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Abstract
Free-space optical communications (FSOC) is becoming an important option for both atmospheric and space-based high data rate networks. Long-range, mobile FSOC links in the former environments must mitigate the effects of turbulence if they are to provide reliable, high link availability under cloud-free atmospheric conditions. Adaptive optics (AO) has been proposed as one means of reducing link degradation in turbulence, but field validated AO performance models are few and not definitive. These models are important if credible FSOC high performance links are expected to be deployed using AO systems. This paper reviews the Strehl ratio for the Andrews AO model and provides comparisons between predicted AO-based FSOC link budgets and measured link performance derived from several field trials. These results suggest that AO systems perform well under weak turbulence or short range under 10 km, but only offer limited tip/tilt gain in moderate turbulence and no gain under high/saturation regime turbulence at longer ranges. Long range links close to the ground in high moderate turbulence may degrade AO performance further.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Free-space optical communications (FSOC) has the potential to provide the needed communications capacity and performance, but a practical FSOC system for high-throughput; long-range communications have not yet been fielded [1–7]. FSOC can provide multi-gigabit capacity per link, and high directionality provides extremely high spectrum reuse as well as low probability of detection, interception, and exploitation by adversaries in a contested area of operations. FSOC links, however, encounter extreme propagation effects that create rapidly-changing optical signal strength across a wide dynamic range at the receiver. That effect generates instability and has prevented FSOC systems from attaining the requisite link reliabilities, throughput, and ranges for the past five decades.
During last decade, atmospheric hybrid radio frequency (RF)/FSOC network systems have demonstrated error-free 10 gigabit per second (Gbps) FSOC performance at ranges up to 200 km when the refractive index structure parameter $C_n^2 \le {10^{ - 13}}\,{m^{ - {2/3}}}$ (∼85% turbulence level) [7]. The link used adaptive optics (AO), an optical automatic gain control (OAGC) and Reed-Solomon forward error correction (FEC) Code to achieve that performance. That demonstration showed good agreement between theory and measurement using the Rayleigh range concept. That concept proposed that AO systems perfectly corrected turbulence degradation the first 4.5 km of the link after the transmitter and the last 4.5 m of the link before the receiver. For ranges more than 9 km, the OAGC and FEC mitigated the remaining degradation induced by the remaining link range as best they could. When the turbulence was above the 85% percentile, network retransmission/rerouting was necessary to achieve error-free operation. Although the model worked, it did not provide any insights into how many Zernike modes were needed for the measured link gain as a function of the turbulence level and/or range.
This paper will describe the AO performance model proposed by one of the authors (LCA) and will compare its predictions with measured field data taken from several field experiments. These comparisons will suggest that AO systems perform well under weak turbulence conditions or short range under 10 km, but only will provide limited tip/tilt gain in moderate turbulence and long range, and no gain under high/saturation regime, long range turbulence. Long range links close to the ground in high moderate turbulence may degrade AO performance further.
2. Andrews AO model
For FSOC cross-links in space/extremely-high-altitude environments, the power at the receiver aperture is the propagated transmitter irradiance multiplied by the area of the receiver, or
For FSOC uplinks with the Earths’ atmosphere where turbulence can affect the received beam quality, the power at the detector is given by
AO systems are designed to reduce the severity of the atmospheric effects by reducing phase aberrations induced by the turbulence, attempting to create a received Point Spread Function (PSF) that optimally couples into a detector/focal plane element or erbium-doped fiber amplifier (ERDA) [12,13]. In general, an AO system design incorporates both tip/tilt (N = 3) and higher order (N > 3) deformable mirror corrections. The deformable mirror is driven by N actuators responding to the phase variations detected by a wavefront sensor. The sampling and correction bandwidth are designed to be well within the Greenwood time interval of the turbulence, which is a measure of how rapidly the atmosphere changes, to keep the deformable mirror operating at reasonable rate.
To get the AO theory to follow his Strehl ratio formalism, Andrews modified his original SR equation to account for AO gain. Specifically, he proposed the transmitter and receiver Strehl ratios be of the form [10]:
The first value of m represents the original Andrews SR for no AO. The second value of m for tip-tilt was based on removing tilt from the PSF and defining the resulting SR as the ratio of PSF in atmospheric turbulence with tip-tilt correction to that without tip-tilt in free space [9, p. 621]. The last two values of m were assumed equal to ${({1/N} )^{5/6}}$ with N = 16 and N = 35, respectively which comes from seeing what value function of N in Eq. (8) would follow Roddier’s maximum gain [10].
Table 1 compares predictions from Eq. (8) predictions for N = 3, 16 and 35 with measured Strehl ratio data taken on 27 August 2008 over a 10 km link between Saratoga and Campbell, CA [14]. Figure 1 shows AO-Corrected PSFs after turbulence degradation as compared to a Perfect PSF [15]. This data comes from 3.5 second time-averaged exposures using a focal-plane camera. The measured Strehl ratio values comes from the light intensity ratio of the point spread function maximum with turbulence to the point spread function maximum without turbulence, both derived using the same system. This data set contains AO performance measurements using tip/tilt only and 35-Zernike Component configurations. Fried Parameter measurements were taken at the receiver site in Campbell. Table 1 shows good agreement within a couple of dBs for all the measured data and analytical predictions.
Table 1. Comparison of Andrews Strehl Ratios to Measured Strehl Ratios
Tables 2 and 3 compare PIB and PIF predictions, respectively, for N = 3, 16 and 35 with measured data taken on 27 August 2008 over a 10 km link between Saratoga and Campbell, CA [14]. These tables show agreement within a few dBs for all the measured data and analytical predictions. However, like Table 1, the lower N = 16 predictions are closer to the measured Full AO data than the N = 35 predictions. This suggests that the AO system’s performance improvement comes predominantly from a smaller number of Zernike modes; therefore, further increasing the number of Zernike modes provides little to no improvement in performance. For the remainder of this paper, we will limit our analysis to N = 3 and N = 35 Strehl ratios but note that a lower N value may be more accurate.
Table 2. Comparison of PIB Predictions With Measured PIB Data
Table 3. Comparison of PIF Predictions With Measured PIF Data
3. PAX and NTTR field data comparison
In this section, we will compare the Andrews AO Model with the measured data from the ORCA field experiments given in [7] The first communications experiment was conducted at Patuxent River Naval Station (PAX) on 12 May 2009, during which air-to-ground tests of the hybrid RF/FSOC duplex links were performed. The PAX experiment was conducted with a ground station located at PAX (near sea level) and the BAC1-11 aircraft flying off the coast of Maryland. The next experiments were conducted at the Nevada Test and Training Range (NTTR) on 16–18 May 2009 [7,16,17]. The NTTR testing was conducted with a ground station located at Antelope Peak at an altitude of 7540 ft. MSL and the BAC1-11 flying to the southeast.
Figure 2 shows the refractive index structure parameter $C_n^2$ as a function of time at the NTTR ground station using a scintillometer during the 6 flights conducted on May 16 and 18, 2009 [18]. Daytime ground temperatures were near 81° F. This figure shows that the ground refractive index structure parameter measurements were on the order of $1 \times {10^{ - 12}}\,{m^{ - {2/3}}}$, which is considered strong turbulence since it is well above $C_n^2 \sim 1 \times {10^{ - 13}}\,{m^{ - {2/3}}}$[10]. In this section, all field-test $C_n^2$ predictions are specified in terms of the Hufnagle-Valley 5/7 (HV5/7) Refractive Index Structure Parameter model [14]. The rationale is shown in Fig. 3. This figure compares multiples of HV5/7 Model to annual Korean turbulence statistics, measured by the Air Force in 1999. Specifically, it plots multiples of $0.2 \times ,\;1 \times $ and $5 \times $ of the HV5/7 model values against measured turbulence occurrence statistics of 15%, 50% and 85%. The percentages in the legend reflect the amount of time during the year the measured refractive index structure function $C_n^2$ occurred. If this Korean data is representative of conditions to be expected by FSOC systems, one must be able to compensate for turbulence effects up to a 5xHV 5/7 atmosphere, if not beyond, to be considered a high availability link. The subsequent analysis will reference the turbulence conditions as an equivalent multiple of HV5/7 and thus suggest what percentage of the environments we can expect that the FSOC link will close.
Tables 4 and 5 show the best predicted versus measured median and 99%-percentile Power in the Fiber (PIF) for data taken at NTTR and PAX), respectively, for various turbulence conditions and ranges [7,17]. Here, PIB represents the Power in the Bucket, the amount of power received at the Receiver aperture. The mapping equations changing the median PIF to the 99%-percentile PIF is given by
Table 4. Comparison Predicts Median PIF and 99% PIF With Measured NTTR Data
Table 5. Comparison Predicts Median PIF and 99% PIF With Measured NTTR and PAX Data
One often overlooked parameter that is extremely useful in systems analysis, is the scintillation index ${\sigma _I}^2$ [9, p299]. The Scintillation Index is an indicator of the strength of turbulence along the integrated path. For spherical wave propagation under weak intensity fluctuations, it is given by
This equation predicts that the Scintillation Index increases without limit as $C_n^2$, or the path length increases. This is not true and there is a limit. This can be seen in Fig. 4. This figure depicts measured square-root of the Scintillation Index versus predicted square-root of the Scintillation Index [18] plotted with selected Scintillation Indices from the NTTR/PAX experiments. It plots the observed strength of scintillation (marker points) versus scintillation predictions from Rytov theory (solid line) for various path lengths and turbulence conditions. This figure clearly shows scintillation saturation. The observed ${\sigma _I}$ peaks when the at the point where the theoretical ${\sigma _I}$ is approximately unity. When the theoretical ${\sigma _I}$ is around 0.7 or less, we are in the regime where the Rytov approximation is valid, i.e., weak intensity fluctuations where phase fluctuations dominate. Above 0.7, strong scintillation (fading) grows linearly but is created by amplitude fluctuations rather than phase fluctuations. When the theoretical ${\sigma _I}$ exceeds 1.0, the plot shows that measured ${\sigma _I}$ essentially flattens out (slight decrease, actually). This indicates the saturation propagation regime. That is, when we have strong-to-severe turbulence and/or long paths, the light is so mixed that it does not retain any of its original attributes, i.e., this is where 2π-ambiguity for AO and other non-linear effects occur. The simple phase correction relationship needed for AO no longer exists. Amplitude scintillation, which AO systems do not correct, is the dominate turbulence effect and must be mitigated by other means than AO [7].
Fig. 4. Observed square-root of the scintillation index versus predicted square-root of the scintillation index plot with numbers from NTTR/PAX experiments.
The above comparisons involved optical links not close to the ground. Let us now see if the above trend holds for links near the Earth’s surface.
4. Hollister-Fremont Peak field data comparison
The HV5/7 $C_n^2$ model is given by
It has long been recognized that the advantage of this model over other atmospheric models is its inclusion of the rms wind speed, w, and the ground level refractive index structure parameter $C_n^2(0 )$. Their inclusion permits variations in high-altitude wind speed and local near-ground turbulence conditions to better model real-world profiles over a large range of geographic locations. It also provides a model consistent with measurements of the Fried Parameter ${r_0}$ and the isoplanatic angle ${\theta _0}$ [9,10]. However, Eq. (12) has a slowly decreasing exponential term with altitude [18,19]. This conflicts with the $C_n^2(h )$ behavior of ${h^{ - {4/3}}}$ noted by Walters and Kunkel [20] and supported by several other early measurements. To better represent this trend, Andrews and Phillips modified the HV5/7 model to yield
During June 7–9, 2011, measurements were made on the FOENEX laser beam (1550 nm) transmitted over a 17-km path between a ground station at Hollister Airport, CA and a ground station on Fremont Peak located at more than 800 m above the airport level [17,21,22]. The FOENEX data beam was transmitted from a 10-cm aperture and received by a 10-cm aperture in both directions. AO systems were employed at both ends of the path that included up to 35 Zernike modes of correction. A parallel test was conducted by a University of Central Florida (UCF) team using the alignment laser beacon transmitted from the ground station at Hollister Airport to Fremont Peak. The beacon beam with a large beam divergence angle operated at 780 nm from a 2.54 cm Tx aperture. The purpose of the UCF testing was to characterize the atmospheric channel between the ground stations at Hollister Airport and Fremont Peak using a three-aperture scintillometer developed by UCF for long ranges. From the weighted path-average $C_n^2$ values and an algorithm developed by UCF researchers, a $C_n^2$ HAP profile model as a function of altitude was constructed that estimated $C_n^2({{h_0}} )$ values at 1.5 m above ground at Hollister Airport and high-altitude background turbulence levels M for the HAP model.
The ground profile for the propagation path between Hollister Airport and Fremont Peak is shown in Fig. 5 along with a piecewise linear approximation introduced by UCF to account for altitude changes over the laser path. The piecewise linear approximations were used in the algorithm developed by UCF to make calculations for the HAP model parameters.
Fig. 5. Ground profile (upper) and UCF piecewise linear approximation (lower) between Hollister Airport and Fremont Peak.
Path-averaged values of $C_n^2$ over various time intervals on June 7–9, 2011, are shown in Fig. 6. Figure 7 shows ground-level measurements of $C_n^2$ at 1.5 m above ground at Hollister Airport using a commercial Scintec BLS900 scintillometer (filled triangles) and those inferred from the HAP model (open circles). The solid and dashed lines in these graphs are based on averages of $C_n^2$ measured along the propagation path during the total measurement times.
Fig. 6. Measured path-average values of Cn2 between Hollister Airport and Fremont Peak on June 7–9, 2011. Solid and dashed lines are the average value of Cn2 during the given time interval.
Fig. 7. Measured data (filled triangles) from the Scintec BLS900 instrument based on 1-min averages of Cn2 at 1.5 m above the ground at Hollister Airport. The open circles are estimated values from the algorithm for the HAP model and the solid and dashed lines are the HAP model averages. Time is local including both sunrise and sunset times.
Tables 6 and 7 show the best predicted versus measured median PIB and PIF at this site for various turbulence conditions and ranges [21]. Again, tables were created for the various “m” possibilities and looking for the combination that had the best match. The predicted PIB and PIF were calculated using the Fried Parameters derived from the HAP model matching its $C_n^2$ value to the scintillometer measurement; comparisons of these entities are given in Table 5. The daytime values used the “No AO” setting at both terminals. The evening values has a “No AO” setting at the receivers and “Tip/Tilt only” setting at the transmitters.
Table 6. Comparison Predicts Median PIF with Measured Hollister-Fremont Peak PIF
Table 7. More Comparison Predicts Median PIF With Measured Hollister-Fremont Peak PIF
These tables exhibit good agreement between theory and measured data, i.e., within a few dB.
The one exception is the 17:05 Fremont Peak measurement that has a 5 dB difference. However, given the strong turbulence conditions, it is not surprising to have one statistical outlier measurement. The daytime, strong turbulence measurements were consistent with the findings of the previous NTTR/PAX data comparisons that the AO system offered negligible turbulence mitigation [7]. However, the evening experiments are close to the moderate – strong turbulence boundary cited earlier. On the other hand, the AO system did not help the receiver focus the beam better into the fiber during the evening experiments but seems to improve the beam quality a little bit at the transmitter end. The proximity to the ground appears to negatively affect the AO’s performance in the moderate to strong turbulence regime. So, our finding in the last section were essentially confirmed, with one caveat. That is, AO has negligible turbulence mitigation under strong turbulent conditions at long ranges, limited turbulence mitigation under moderate ($1 - 3 \times {10^{ - 14}}\,{m^{ - {2/3}}}$) turbulent conditions, and good turbulence mitigation under weak turbulent conditions for short ranges (∼10 km), but proximity to the ground could degrade the AO system performance even more.
5. Summary
This paper described a new AO performance model proposed by one of the authors (LCA) and compared its predictions with measured field data taken from several field experiments. These comparisons suggest that AO systems with smaller numbers of Zernike modes may be all that is necessary for turbulence mitigation in real atmospheres, if at all. They also suggest that (N > 3)-AO systems perform well under weak turbulence conditions or short range under 10 km, but only will provide limited tip/tilt gain in moderate turbulence and long range, and no gain under high/saturation regime, long range turbulence.
Long range links close to the ground in high moderate turbulence may degrade AO turbulence mitigation further. In practice, tip/tilt centroid trackers still may be always required in all situations to counter beam wander. In general, the use of low Zernike mode AO system will be applications dependent, but will reduce size, weight, power, and cost (SWAP-C) of the optical terminals in all communications applications.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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