Laser propagation at 156 μm and 360 μm in maritime environments

Laser propagation at 1:56 μm and 3:60 μmin maritime environments

Frank Hanson,* Pete Poirier, Delmar Haddock, Dan Kichura, and Mark LasherSpace and Naval Warfare Systems Center Pacific, San Diego, California 92152, USA

*Corresponding author: [email protected]

Received 5 February 2009; revised 5 May 2009; accepted 18 June 2009;posted 24 June 2009 (Doc. ID 107150); published 14 July 2009

We report results from field experiments that have compared laser propagation at 1:565 μmand 3:603 μmin a variety of atmospheric conditions in a low-altitude maritime environment in order to quantify therelative effects of turbulenceunder realistic conditions. Intensity scintillationandnormalized focused spotsizes were found to be significantly less affected by turbulence at the longer wavelength, in general agree-mentwith theoretical predictions. Also, the longerwavelength beamwasnoticeably less degradedby aber-rations in the transceiver optical components. These advantages should be considered when evaluatingthe wavelength trade-offs in laser communication systems. © 2009 Optical Society of America

OCIS codes: 010.4458, 060.2605, 060.4510, 190.0190, 290.7050.

1. Introduction

Free-space optical communication and laser radarhave advantages over more conventional RF ap-proaches that are attractive for many applications.In particular, the much shorter carrier wavelengthallows greater modulation bandwidth and narrowerbeam divergence that offer a higher level of covert-ness. However, it is well known that optical propaga-tion in low-altitude environments is sensitive toatmospheric conditions. The effective range is lim-ited by scattering and absorption, and, in addition,turbulence causes intensity fluctuations and beamdegradation. It is expected from theory that scatter-ing and turbulence should have relatively less effectat longer wavelength; however, quantitative mea-surements in real world conditions are important be-cause of the complexity and simplifying assumptionsrequired in the theory. In one early experiment [23],collimated laser beams at 1:06 μm and 3:8 μm werepropagated 10:5km over land, and focused imagesof the beams were collected. An analysis of short-term images generally showed significantly higherdistortion at the shorter wavelength. In conditions

where the instantaneous spot sizes were ∼50 timesthe diffraction limit at 1:06 μm, the spot sizes werefound to be ∼7:5 times the diffraction limit at3:8 μm, resulting in a scaling of ∼1=λ1:5.

Theoretical models [2] have been quite successfulin giving insight into how turbulence can affect pro-pagation; however, it can be very difficult to makequantitative predictions that can be compared to ex-perimental measurements. Fundamentally, this isbecause the exact spectrum of refractive index fluc-tuations along the propagation path is never known.Various approximate analytic models that are usual-ly uniform and isotropic must be used with assump-tions about inner and outer spatial scales. Even withthese simplifying assumptions, the theory becomesvery complex in conditions other than weak turbu-lence. Intensity fluctuations are detrimental to free-space optical communication systems because theylead to signal fading and increased bit error rate.The scintillation index σI2, or normalized varianceof intensity at a single point, is known to saturateat high levels of path-integrated turbulence, but the-oretical predictions of the approach to saturation arevery sensitive to the size of the inner scale [3]. In par-ticular, pronounced maxima in σI2 are predicted asthe inner scale increases from zero to a few milli-meters and have been observed [4]. Further, the

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details of this behavior will depend on wavelength,and therefore it is problematic to predict how σI2 willscale with wavelength in unknown conditions. An-other fundamental metric of optical propagation isthe transverse coherence length ρ of the optical field.High spatial coherence is usually desired because itallows the received light to be focused close to the dif-fraction limit. For coherent communication, the het-erodyne efficiency of the receiver η is given by theoverlap integral of the signal field EsðrÞ and the es-sentially Gaussian TEM00 field of the local oscillatorE0ðrÞ,

η ¼��

ZAEsðrÞE0ðrÞdr

��2�; ð1Þ

where both fields are normalized to unit intensity [5].In other applications, it is desirable to couple thelight into a single mode optical fiber to simplify sig-nal routing or, with wavelengths near 1 μm and1:55 μm, for amplification in fiber amplifiers. Thiscoupling efficiency is also given by Eq. (1), whereE0ðrÞ represents the fundamental mode of the fiberand is nearly a Gaussian TEM00 mode [6]. In weakKolmogorov turbulence with infinite plane or spheri-cal waves, theory predicts that σI2 will scale withwavelength as λ−7=6 and ρ as λ6=5, and therefore long-er wavelengths will be less affected. In more generalconditions, with stronger turbulence, we should stillexpect longer wavelengths to be preferred, but thisscaling will no longer be exact.Also, as already noted, laser propagation will be

affected by extinction due to absorption and scatter-ing in the path. Figure 1 shows a representativetransmission spectrum from 1 μm to 11 μm thatwas calculated using MODTRAN for a midlatitudesummermodel atmosphere with 70% relative humid-ity and rural aerosol extinction that corresponds to ameteorological range of 5km. Two important trendsare apparent. Transmission is reduced at shorter

wavelengths due to increased scattering from aero-sols and at longer wavelengths because of broadbandH2O continuum absorption that scales with humid-ity. For this model atmosphere, these opposing trendsresult in optimum transmission at intermediatewavelengths near 4 μm. Weather conditions includ-ing visibility and humidity do vary greatly; however,a previous analysis of an extensive historical data-base of maritime weather observations, taken overseveral years and in a range of littoral regions, con-cluded that the median transmission in the midwaveinfrared (MWIR) (3:823 μm) would generally begreater than at 1:555 μm or 9:115 μm [7,8].

Currently, free-space laser communications sys-tems generally operate in the short-wave infrared(SWIR) near the eye-safe telecom band at 1:5 μmbecause laser sources and detectors are readily avail-able, efficient, and capable of high-bandwidth modu-lation. In addition, the average transmit power canbe boosted significantly with erbium-doped fiber am-plifiers. Sources and detectors in the MWIR from3–5 μm and long-wave infrared (LWIR) from8–12 μm are continually being improved [9], but atpresent these devices do not have the power or effi-ciency of SWIR devices that operate in the 1:5 μmband. There has been significant progress in improv-ing the performance of semiconductor quantum cas-cade lasers covering theMWIR and LWIR bands [10].Alternatively, MWIR sources can be based on non-linear optical conversion from 1 μm or 1:5 μm pumpsources. These outputs can be single frequency withvery high beam quality and could be used in coherentcommunication or laser radar systems [11,12].Although atmospheric propagation will be superiorat longer wavelength, the sources and detectorsshould not be expected to perform as well. This workwas motivated by the need to understand and quan-tify the advantage for propagation in the MWIRrelative to the SWIR in order to assess the potentialfor overall system performance operating in thesebands.

2. Laser Sources and Optical Layout

Coherent, continuous wave (cw) sources emitting inthe SWIR and MWIR bands were used in thesepropagation tests. The SWIR source was a single-frequency distributed feedback laser diode (NELmodel 914) with fiber-coupled output power of∼25mW and temperature tuned to emit at1:5655 μm. The MWIR source was a cw-pumpedoptical parametric oscillator (OPO) built by Light-wave Electronics (model M640) that emitted up to∼90mW at 3:603 μm. This OPO was packaged witha cw, single-frequency, Nd:YAG 1:064 μm monolithicnonplanar ring oscillator (NPRO) used as a pumplaser. It has been extensively characterized and de-scribed in detail elsewhere [13]. The OPO ring cavityresonated the signal wave near ∼1:5 μm and was ac-tively length stabilized to also resonate the pumpwavelength. The frequency stability of the MWIRoutput was thus derived from the inherent high

Fig. 1. Transmission calculated with MODTRAN at 1 cm−1 reso-lution for a low-altitude horizontal 10km path for the midlatitudesummer atmosphere model with rural aerosol extinction (leftscale). The relative wavelength dependence of the Rytov varianceσ12 ∼ λ−7=6 and the transverse coherence length ρ∼ λ6=5 expectedin weak turbulence are shown with a common scale.

4150 APPLIED OPTICS / Vol. 48, No. 21 / 20 July 2009

stability of the NPRO pump laser. The wavelength ofthe idler wave at ∼3:6 μm was tuned by controllingthe temperature of the nonlinear periodically poledlithium niobate (PPLN) crystal, which affects thephase-matching condition. Single-frequency opera-tion was obtained for the signal and idler waves bycareful adjustment of operating parameters. The op-erating wavelengths of both sources were carefullychosen to fall in atmospheric transmission windowsbetween very sharp molecular water absorption linesas shown in Fig. 2. These high-resolution transmis-sion spectra, unlike the spectrum in Fig. 1, werecalculated with FASE [14] using the HITRAN data-base with high visibility conditions (67km meteoro-logical range).The two sources (S) were coupled into a common

aperture transmitter as shown schematically inFig. 3. Both beams were collimated and magnifiedwith an ∼20× telescope consisting of separate∼5 cm positive focal length secondary lenses (LS)for each beam and a common 10 cm diameter pri-mary off-axis parabolic reflector (P) with focal lengthf p ¼ 101:5 cm. The beams were combined after thesecondary lenses with a dichroic beam splitter(BS1) fabricated on a clear YAG substrate to trans-mit the MWIR and reflect the SWIR. A small irisaperture was placed at the telescope focus in orderto define a field of view (FOV) and to ensure that bothbeams were aligned within this tolerance. Coursealignment of the transmitter was done with a smallvisible wavelength camera and a flip mirror (notshown) in the SWIR beam line before the telescope

optics that showed the field of view set by the iris.The near-field transmitter beam profiles were mea-sured by imaging the diffuse reflection from a Spec-tralon [15] target board. Both beams were nearlyGaussian with a 1=e2 spot radii Wout of ∼2:4 cm(SWIR) and∼3:6 cm (MWIR); however, the estimatedradii of the embedded Gaussian beams were ∼2:0 cmand 2:2 cm respectively, as discussed below.

3. Propagation Tests Over Land

The first set of experiments measured scintillationover a 1:26km land path on the Point Loma penin-sula in San Diego, California, USA. Although thepath running north to south along the middle ofthe peninsula was at a ground elevation of ∼90mabove sea level, there was a substantial marine influ-ence since the peninsula is only about 1:5km wideand fully exposed to the typical onshore winds fromthe ocean. The transmitter was located on the groundfloor of the building, and the beams exited throughan open window and immediately crossed a short∼10m parking lot at a height of ∼2:5m, then passedin a southerly direction over a variety of surfaces in-cluding land, vegetation, asphalt, and building struc-tures at an altitude that ranged up to ∼20m. TheSWIR and MWIR receivers were mounted together∼30 cm above ground level and were separated byless than 3 cm. Neither the transmitters nor the re-ceivers were exposed to direct sunlight. The SWIRreceiver had a silicon window that blocked light be-low∼1 μm, and the MWIR receiver had a germaniumwindow that blocked light below ∼1:8 μm includingthe SWIR beam. Light was collected in the adjacent23mm apertures and focused onto detectors. Bothdetectors had sufficient field of view to ensure mod-erate alignment requirements. The SWIR detectorwas an InGaAs PIN diode with a long wavelengthcutoff of ∼1:8 μm, and the MWIR detector was anInAs PIN diode operated at ambient temperaturewith a peak sensitivity near 3:6 μm. Both detectorswere followed by transimpedance amplifiers, and

Fig. 2. Atmospheric transmission spectrum in the SWIR (bottom)and MWIR (top) calculated with FASE for a 2:8km path for a mid-latitude summer atmosphere and marine aerosol model (67kmmeteorological range). The wavelengths of the SWIR and MWIRsources lie in transmission windows as indicated by the arrows.

Fig. 3. (Color online) The optical layout for the two-way propaga-tion tests using a common retroreflector for both the SWIR (top,blue) and the MWIR (bottom, red). The transmitter portion wasfunctionally the same as used in the first experiment. The receivedbeam paths are shown as dashed lines.


the signals were simultaneously digitized at 2000samples per second and stored. The initial telescopealignment was sufficient to obtain nominal signal le-vels, and fine optimization of the telescope pointingalignment and focusing were based on maximizingthe average received signal levels. However, thiswas generally difficult because of large signal fluc-tuations. Assuming optimal focusing and the esti-mated beam parameters discussed below, the spotsizes at the detectors would be ∼3:8 cm and∼10:6 cm for the SWIR and MWIR, respectively.Propagation tests were conducted during 3 days in

November and December of 2006 in conditions thatwere sunny with mild crosswinds. Often, after initialtelescope alignment, the mean signal level might de-grade noticeably within ∼30 min due to changes inthe vertical refraction over the path caused by tem-perature changes on the ground. Occasional slightadjustment of the common primary mirror wasnecessary to maintain beam alignment on the detec-tors. At intervals in the data collection, the beamswere blocked in order to record background signal le-vels. The scintillation index or normalized intensityvariance shown in Fig. 4 was calculated over 2-minsegments and corrected for the small variance of de-tector noise measured when the beams were blocked.Irregular heating of the varied terrain by solar irra-diance led to quite strong turbulence that generallyincreased during the morning and decreased later inthe afternoon. Except for the short period nearsunrise on December 5, the SWIR scintillation wassignificant, varying between ∼1 and 2. The MWIRscintillation was substantially less in all conditionsand ranged between 31% and 68% of the SWIR val-ues. It is interesting to note that the ratio was notalways the same at a given level of SWIR scintilla-tion. For example, when the SWIR scintillationwas ∼1:0, the MWIR scintillation during differentdays ranged from∼0:30 to∼0:65. The most likely ex-planation is that the relative beam alignments on thedetectors varied slightly during the tests. For finitebeam waves, scintillation depends on radial position

within the beam profile and increases with distancefrom the average beam axis because of short-term beam wander. For infinite spherical or planewaves in weak Kolmogorov turbulence, theory pre-dicts the ratio will scale as σI-MWIR

2=σI-SWIR2 ¼

ðλSWIR=λMWIRÞ7=6 or ∼0:38 for these wavelengths.This prediction is at the low end of the values we ob-served, but during much of this time the turbulencewas not weak for the SWIR, and the scintillation wasprobably beginning to saturate. In addition, the ob-served scintillation was reduced because of the aver-aging effect over the finite 23mm receiver apertures.The spatial scale of scintillation is characterized bythe Fresnel zone ðλz=2πÞ1=2, and this is 0.77 and 1.17of the aperture diameter for the SWIR and MWIR,respectively. Therefore the measured intensity var-iance in these tests was reduced more in the SWIRthan in the MWIR by aperture averaging.

4. Propagation Tests Over Water

A second series of tests was designed to investigateatmospheric effects on the spatial coherence of thebeams by measuring focal-plane intensity profiles.Turbulence will reduce the coherence of the electricfield at the receiver and lead to a broadened image inthe focal plane relative to the diffraction-limited per-formance of the optical system [16]. For a pointsource and uniform Kolmogorov turbulence, theorypredicts the time-averaged on-axis peak intensitywill be reduced by the Strehl ratio,

SR ¼ 16π

Z1

0

u½cos−1u

− uð1 − u2Þ1=2� exp½−3:44ðDu=r0Þ5=3�du; ð2Þ

where

r0 ¼ ð0:16C2nk2LÞ−3=5 ð3Þ

is the atmospheric coherence length (r0 ¼ 2:1ρ inweak turbulence), D is the diameter of the receiveraperture, and L is the path length [17]. The Strehlratio is closely approximated by SR ≈ 1=½1þðD=r0Þ5=3� in weak turbulence (r0 ≫ D) and by SR ≈

1=½1þ ðD=r0Þ5=3�6=5 in more general conditions in-cluding strong turbulence (r0 < D) [18]. Since thetime-averaged image is expected to be Gaussian inboth weak and strong turbulence, the normalizedspot radius, given by

ω=ω0 ¼�1þ ðD=r0Þ5=3

�3=5

; ð4Þ

provides a useful and practical metric from whichspatial coherence can be inferred.

The SWIR andMWIR beamswere propagated overa round-trip (2 × 1:41km) east–west path across theentrance channel to the San Diego Bay between thecommon-aperture telescope on Ballast Point and a

Fig. 4. (Color online) Scintillation data measured for the SWIR(circles) and the MWIR (squares) for the 1:26km path over landduring three days of measurements. The normalized intensity var-iance was calculated for 2 min of data.


fixed retroreflector on Zuniga Point. The transmitterand receiver were combined on a single optical bread-board in a small building located on a slight bluffabout 10m above sea level. The retroreflector wasmounted close to shore in a protective tube about5m above sea level. Both SWIR and MWIR beamspropagated over a common path almost entirely overseawater and were subject to the same atmosphericconditions. The transmitter optics shown in Fig. 3were essentially the same as described in the firstexperiment except that each beam line included anadditional beam splitter (T/R) between the lasersource (S) and the dichroic beam splitter (BS1) toseparate the transmit and return beams. Followingthe T/R splitter, a similar optical arrangement wasused for both the SWIR and MWIR return beamsas follows. A beam splitter (BS2) reflected a fractionof the total returned intensity onto a detector (D2) tomeasure the total returned power. The remainingbeam was focused by L1 and the image was magni-fied by L2 onto the focal plane of the camera (C). Inthe case of the MWIR, the magnification associatedwith L2 was carefully calculated from precise posi-tion measurements and lens specifications. For theSWIR, the magnification M from the focal plane ofL1 to the camera focal plane was directly measured.The total effective focal length of the optical com-bination of the primary mirror and lenses was calcu-lated as f ¼ Mðf p=f sÞf 1;where f s is the focal length ofthe secondary lens (LS). As in the earlier experiment,the telescope was roughly collimated, and the returnsignal from the retroreflector (RR) was maximized byadjusting the beam alignment into the telescope andthe position of the secondary lens. The retroreflectorwas a 6:25 cm diameter hollow corner cube (Newportmodel UBBR2.5-11) with a broadband protected goldcoating (reflectivity >82% from 1–12 μm) and withsurfaces aligned to within 1 arc sec.Three computers were used to control the experi-

ment and to collect data from the cameras and thephotodetectors. Each camera had a dedicated compu-ter to record video data, and the third computer re-corded the transmitted and received signals from thefour photodetectors. The data were recorded asyn-chronously on all three computers, but the systemclocks were manually synchronized to better than1 s prior to each run. The SWIR camera, an IndigoSystems Alpha NIR with a 320 × 256 pixel InGaAsfocal plane array (30 μm pixel pitch), recorded12 bit raw data at 30 frames/s. A 100nm bandpassfilter centered at 1:55 μm was used to block the am-bient background. The MWIR camera was an AmberGalileo with a cooled 128 × 128 InSb focal plane ar-ray that recorded 12 bit data at ∼100 frames/s. Theframe integration times of each camera were lessthan a millisecond, much shorter than the dynamicaltime scales of the atmospheric turbulence.Ideally, the focused images of the return beams

would have been recorded in the absence of turbu-lence in order to show the limiting optical perfor-mance of the source and optical elements. Such

conditions were nearly achieved during one earlymorning test. Prior to the field tests, the beam qual-ity of the focused return was measured in the labora-tory with the retroreflector immediately in front ofthe telescope aperture. Referring to Fig. 3, lensesL1 and L2 were replaced with a single lens with nom-inal focal length of∼20 cm for each beam, and imageswere recorded as the cameras were positioned over arange of distances z from the focus. The variancesσðzÞ2 of the intensity profiles were then calculatedfor each image in the horizontal (x) and vertical (y)directions. The standardM2 analysis of beam qualityassumes that the beam profile is composed of asuperposition of modes from a stable laser cavity,and the spot size WðzÞ ¼ 2σðzÞ is given by [19]

W2ðzÞ ¼ W20 þ

�M2λπW0

�2ðz − z0Þ2: ð5Þ

Calculated values of the overall M2, determined byleast-squares fitting of the data, are given in Table 1.The relatively large values (2.4–2.9) for both wave-lengths were consistent with noticeable aberrationsin the images. Measurements of the second momentsof beam profiles are notoriously sensitive to back-ground levels and beam truncation, and there is con-siderable uncertainty in these values. Beam qualitymeasurements were not made of the isolated sources,but the SWIR source was assumed to be nearly dif-fraction limited because the laser diode output wascoupled into a single-mode fiber. For the SWIR, weattribute essentially all of the aberrations to the op-tical components. On the other hand, the beam qual-ity of the MWIR source must have contributedsignificantly to the overall measured M2.

It is useful to relate the M2 measurements to theStrehl ratio of the optical system in order to predictthe limiting focused spot sizes that could be expectedin the field test configuration without turbulence. Forsmall aberrations, the Strehl ratio of an opticalsystem is given by [20]

SRopt ≈ 1 − k2hΔΦ2i; ð6Þ

whereΔΦ is the aberration of the optical component,and the expectation is weighted by the intensity pro-file across the beam. We also assume that all of theoptical components are effectively in the near-field,and therefore ΔΦ is the accumulated aberrationfunction of all the components. Since the focused pro-files in the M2 tests were nearly Gaussian, we canestimate the two-way Strehl ratio for the SWIR tobe SR2−SW ≈ 1=M2 ¼ 0:40. If we also assume thatthe mean square aberrations for the transmit andreceive paths are equal and add, we estimate theone-way Strehl ratio to be SR1−SW ≈ ð1þ 1=M2Þ=2 ¼0:70. The corresponding Strehl ratios (due to theoptical components) for the MWIR should then begiven by SRMW ≈ 1 − ð1 − SRSWÞðλSW=λMWÞ2. Anestimate of the embedded fundamental Gaussianspot size of the SWIR output beam would be


ωout ≈WoutSR1=21−SW ¼ 2:0 cm. However, the MWIR

fundamental spot size would be largely determinedby the mode quality of the source, and we estimatethat ωout ≈Wout=ðM2

xM2yÞ1=4 ¼ 2:2 cm . All of these va-

lues and the corresponding Rayleigh ranges zR ¼πω2

out=λ are summarized in Table 1.Since zR is substantially less than the distance to

the retroreflector (1:41km), the telescope would havebeen adjusted to give nearly collimated beams in or-der to maximize the return intensity at the telescopeaperture. Some partial clipping of the SWIR beamwould occur at the retroreflector, and therefore thelimiting spot size at the camera would be scaledby a factor intermediate between 1=SR1=2

1−SW ¼ 1:2and 1=SR1=2

2−SW ¼ 1:6. However, the retroreflectorwould significantly clip the MWIR beam. This clean-up effect would effectively strip the higher-ordermodes from the source beam, and therefore the limit-ing spot size at the camera would be approximatelyscaled by 1=SR1=2

1−MW ¼ 1:03. Since both the returnbeams would substantially overfill the telescopeaperture, it is useful to consider the diffraction-limited Airy profile of the receiver given byIAðrÞ ¼ J2

1ð2πar=λf Þ=r2, where a is the 5 cm radiusof the telescope aperture. A Gaussian profile with1=e2 spot radius ω0 ¼ 1:29λf =πa closely approxi-mates the Airy profile and ω0 is used as a referenceparameter in the analysis of the images from the pro-pagation tests using effective focal lengths of 20:5mand 16:15m for the SWIR and MWIR, respectively.The channel propagation tests were conducted on 6

days in the fall of 2007. The times and observedweather conditions of these runs are summarizedin Table 2. During each run, video and signal datawere collected continuously for 10 s on 1-min inter-vals over periods of approximately 1 h. Multiple setsof background data were recorded during the mea-surement periods by blocking the return beamoutside the optics box. In fact, there was no measur-able difference between the background levels re-corded in this manner or by blocking the transmit

beams before the T/R splitter; that is, the backgroundwas electronic rather than optical. There was often anoticeable change in background during the experi-ment, especially from the cooled MWIR camera. Allof the video and photodetector data were correctedby using a background that was obtained from alinear time interpolation between the measuredbackgrounds.

A good visual indication of the relative effect of tur-bulence on the SWIR andMWIR beam images in con-ditions of low and moderate turbulence is shown inFig. 5. These images represent the average intensityof all frames during 10 s of data collection. Note thatthe fringing evident in the SWIR data is an artifactdue to interference within the InGaAs focal plane.The low turbulence images were taken during theearly morning (06:49 on October 17) with light fogand drizzle and no wind. Transmission was impairedbut the weakest turbulence was observed in theseconditions. The effect of turbulence on the SWIRimages is significantly more pronounced than onthe MWIR images.

The size of the focused images was considered to bethe most significant metric to compare the effects ofturbulence on each of the beams. Images in indivi-dual frames varied greatly and were often highlydistorted, but the time-averaged images were ap-proximately Gaussian as expected. Due to the largeamount of data and the number of pixels in eachframe, fitting the image data to a two-dimensionalGaussian function was not practical. Rather, theturbulence-broadened average spot size ω for each10 s of data was calculated by fitting a one-dimensional Gaussian function, e.g., pðxÞ ¼p0 exp½−2ðx − xcÞ2=ω2

x �, to the projection of the imageonto the horizontal and vertical axes in successionand taking ω ¼ ðωxωyÞ1=2. This procedure wasfound to give nearly the same result as a singletwo-dimensional fit. In Fig. 5 a circle representingthe diffraction limited spot radius of the receiverω0 is superimposed at the centroid of each image

Table 2. Summary of Propagation Tests Across the San Diego Bay Channel in the Fall of 2007

Day Time Weather Conditions

17 October 06:39–07:50 Fog and drizzle22 October 09:23–10:33 Multiple fires throughout San Diego county, Santa Ana winds24 October 13:50–14:40 Hazy, visibility less than 6km, smoke and fog covering sky15 November 14:58–15:43 Warm, slightly hazy26 November 09:53–10:38 Cool, slightly hazy29 November 09:34–10:15 Cool, slightly hazy from brush fires, visibility ∼10km

Table 1. Beam Parameters for Propagation Over the 2×1:41 km Round-Trip Path

Wavelength Wout (cm) M2 (2-way)a SRopt (2-way)a SRopt (1-way)a ωout (cm)a πωout2=λ (m)a

1:565 μm 2.4 2.5 (x) 0.40 0.70 2.0 8102.5 (y)

3:603 μm 3.6 2.9 (x) 0.89 0.94 2.2 4302.4 (y)

aStrehl ratios due to one- and two-way propagation through the optical components (SRopt) and the embedded Gaussian beamparameters (ωout) are estimated from laboratory measurements (see text).


and the calculated normalized spot size ω=ω0 is gi-ven. Another measure of spot size is related to theeffective area (Aeff ) of the focused image, defined as

Aeff ¼�Z

Iðx; yÞdxdy�

2=

ZI2ðx; yÞdxdy: ð7Þ

For an elliptical Gaussian beam, Aeff ¼ πωxωy, andgenerally the calculated values of ðAeff=πÞ1=2 werewithin a few percent of ω obtained from the Gaussianfitting procedure and support the assertion that thetime-averaged intensity distributions were nearlyGaussian.The Gaussian fitting procedure described above

was applied to the averaged intensity distributions(10 s duration) for the complete time series of mea-surements, and the values of ω=ω0 are shown inFig. 6. Over a fairly wide range of conditions, theMWIR images were significantly less affected by tur-bulence than the images in the SWIR. The ratio ofthe normalized spot sizes in the SWIR to the MWIRwas found to vary from ∼1:6 to ∼2:5 over the courseof the measurements. According to the theoreticalpredictions of Eqs. (2)–(4), this ratio should be unitywith no turbulence and should asymptotically ap-proach ðλMWIR=λSWIRÞ6=5 ¼ 2:7 at high levels of Cn

2.Further, since Cn

2 should be insensitive to wave-length, the theory and approximations can bechecked for consistency by computing an effective(uniform path) Cn

2 based on the data in Fig. 6. Thesevalues of log½Cn

2� shown in Fig. 7 are generally high-er for the SWIR data, and during the conditions of

least turbulence the discrepancy is ∼0:25. Clearlythe aberrations in the optics had a greater effecton the SWIR beam and were most pronouncedin weaker turbulence. For example, increasinglog½Cn

2� from −14:3 to −14:05 in Eqs. (3) and (4) wouldincrease the SWIR spot size by ∼19%, which is com-parable to the factor (1=SR1=2

1−SW ¼ 1:2) expected fromthe laboratory measurements of the Strehl ratio dueto one-way passage through the receiver for theSWIR beam. Over the course of the experiments,the derived values of log½Cn

2� ranged between∼ − 14:4 and −13:1, corresponding to a Rytov var-iance σ21 ¼ 1:23C2

nk7=6L11=6 that ranged from 0.52 to10.5 for the SWIR wavelength with L ¼ 2:82km.

Since our experiments were carried out over around-trip path using a corner-cube retroreflectorwith finite aperture, the theory based on Eqs. (2)–(4) is not directly applicable. Although theoreticaltreatments of optical propagation in atmosphericturbulence of partially coherent beams [21] and of co-herent beams over a round-trip path [22] have beenpublished, reasonably simple expressions that couldbe used in place of Eqs. (2)–(4) are apparently not

Fig. 5. (Color online) Typical images of the SWIR and MWIR fo-cused beams, averaged over 10 s, in low turbulence (top) and mod-erate turbulence (bottom). The calculated diffraction-limited spotis shown as a circle with radius ω0, and the normalized spot sizesbased on a Gaussian fit are given.

Fig. 6. (Color online) Normalized image spot sizes (ω=ω0) aver-aged over 10 s during 5 days of measurements for the SWIR (cir-cles) and the MWIR (squares).

Fig. 7. (Color online) Cn2 calculated for the SWIR (circles) and

the MWIR (squares) from spot size data in Fig. 6 using Eqs. (3)and (4).


available. In particular, there would be some correla-tion of the turbulence over the outward and inwardpaths, even considering the transverse inversion ofthe path due to the retroreflector. Also, the finiteaperture of the retroreflector would apparently miti-gate the effects of turbulence differently for eachbeam. Therefore the absolute values of Cn

2 derivedfrom the approximate theory using a single path of2:82km are probably systematically in error. How-ever, the ratios of the measured spot sizes are consis-tent with the simple theory if the effects of opticalaberrations are considered.Another critical issue for communication or laser

radar systems is related to the fluctuation in the po-sition of the image centroid around the long-timeaverage, since this can affect system efficiency basedon the overlap integral defined by Eq. (1). The posi-tion of the image centroid is related to the averageangle of arrival, or average phase gradient, of thereceived beam across the telescope aperture. For in-finite spherical waves in uniform Kolmogorov turbu-lence, the variance of the angle of arrivalσ2β ¼ 1:093C2

nLD−1=3 is not sensitive to wavelengthwhen the Fresnel zone ðλz=2πÞ1=2 ≪ D, the aperturediameter [2]. For these measurements, ðλz=2πÞ1=2 ¼1:1 cm and 1:6 cm based on the round-trip path L ¼2:82km for the SWIR and MWIR, respectively. Thetheoretical variance is larger for infinite plane wavesin similar conditions, σ2β ¼ 2:914C2

nLD−1=3. There is anatural advantage at longer wavelengths, since thestandard deviation of the position of the centroidσc ¼ σβf , normalized to the diffraction-limited scaleof the optical system σc=ω0, should scale as 1=λ. Val-ues of σc=ω0 shown in Fig. 8 were calculated for allthe frames collected during the 10 s periods duringthe series of experiments. It is interesting to notethat the measured wavelength ratio of the normal-ized centroid wander was often significantly largerthan λMWIR=λSWIR ¼ 2:3. A partial explanation mightbe that because the Rayleigh range is smaller for theMWIR beam, σβ is more characteristic of a spherical

wave. We note that for a finite beam wave, the the-oretical expression for σβ2 leads to values intermedi-ate between the spherical wave and plane wavecases [23].

5. Summary

The issues related to laser propagation in the SWIRand MWIR for surveillance or communication appli-cations based on atmospheric transmission and tur-bulence are discussed, and experiments to measurethe effects of turbulence on laser propagation in low-altitude maritime environments are described. Sin-gle-frequency coherent laser sources at 1:565 μmand 3:603 μm were coupled into a common aperturetelescope and propagated along a 1:26km path overland and a 2:82km round-trip path over water in twoseparate tests. We observed scintillation or normal-ized intensity variance that ranged from ∼0:25 to∼2:5 in the SWIR. The scintillation in theMWIR var-ied between ∼30% and ∼70% of the SWIR values.Focal plane images of the propagated beams werealso recorded. Long-term (10-s) spot sizes (normal-ized to the diffraction-limited spot size) were ob-served to be 1.6 to 2.5 times larger for the SWIRthan for the MWIR beam. It is likely that aberrationsin the optical components led to significantly greaterdegradation of the SWIR beam. In conditions ofweaker turbulence, these aberrations were the limit-ing factor in the quality of the focused SWIR imagesbut only had aminor effect on theMWIR images. Thevariance of the short-term absolute angular jitter ofthe image centroids was also significantly larger forthe SWIR beam. These measurements support theo-retical predictions that in a wide range of conditionsthere can be significant practical advantages for pro-pagation in theMWIR rather than the SWIR becausethe longer wavelength is less sensitive to atmo-spheric turbulence and the aberrations of opticalcomponents.

We are grateful for support from Dr. Stephen Pap-pert and the Defense Advanced Research ProjectsAgency (DARPA), which funded this work, and forhelp from Richard Bates in designing and buildingequipment used in the field tests.

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Laser propagation at 156 μm and 360 μm in maritime environments

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