Larry B. Stotts,1,* Paul Kolodzy,2 Alan Pike,3 Buzz Graves,4
Dave Dougherty,4 and Jeff Douglass4
1Defense Advanced Research Projects Agency, 3701 North Fairfax Drive, Arlington, Virginia 22203, USA2Kolodzy Consulting, P.O. Box 1443, Centerville, Virginia 20120, USA
3Defense Strategies and Systems, Inc., 593 Greenfield Road, Front Royal, Virginia 22630, USA4AOptix, 695 Campbell Technical Parkway, Campbell, California 95008, USA
There is a need for high-capacity communicationlinks for the tactical level of warfare because of theincreasing need to transmit and receive video andthe aggregation of low-rate data sources from for-ward areas back to tactical operations centers [1].These data requirements are placing increased de-mands on the throughput of current radio-frequency(RF) systems and RF satellite links. In addition, in-creasing commercial demands on satellite links andthe RF spectrum require the incorporation of opticalcommunication to relieve RF congestion and more ef-ficiently use allocated RF capacity for the most criti-cal traffic. Current technology is now mature enoughto design and prototype an airborne reach-back sys-
tem capable of transmitting data, voice, and videotraffic over an IP-compatible network utilizing hy-brid links of RF and free-space optical communica-tions (FSOC) equipment. Discussions of this can befound in several papers in the literature [2–5].
Successful communications link closure has beenachieved through atmospheric turbulence by severalauthors over ranges from 10 to 150 km [2–6]. Ele-ments of such an FSOC system include (i) 1:55 μmwavelength lasers with up to 10 W output; (ii) acqui-sition, tracking, and pointing systems with near-microradian (μrad) accuracy; (iii) deformable mirrorsthat use measurements of the incoming optical phasefronts to compensate for atmospheric turbulence andother aberrations; and (iv) optical automatic gaincontrol systems that protect the detector fromdamage from high optical power and provide fulluse of 40 dB of dynamic range [2–6]. Details of thesecomponents have been described separately [6]. The
challenge today is to characterize the link degrada-tion by turbulence that allows estimation of perfor-mance under various atmospheric conditions.
Given the trend today in FSOC, adaptive optics(AO) plays a key role in reducing signal degradationand focusing the light into fibers or erbium-doped fi-ber amplifiers. To aid the communications engineer,we propose a methodology to estimate FSOC perfor-mance over long ranges and through strong atmo-spheric turbulence.
This methodology builds on the assumption thatthe capacity of an AO system to compensate for tur-bulence along a path is limited by the Rayleighrange, a factor proportional to the square of thediameter of the optics, d, and inversely proportionalto the wavelength, λ, of light utilized, because beyondthat range, the optical system cannot resolve phaseor amplitude changes smaller than its diameter [2,6].Specifically, we previously define the Rayleigh range,RRR, over which AO can compensate turbulencephase perturbations to be given by
RRR ¼ 0:7d2=λ ¼ 0:7RFraun=2;
where RFraun ¼ 2d2=λ is the Fraunhofer distance.This parameter is illustrated in Fig. 1, which repre-sents a 200 km horizontal FSOC link, using d ¼10 cm and λ ¼ 1:55 μm, [6]. The figure illustratestwo important points of this paper: namely, the AOsystem only compensates within the Rayleigh rangesof the transmitter and receiver, and the system loss isdefined by the turbulent degradation outside of thosesegments. When the total range of the link is muchgreater than the sum of the two Rayleigh ranges, theengineer must use other techniques, such as the for-ward error correcting code, optical automatic gaincontrol, and retransmission to provide high-qualityservice (e.g., error-free communications) to reducethe effect of the residual range for FSOC link perfor-mance [2–5].
2. Background: Diffraction Spreading
It is useful to begin our paper with a discussion of thespreading of the beam between the transmitter and
the receiver. In the absence of atmosphere or otheraberrations, the Fraunhofer equation gives us thepeak irradiance in the far field, Iff0, at a range Rand wavelength λ, as the area of the transmitter,ATX, times the transmitted power, PTX, divided by(the wavelength times the range) quantity squared:
Iff0 ¼ ATXPTX=ðRλÞ2:The power entering the receiver aperture, PRX, then,is the area of the transmitter, ATX, times the trans-mitter power times the area of the receiver, ARX,divided by the quantity R2λ2:
PRX ¼ PTXATXARX=ðRλÞ2;assuming the far-field beam diameter is much largerthan the receiver diameter. This is similar to theclassical radar equation.
3. Degradation of FSOC Links by Turbulence
Whenaberrations are induced by the atmosphere, thetransmitted irradiance is reduced by a factor com-monly called the Strehl ratio {(SR) [7], p. 7}. The mod-ern definition of the SR is the ratio of the observedpeak intensity at the detection plane of a telescopeor other imaging system from a point source com-pared to the theoretical maximum peak intensity ofa perfect imaging system working at the diffractionlimit. In other words, it is a good measure of the qual-ity of the incoming irradiance to anoptical system ([8],p. 462). Mathematically, the SR is defined as
SR ¼ expð−σ2φÞ;
where σ2φ is the residual phase variance ([9], p. 50). Forpurposes of this paper, we find, under more generalconditions pertaining to turbulent propagation, theSR can be rewritten as
SR ≈ 1=½1þ ðd=r0Þ5=3�6=5;where d, as before, is the diameter of the opticalsystems and r0 is the Fried parameter ([9], p. 50).
Fig. 1. Rayleigh range limitation in AO compensation for turbulence.
where ζ is the zenith angle, k≡wavenumber ¼ 2π=λ,h is the height above the ground, L is the length of theturbulent regime, and C2
nðzÞ is the refractive indexstructure function ([10], p. 47). In Section 5, we willspecify theC2
nðzÞmodelwewill use in our calculations.The Fried parameter is the atmospheric coherence
length and is the distance over which the phasevaries no more than �π. It is the largest effective di-ameter for image resolution and for maximizing sig-nal-to-noise ratio in coherent detection systems [10].It also is related to the plane wave coherence radi-ance, ρ0, by the relation
r0 ¼ 2:1ρ0:
In terms of the measurements discussed in this re-port, the far-field beam diameter is much larger thanthe receiver aperture. As a result, we can use theFraunhofer equation modified by the second defini-tion of the SR, i.e., dependent on the ratio of d=r0,to calculate the peak irradiance that is incident onan aperture, subject to the Raleigh range reduction.{The use of the compensation range limitation inthese calculations assumes that the AO system hasadequate spatial compensation and a frequency re-sponse greater than the Greenwood frequency ([11],p. 622).} In particular, we assume that the transmit-ter AO systems will correct all turbulent effects with-in RRR from that transmitter aperture and near thereceiver aperture, and the turbulent effects onlycome from the range between RTxRR < r < L−RRxRR, where L is the total distance between trans-mitter (Tx) and receiver (Rx). The total downlink anduplink received power, then, are proportional to theproduct of their respective SRs over the reducedresidual distance, L − RTxRR − RRxRR. To see this,let us relate this discussion to two key performanceparameters in optical laser communications systemsanalysis, power in the bucket (PIB) and power in thefiber (PIF).
The PIB analysis is a direct measure of the averageirradiance at the receiver aperture. Thus, it is a mea-sure of the far-field irradiance times the SR. In thiscase, it is the transmitter SR, with the turbulenceweighted most heavily toward the transmitter (irra-diance measure definition). On the other hand, thePIF is a measure of the ability of the receiver opticsto couple light into the optical modem, which is theinterface in laser communications systems. In theabsence of degrading effects, the resulting focusedbeam from the receiver optics would couple light intothe single-mode fiber with near perfect efficiency, i.e.,the SR essentially would approach unity; otherwise,with degrading effects, the SR will be less than 1, re-flecting suboptimal coupling into the fiber. This im-plies the PIF is approximately the PIB times the
receiver SR, where that SR weighs most heavilythe turbulence nearest the receiver (classical defini-tion). If the distribution of the turbulence betweenthe two systems was symmetric and the receiverand transmitter aperture diameters were equal,the receiver PIF would then be proportional to theSR squared; otherwise, it is the product of the trans-mitter and receiver SRs. This is the second importantpoint of this paper.
4. Degradation from AtmosphericAbsorption and Scattering
In addition to other optical transmittances, thepower at the receiver is reduced by the absorptionand scattering by molecules and aerosols along thepath. The Infrared Handbook [12] provides estimatesof the attenuation coefficients in the rural aerosolmodel and the maritime aerosol model as a functionof wavelength and in the variation with altitude formoderate volcanic conditions. For a wavelength of1:55 μm, the rural aerosol model attenuation coeffi-cient, α, is given as 0:036=km and the maritime aero-sol model is 0:120=km. The transmission over aconstant altitude path is then e−αR. When the alti-tude is not constant, we integrate this transmissionover the path length. In the analysis to come, we re-cognize that the maritime attenuation is appreciablygreater than the rural value, due largely to the pre-sence of salt aerosols. When propagating over thebrackish portion of the Chesapeake Bay, on the otherhand, we use half the maritime value because thesalt aerosols are less frequent.
5. Relationship of Real Turbulence to the Hufnagle-Valley Models
Degradation of diffraction-limited laser beams in theatmosphere occurs due to atmospheric turbulenceand also turbulent airflow past the transmitter/receiver apertures in airborne systems. The latterdegradation is known as the aero-optic effect. Amajor question is whether one can effectively com-pensate for this degradation when it is createdthrough long-range light propagation under high at-mospheric turbulence and nonlaminar airflow condi-tions created by the use of protruding windows, pods,and external terminals. The intent of this section isto establish the basic C2
n model that will be used todefine the various effects and key parameters of at-mospheric degradation over long, arbitrary rangesand how they are related to the occurrence of realturbulence measured statistically and estimatedduring the various experiments described. In ourproposed methodology, we use the Hufnagle–Valley(HV) 5/7 mode for C2
n. Here, the term 5/7 means thatfor a wavelength of 0:5 μm, the value of 5 representsa Fried parameter of 5 cm and the value of 7 repre-sents an isoplanatic angle for a receiver on theground looking up of 7 μrad. The HV 5/7 model is de-scribed, for example, in Tyson ([8], p. 33).
Figure 2 compares multiples of the HV 5/7model toannual Korean turbulence statistics, measured by
the Air Force in 1999. In this figure, we plot multiplesof 0:2×, 1×, and 5× of the HV 5/7 model values againstmeasured turbulence occurrence statistics of 15%,50%, and 85%. The percentages in the legend reflectthe amount of time during the year that the mea-sured refractive index structure function, C2
n, oc-curred. If this Korean data are representative ofconditions to be expected by FSOC systems, onemustbe able to compensate for turbulence effects up to a5× HV 5/7 atmosphere, if not beyond, to be consid-ered a high availability link. The subsequent anal-ysis will reference the turbulence conditions as anequivalent multiple of HV 5/7 and thus suggest whatpercentage of the environments we can expect thatthe FSOC link will close.
6. Defining the Cumulative Distribution Function ofAtmospheric Turbulence
Over the past five years, DARPA and the U.S. AirForce Research Laboratory (USAFRL) both haveconducted field trials to generate data on which tovalidate optical link budgets. These include theAFRL-sponsored 2006/2008 Integrated RF/OpticalNetworked Tactical Targeting Networking Technolo-gies (IRON-T2) static experiments over a 147 kmpath between Haleakala and Mauna Loa in Hawaii[13] and the 2008 AFRL-DARPA-sponsored OpticalRF Communications Adjunct (ORCA) static experi-ments over a 10 km path at Campbell, California.Recently, validation of these estimates under dy-namic conditions occurred in the ORCA Programusing 70 km sea-level ground to low-altitude aircraft(8; 000 ft above ground level) tests at the PatuxentRiver Naval Air Station (PAX), and in 50 to 200 kmtests between Antelope Peak and a 26; 000 ft MSL al-
titude BAC1-11 aircraft at the Nevada Test andTraining Range (NTTR). Let us begin our data analy-siswith themeasurements fromour two static experi-ments and then see how they can be used to define thecumulative distribution function (CDF) for atmo-spheric turbulence.
Figure 3 shows estimated results for the atmo-spheric conditions experienced during the referencedAugust 2008 10 km Campbell experiments. TheRayleigh range estimated for this link is 4:5 km(see Fig. 1). In Fig. 3, we have computed the PIBand PIF derived for the resulting reduced turbulencerange in decibels relative to a milliwatt or 0 dBmW.For our model comparison, we have modified theFried parameter to reflect the receiver and transmit-ter coherence lengths of spherical waves and the re-duced integration range; specifically, we write
Receiver coherence length≡ r0R
¼�16:71 sec ðζÞ
ZL−RRxRR
RTxRR
C2nðrÞðr=RÞ5=3dr=λ2
�−3=5
;
Transmitter coherence distance≡r0T
¼�16:71 sec ðζÞ
ZL−RRxRR
RTxRR
C2nðrÞð1−r=RÞ5=3dr=λ2
�−3=5
:
(See, for example, Beland [14], Eqs. 2.135 and 2.155.)Using these equations, we estimate the downlinkand uplink SR using SR ≈ 1=½1þ ðd=r0Þ5=3�6=5. The
Fig. 2. Multiples of HV model compared to Korean turbulence.
strength of turbulence was assumed constant overthe path and was chosen to give the best fit to themeasured data, as specific C2
n were not available. Fol-lowing our model, the coherence distance equationsassumed that C2
n was zero for the first and last4:5 km when the AO status was “ON.” The modeleddata in Fig. 3 show a good fit to the measurements.Like the other data comparisons to come, the Rytovnumber was well into the saturated regime, with va-lues ranging from 1 to 25. The Rytov number, or thelog amplitude variance, is an indicator of thestrength of turbulence along the integrated path.(Note, the variance of the log intensity is sometimesknown as the Rytov variance.) Mathematically, theRytov number is defined as
Rytov number≡ σ2r
¼ 4:78ZR
0
drC2nðrÞr5=6ð1 − r=RÞ5=6=λ7=6
[15]. For our purposes, the above is modified to be
Rytovnumber≡σ2r ¼4:78ZL−RRxRR
RTxRR
drC2nðrÞr5=6
×ð1−r=RÞ5=6=λ7=6;
where this integral reflects the reduced range of tur-bulent influence. When the Rytov number is below0.2, little scintillation is to be expected. Above 0.3,scintillation is likely. When it exceeds 1.0, wave op-tics simulations often fail to converge and we havehad problems in predicting FSOC link performancefor several decades. As will become apparent inthe next section, the proposed methodology appearsto be applicable to weak through strong turbulence,as we will see good agreement between predicted andmeasured values of PIB and PIF. As a final note, wecan see that the Rytov number weighting function
Fig. 3. Modeled and measured results using Rayleigh range limitation in AO compensation for atmospheric turbulence.
Fig. 4. Statistical distribution of the PIF with AO produces a consistent linear relationship between log optical power and log cumulativedistribution.
peaks halfway between the transmitter and thereceiver in the above equation.
The above characterization is for the average PIBand PIFat the detector. In general, one usually wantsto know if the FSOC link is available during high tur-bulence conditions, e.g., the saturation regime, wherethe deep fade depths below themeanPIFoccur. Giventhe above, let us now use the data from the static ex-periments to plot the CDFs for both PIB and PIF, andhopefully, derive relationships between themean andthe 99% fade depths of the PIB and PIF.
Figure 4 shows the CDFas a function of PIF for theCampbell experiments. It is clear in this log-log plotthat the mean level and all higher order statistics arelinearly related. The same relation holds for the PIB.This means we should be able to derive a linear map-ping between the 99% and mean levels for these twomeasurements.
Figure 5 plots the transmitter and receiver SRs asa function of the mean PIB from the 2008 IRON-T2Hawaii experiment [13]. This graph shows that thereis a linear relationship, on a log-log plot, between the
Fig. 5. Transmitter and receiver SRs versus PIB.
Fig. 6. Hawaii 99% PIF fade depths versus mean PIF.
mean PIB and the two SRs. In other words, it demon-strates the PIB statistics follow a lognormal distribu-tion, as expected.
From data such as that shown in Fig. 4, we can plotthe 99% PIF as a function of the mean PIF and findthat the former is nearly linearly proportional to thelatter, with a constant of −17 to −22 dB mW. An ex-ample from the IRON T2 tests in October 2008 isshown in Fig. 6 and another from the Campbell testsin August 2008 in Fig. 7, when appropriate curve fitsto the data shown. Again, the data are well into thesaturation region of the log amplitude variance orRytov number (see, for example, in The InfraredHandbook pp. 6–21 [12]). By processing the availabledata, we conclude that the 99% fade depths overthese long ranges are 19 dB� 2 dB and we canuse this value in building our link budget.
7. Applying our Model to a FSOC Link Budget
With the above information, we are now in the posi-tion to create a link budget for a FSOC system andsee how it compares to field measurements. Follow-ing normal engineering convention, it is convenientto construct the link budget using logarithmic val-ues; specifically, in dBmW. Let us now look at moreresults from the 2008 IRON-T2 Hawaii tests [13].
As noted above, the Fried parameter, r0, is impor-tant to our calculation. Unfortunately, it cannot beexplicitly measured. However, video images of thebeam near the Haleakala receiver allowed us to es-timate r0 to be frequently less than 20 cm by recog-nizing that the received speckle size should be on theorder of r0. The terrain around the Mauna Loa Vol-cano slopes gradually downward, and the beam iswithin 1; 000 m of the ground until it is 10 km away
Fig. 7. Campbell 99% PIF fade depths versus mean PIF.
Fig. 8. Assumed profile of strength of turbulence: 0:2× HV 5/7 plus 100× boundary layer.
from the transmitter. The Haleakala Volcano wall ismuch steeper near the receiver and drops awaybelow 1; 000 m at 3 km from the receiver. So to firstorder, one might expect a uniform value of the refrac-tive index structure function like Campbell for mostof the link, with a gradient existing near the MonaLoa terminal. To account for this situation, we canadd a boundary layer near the transmitter corre-sponding to these beam heights and 100 times stron-ger than the value given by the HV 5/7 at thesealtitudes. That profile is shown in Fig. 8. ThisFig. 9. Link budget developed from Hawaii test results.
Fig. 11. Summary of the refractive index structure function, C2n,
measured on the ground during the six flights conducted on 16–18May 2009.
Fig. 10. Weather Research and Forecasting r0 results for all NTTR flights.
assumed profile produces a calculated r0 of 16 cm,which is consistent with the estimates indicatedabove.
Figure 9 shows the calculated link budgets for datataken during the 2008 Hawaii IRON-T2 tests refer-enced above. Two cases are shown in Fig. 9; the firstcase uses the normal 0:2× HV 5/7 model shown inFig. 1; the second uses the 0:2× HV 5/7 and the afore-mentioned 100× boundary layer. While the 0:2× HV5/7 model includes a significant boundary layer ataltitudes closer to sea level, and the latter modelassumes that boundary layer at the altitudes in theHawaii tests, above 10,000 feet it is clear in thetwo cases that measurements and predictions showno significant difference in turbulence strength andcalculated numbers, despite the presence of differentground effects near each end of the beam. This goesback to our previous point that the transmitter AOsystems will correct all turbulent effects withinRRR from that transmitter aperture and near the re-ceiver aperture, and all turbulent effects come frominterval RTxRR < r < L − RRxRR. Here the Rayleighranges of 4:5 km only comprise a small portion ofthe 147 km total link separation.
The power exiting the transmitter aperture forFig. 9 is estimated to be 14 dB mW. The spreadingloss is calculated as described in Section 2. TheHV 5/7 model, with a 100× boundary layer, predictsthat the C2
n between the transmitter on Mauna Loaand the receiver on Haleakala varies between 6 ×10−16 and 8 × 10−16. This would produce a transmit-ter coherence diameter, r0, of 16 cm over the 147 kmpath length, leading to a transmitter Strehl loss ofonly −2:0 dB. The atmospheric absorption and scat-tering loss is estimated to be 5:0 dB, using the ap-proach described in Section 3, The AO of thetransmitter could compensate for 0:1 dB, using thecalculation as described in Section 7. This leads toa predicted PIB of −20:9 dB mW, compared to a mea-sured −19:0 dB mW. This is quite good agreement,given the assumptions involved.
Using reported values for the receiver transmit-tance and the circulator loss into the single-mode fi-ber and the Strehl loss of −1:1 dB, the link budgetpredicts a PIF of −30:2 dB mW, compared to a mea-sured value of −29:4. Using the 99% dB spread of19 dB, as described in Section 4, leads to an expected99% fade power out of the fiber of −49:2 dB mW ascompared to a measured value of −47:5 dB mW.
8. More Link Budget Validation—NTTR and PatuxentRiver Naval Air Station Test Results
As described earlier, there also was ORCA testing be-tween an aircraft at 9,000 to 10; 000 ft altitude and asea-level ground site at the PAX and between an air-craft at 26; 000 ft and a mountain top at the NTTR inMay of 2009. At the NTTR site, an independent es-timate of r0 was obtained from a Weather Researchand Forecasting (WRF) model, as described in [16].Those predictions are reproduced here in Fig. 10.
Figure 10 shows a more detailed look at the Friedparameter during all the NTTR tests. This pictureshows the Fried parameter r0 derived from WRF,plotted against the aircraft distance from AntelopePeak, for the six flights on 16–18 May, 2009. Valuesare for air-to-mountain to simulate air-to-air. (Itshould be noted that aero-optics effects are notincluded in the WRF modeling.) Each flight is shownin a different color. Although there is a large spread inr0 values between different flights, each flight showsthe correlation of r0 with path length. Figure 11 showsthe associated ground-level refractive index structurefunction, C2
n, for the set of tests shown in Fig. 8. It isclear that the middle of the day had C2
n∼
1 × 10−12 m−2=3; because strong turbulence is ratedas C2
n ∼ 1 × 10−13 m−2=3 or more ([14], p. 11),for most of the middle of that day, testing was accom-plished with turbulence 10 times that seen in priorIRON-T2 testing [2].
Referring to Fig. 10, many of the flights had pre-dicted strengths of turbulence of 25× HV 5/7 model,which is five times the Korean 85% value of 5× HV 5/7. Let us first look at the 5× HV 5/7 ORCA data withprediction, and then how the other daytime datacompare at this much higher value. Figure 12 shows
Fig. 12. Comparison of predicted andmeasured link performancefor 17 May flight 2 (5× HV 5/7).
predicted and measured PIB and PIF for data takenat NTTR on 17 May 2009, 18:54 local time. Here PIBand PIF are median values of measurements and99% PIF is derived from median PIF using the linearequation specified above. Once again, close agree-ment is shown between PIB and PIF predictionsand measurements, all within 2 dB.
Figure 13 shows predicted PIB and PIF and mea-sured PIF for data taken under 25× HV 5/7 condi-tions on 17 May 2009. As can be seen from thetable in this figure, the PIF predictions for the 25×HV 5/7 model, agree well with the measured resultsfor most cases.
Note that the NTTR transmitter predicted AOgains are small, because the HV 5/7 model predictsweak turbulence at 26; 000 ft. In fact, there wasother evidence that the turbulent boundary layeraround the aircraft may have contributed a 5 to10 dB loss, as described in [6].
Finally, Fig. 14 shows predicted PIB and PIF andmeasured PIF for data taken under 3× HV 5/7 con-ditions at PAX for 50 and 70 km ranges on 12 May2009. The PAX results also show good agreementwith the values predicted from the FSOC link bud-get. The low elevation angle in the PAX tests, be-
tween 2:25° and 3:5° produces an expected strongturbulence layer near the ground. This shows an ex-pected 7 to 9 dB AO gain at the receiver, in goodagreement with the measured results.
9. Summary
This paper described a new methodology of estimat-ing the FSOC link budgets to be expected in condi-tions of severe turbulence. The approach is derivedfrom observing that the ability of an AO system tocompensate turbulence along a path is limited bythe transmitter and receiver Rayleigh range, propor-tional to the diameter of the optics squared and in-verse of the wavelength of light utilized. Themethod uses the Fried parameter over range outsidethe two Rayleigh ranges and inserts that value intothe transmitter and receiver SR to yield reasonableprediction of the light impinging on the receivingtelescope aperture and the power coupling into thefiber. Comparisons were given between theory andfield measurements. These comparisons show thatAO is most effective within the Rayleigh ranges orwhen an atmospheric gradient is present, e.g., theaero-optic effect, upslope wave effect, and lesser so
Fig. 13. Comparison of predicted and measured link performance for 17 May 2009.
when the total range is much greater than the sum ofthe Rayleigh ranges.
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Fig. 14. Comparison of predicted andmeasured link performancefor 12 May 2009.
