applied to the beam in a transverse direction. The Enhanced Back Scatterer (EBS) effects produced by the two types of turbulence are compared as turbulence is placed at various locations along the channel. The data reveals the spatial stability of the EBS intensity in the detected beam in both cases, while the whole beam centroid generally appears to be off-centered, due to deterministic and random temperature gradients. The strongest EBS effect was observed with the localized turbulence placed close to the retro-reflector. The studied situations may appear in urban/industrial/coastal atmosphere and are of importance for free-space optical communications with retro-modulation.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The phenomenon of spatial redistribution of the received energy in the double-passage atmospheric propagation links with plane mirrors or corner (retro-) reflectors [1] has been known for several decades [2–16]. This effect occurs only in the situations where the transmitter and the receiver are collocated (monostatic configuration) and vanishes if they are sufficiently separated (bistatic configuration). For the monostatic scenario with the retro-reflector the on-axis average intensity is larger compared with that in the bistatic case producing the Enhanced Back Scattering (EBS) effect. The monographs and review articles on this topic providing physical explanation of the effect and its mathematical treatment are widely available [17–22]. The experimental verification of the EBS effect belongs to numerous publications [23–28]. The computer simulations have also been performed by several groups in order to build the link between the theoretical and experimental campaigns [29–32]. In most of the aforementioned papers the statistics of turbulence were assumed to be homogeneous, isotropic and non-stationary (but with stationary increments), constituting the case of classic Kolmogorov turbulence.
However, in a number of practical situations the atmospheric channels can be of a non-classic nature, e.g. in the vicinity of the ground surface, where they are affected by the slowly-varying temperature gradients leading to the mirage-like effects [33–35], within the engine exhaust volumes with the well-pronounced direction of the air flow [36–43] or the Earth’s jet-stream with the stratification spanning several kilometers in the vertical direction and tens of kilometers in the horizontal direction [44–46]. The double-passage links embedded in the non-classic atmospheric channels have not been tackled so far and will be the target of this investigation. The renewed interest in the double-passage problems has recently emerged following the development of the Retro-Reflector Modulation (RRM) technology which prompted the use of monostatic channels for the enhanced information transfer from the reflector side to the transceiver side using the coherent mode around the optical axis, which is the direct cause of the EBS effect [47–57].
In this paper we investigate the effects of the type and the location of non-classic turbulence in the double-passage atmospheric channel with the length of 21 meters (in single pass). The very weak background ambient laboratory turbulence is modulated by the local strong turbulence in one of two ways: by means of a single heat gun blowing hot air in a direction transverse to the laser beam and by means of a 1.8-meter long turbulent chamber in which partially homogeneous and isotropic temperature, and hence, refractive index statistics are created (with a possibly constant temperature gradient). In both situations the turbulence in the channel is created effectively locally and, as we found, the location of turbulence (heat-gun or chamber) substantially affects the EBS effects. Additionally, we have observed the fundamental differences in the EBS statistics due to different turbulence regimes produced by heat guns and by the distributed turbulence chamber.
The paper is organized as follows: in Section 2 we discuss the experimental method for obtaining the EBS statistics in the turbulent channels with a retro-reflector; Sections 3 and 4 provide the EBS average intensities for the jet-stream turbulence and the 3D distributed (chamber) turbulence; Section 5 gives further comparative analysis of the two approaches in terms of the Second-Order Moment (SOM) of the fluctuating intensity at a single point and the NCF at two points, respectively, Section 6 gives characterizes the turbulent chamber, and Section 7 summarizes the results.
2. Experimental setup for measuring the EBS intensity
In our experiment, we utilized two different approaches to generate the localized turbulence along the double-pass optical channels, as shown in Fig. 1. The first approach involved a jet stream produced by a single heat gun (Porter Cable, 1500W), set to the highest temperature (1100ᴼF) and the highest fan speed setting. The second approach involved using a parallelepiped-like wooden chamber (15cm × 15cm × 180cm), wrapped in aluminum foil, having 9 holes drilled into one side. Either one or three heat guns were placed into the adjacent holes (the nearest to the retroreflector) and set to the same regime as mentioned above. For each measurement the heat guns were fired from the same side of the channel to ensure consistency.
Fig. 1 Schematic diagram of the experimental setup used for generation and measurement of the beam intensity statistics in the monostatic double-pass link. AP: Attenuation Plate; BE: Beam Expander; BS: Beam Splitter; NDF: Neutral Density Filter; SPI: Shear Plate Interferometer. The embedded plotted curve shows the average intensity captured by the CMOS camera at the cross-section which passed through the maximum intensity spot. The NDF and AP were used to guarantee the generated images were not saturated.
Figure 1 shows the schematic diagram of the double-passage link which can alternate between the two approaches described above to generate and capture the beam. All the distances used in the experiment are specified in the diagram. A He-Ne Laser (wavelength 632.8nm, 2mW) produced a 1mm (in radius) collimated beam which subsequently passed through an attenuation plate (continuously variable neutral density filter), a 15x beam expander and then a Beam Splitter (BS, 5cm side length, 50:50). The BS splits the beam into two branches, one passing through the optical channel (21m long in single pass), reflecting from the retro-reflector, and returning back along the same path. After passing through the BS again the returned beam was focused by a lens (focal length 50cm) into a CMOS camera (Thorlabs, Color, USB 3.0, pixel resolution 1280x1024). In each measurement the camera captured a 1000 image sequence with the frame rate of 6.55 FPS and the exposure time of 0.02 milliseconds.
To facilitate understanding of turbulence generated at different locations, we utilize the three-dimensional (3D) Cartesian coordinate system as shown in Fig. 1 in blue font. The sign “⊙” indicates that the + z axis is out of the page. During the experiment either the single heat gun or the chamber were placed at five locations marked by I, II, III, IV, and V separating the single optical path into four equal parts (5.25m each). Either the heat gun was simply placed at each location for the first approach or the end of the chamber nearest to the retroreflector was placed at the location for the second approach. To ensure that the beam was collimated well, the second half of the split beam was passed through a Shear Plate Interferometer (SPI, Thorlabs SI254), on which the interference pattern was tuned to be perpendicular to the beam axis by adjusting the beam collimation by the expander setting.
3. Turbulent jet-stream generated by single heat gun (no chamber)
Figure 2 shows the average intensities of the beam captured by the camera. The localized turbulence is comparable to a jet stream which is generated by using a single heat gun placed along the + x axis with exit at distance 15cm away from the beam. The bright spot of the recorded beam can be very well observed when the single heat gun is turned on close to the retroreflector (location I) and it is less pronounced when the heat gun is placed at location II. The EBS bright spot of the average intensity completely disappears when the heat gun is at locations III –V. It is also apparent that the location of the beam centroid in Fig. 2(a) is not consistent with the EBS bright spot location. Also, just like the average intensity in the double-pass optical channel with no turbulence, which is shown in Fig. 2(f), the average intensities captured by the camera with the heat gun at locations III and IV are vertically separated into two patterns, which can be observed in Figs. 2(c) and 2(d). Further, on comparing Figs. 2(e) with 2(f), we see that the average intensity for location V is much like the no-turbulence pattern. The deterioration of the EBS effect in Figs. 2(b)-2(e) compared with that in Fig. 2(a) can be attributed to the presence of substantial deterministic phase discrepancy between the incident and reflected beams. Such phase difference is due to free space diffraction of a finite beam. These are new phenomena which were not previously reported, to our knowledge. It is also apparent that while the bright EBS spot remains in the center of the camera the centroid shifts to the right and slightly up (Figs. 2(a) and 2(b)). This is the manifestation of the phase conjugation of the EBS implying that its location is determined by deterministic factors and is more robust than that of the centroid.
Fig. 2 Average intensity captured by the camera and calculated for the ensemble of 1000 frames. The localized turbulence was generated by one heat gun with no chamber. The heat gun was located at (a) I, (b) II, (c) III, (d) IV, (e) V, and (f) no heat gun was placed.
4. Non-classic turbulence generated in chamber with one or three heat guns
Figure 3 exhibits the average intensities of the reflected beam recorded by the camera. The chamber with turbulence produced by one heat gun is placed at three different distances from the retroreflector (locations I, II and III). The EBS bright spot only forms for location I. It is also observed that the recorded beam centroid is significantly shifted from the camera center for locations II and III (see Figs. 3 (b) and 3(c)). This is due to the fact that when the beam propagates through the turbulent chamber early in its double-pass path the phase tilt induced by the vertical temperature gradient in the chamber is stronger, resulting in a more distinct centroid shift from the camera center.
Fig. 3 Average intensities captured by the camera over 1000 frames. The localized turbulence was generated by using a chamber with one heat gun. The chamber is located at (a) I, (b) II, and (c) III.
In Fig. 4 we present the double-pass average intensities from the retroreflector, while the localized turbulence is produced by the chamber with heat flow produced by three heat guns placed in chamber openings adjacent to each other, as shown in Fig. 1. Compared with the single heat gun case shown in Fig. 3, using an increased number of heat guns has the effect of changing localized turbulence properties, including changing the temperature gradient, anisotropy, and structure constant of turbulence. Figure 4 exhibits a phenomenon which is very similar to that displayed in Fig. 3: by increasing the distance from the chamber to the retroreflector, the beam displays larger physical shift in the upward direction. In addition, Figs. 4(b) and 4(c) display a decreased degree of beam centroid shift when compared with Figs. 3(b) and 3(c). This is because, relative to the single heat gun case, three adjacent heat guns produce a smaller vertical temperature gradient. Specifically, the produced vertical temperature gradient further induces the upward-shifted beam pattern which is analogous to the mirage-image formation in presence of layered atmospheric turbulence [34, 35]. Such beam centroid shift effect is more obvious if we utilize single heat gun rather than three heat guns inserted in the chamber, as the temperature gradient formed in the former case is larger than that in the latter. The deflections of centroids of the beam patterns in Figs. 3 (a) and 3(b) are 0.46cm and 1.4cm, respectively. For comparison, the deflections in Figs. 4(a) and 4(b) are 0.17cm and 0.95cm, respectively. Compared with Figs. 3(a) and 3(b), we can conclude that the beam patterns in Figs. 4(a) and 4(b) experience less deflection when passing through the chamber, resulting in decreased beam shifts from the center of the camera. In Figs. 3(c) and 4(c) such effect cannot be distinctly assessed.
Fig. 4 Average intensities captured by the camera over 1000 frames. The localized turbulence was generated by using a chamber with three heat guns. The chamber is located at (a) I, (b) II, and (c) III.
5. Comparison of the results from the two types of turbulence
Figure 5 exhibits the EBS average intensity profiles captured at the vertical cross-section of the camera from the double-pass optical channel embedded in the four types of localized turbulence: (a) the chamber with one heat gun at location I, (b) the chamber with 3 heat guns at location I, (c) one heat gun with no chamber at location I, and (d) one heat gun with no chamber at location II. It is shown that the EBS intensities with bright spots can be generated for all these cases. The localized turbulence generated by using the chamber with three consecutive heat guns gives rise to the strongest EBS intensity peak in the central region as compared to other three cases. This may be due to the fact that the chamber prevents the loss of the heat flow produced by heat guns, and that three heat guns induce much stronger turbulence for the propagating laser beam than that in the other three cases. On the other hand, the chamber with three heat guns can produce more uniformly distributed temperature, as shown by Fig. 5(b). In addition, it is also interesting to note that the jet stream at position II, which is generated by using single heat gun (no chamber) is still capable to produce a bright spot in the centre of the EBS intensity, as shown by Fig. 5(d), although its maximum peak value is slightly smaller than those displayed in other three cases, as shown by Figs. 5(a)-5(c).
Fig. 5 Average intensities at vertical cross-section captured by the CCD camera over 1000 frames. The localized turbulence was generated by using either (a) single heat gun inside chamber at location I, (b) 3 heat guns inside chamber at location I, (c) single heat gun (no chamber) at location I, and (d) single heat gun (no chamber) at location II.
Figure 6 shows the normalized correlation functions (NCF) of the recorded beam for different types of localized turbulence (generated the same way as those used for Fig. 5). The calculation of the NCF was done in the following way: a pixel with the maximum average intensity was found and correlated to the average intensities at other pixels. Then the result was normalized (divided) to the self-correlation at the maximum average intensity pixel. Analytically the two-point NCF of the beam is defined as
where and are two points in the double-pass optical channel, the bracket denotes the ensemble average over the ensemble of realizations, the subscript represents the maximum value of the NCF. We generally observe that the NCF exhibits almost circular profiles for the turbulence cases when one and three heat guns were turned on inside the chamber. By comparison, the NCF in double-pass turbulence generated by the jet stream (one heat gun without chamber) has elliptical shape, implying that the produced jet stream induces strong turbulent anisotropy [58, 59], compare Figs. 6(c) and 6(d) with Figs. 6(a) and 6(b). Furthermore, the effective widths of the NCF distributions for the chamber turbulence cases are much larger than those in the jet stream cases (no chamber), compare Figs. 6(c) and 6(d) with Figs. 6(a) and 6(b). This implies that the strength of turbulence produced by a single heat gun in the absence of the chamber is much stronger. These conclusions are also applicable to the bright EBS spot.Fig. 6 NCF of the EBS intensity captured by the camera. The localized turbulence in (a)-(d) were generated in the same ways as that in Figs. 5(a)-5(d), respectively.
Figure 7 shows the SOM of the EBS intensity captured by the camera, analytically defined as
The localized turbulence generated for Figs. 7(a)-7(d) is the same as that for Figs. 5(a)-5(d). It is observed from the figure that the SOM further highlights the bright spot produced in the central region of the CCD camera. No matter what type of non-classic turbulence is generated in the double-pass propagation channel, the bright spot remains at the same position for all turbulence cases in Fig. 7. Moreover, if we compare Figs. 7(c) and 7(d) with Figs. 7(a) and 7(b), it can be concluded that the SOM from the turbulence channel generated by a jet stream is generally wider than that produced by using heat guns inside the chamber.Fig. 7 SOM of the EBS intensity captured by the camera. The localized turbulence in subplots (a)-(d) was generated in the same ways as that in Figs. 5(a)-5(d), respectuvely.
Thus, the NCF and the SOM shown in Figs. 6 and 7 provide a convenient approach for optical measurements of the turbulent features, such as its strength and anisotropy. They contain more refined information compared to that inferred from the average intensity.
6. Turbulent chamber characterization
To characterize the properties of the non-classical turbulence in our experiment quantitatively, we measure the second-order temperature structure functions at two points separated by a distance R [20]. For turbulence regime with non-Kolmogorov fluctuations and anisotropy, its temperature structure function takes form [60–63]
where is the generalized temperature structure parameter (with units K2·m3-α), is the structure parameter (with unit K2·m-2/3), β is the dimensional parameter (with units m11/3-α), and are the anisotropic coefficients in horizontal and vertical directions.In the case of the well-developed turbulence the structure function should obey the power-law dependence precisely and hence produce a line in a logarithmic scale. The structure parameter can be measured from the mean value of the squared difference of the temperature T1 and T2 at two positions separated by distance R
Furthermore, the structure constant of turbulence is related to the temperature structure constant by equation [60–63]
where p is pressure of normal air in millibar and T is average temperature in Kelvin. Using Eq. (4), we show in Fig. 8 the variations of the temperature structure functions of the turbulence with separation distances of the thermocouple sensors (Extech TM500). In all cases the structure functions do not exhibit linear dependence on separation distance and, hence, represent the non-classic turbulent regime. It also can be noticed that turbulence is more classic (lines in the log plot can be easily fitted) when it is measured farther away from the heat guns(s).Fig. 8 Temperature structure function of turbulence plotted against the separation distance measured with thermocouple sensors along horizontal and vertical directions of transverse chamber cross-sections, at different locations from the heat gun(s). The sensors are placed along the support frame with separation distances R = 1cm, 1.5cm, 2cm, 2cm, and 2.5cm.
Table 1 shows the structure constants and Rytov variances of different chamber turbulence in our experiment, which are computed using Eqs. (3)-(5) from the measured temperature data. It is observed that turbulence which is the closest to the heat gun(s) (60cm) is weaker compared with the one on the opposite side of the chamber. This happens since the hot chamber air at the chamber exit is being mixed with the room-temperature air more efficiently.
Table 1. Structure constants and Rytov variances of different chamber turbulence in experiment
7. Summary
We have carried out the laboratory experiments measuring the statistics of the EBS of the He-Ne laser beam in the double-passage channel with retro-reflector and the heat-induced atmospheric turbulence. Our data reveals that in both cases, when the turbulence is created by means of a highly directional hot-air flow or by an enclosed turbulence chamber the EBS effect largely depends on the location of the turbulence input, being the greatest at the position close to the retroreflector. Additionally, in both cases, the production of the temperature gradient has been shown to separate the EBS intensity from the beam centroid but in two different directions: the centroid moves up for the chamber case and in the direction of air flow from the heat-gun for the jet-like turbulence. The SOM of intensity at one position and the NCF at two positions reveal a more detailed structure of the EBS distributions, the later also showing anisotropic structure.
Funding
O. Korotkova and J. Li acknowledge the support from the Air Force Office of Scientific Research (AFOSR) (FA9550-121-0449).
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