Temporal Response of the Underwater Optical Channel ... - IEEE Xplore

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IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 38, NO. 4, OCTOBER 2013

Temporal Response of the Underwater Optical Channel for High-Bandwidth Wireless Laser Communications Brandon Cochenour, Member, IEEE, Linda Mullen, Senior Member, IEEE, and John Muth, Member, IEEE

Abstract—This paper describes a high-sensitivity, high-dynamic range experimental method for measuring the frequency response of the underwater optical channel in the forward direction for the purpose of wireless optical communications. Historically, there have been few experimental measurements of the frequency response of the underwater channel, particularly with regard to wireless communication systems. In this work, the frequency response is measured out to 1 GHz over a wide range of water clarities (approximately 1–20 attenuation lengths). Both spatial and temporal dispersions are measured as a function of pointing angle between the transmitter and the receiver. We also investigate the impact of scattering function and receiver field of view. The impact of these results to the link designer is also presented. Index Terms—Communications, laser, optical, propagation, scattering, underwater, wireless.

I. INTRODUCTION

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S the proliferation of unmanned and autonomous underwater vehicles and sensors grows, so does the need to wirelessly transmit data to and from these platforms. While acoustic links have generally dominated the field of wireless communications undersea, they are fundamentally bandwidth limited. Laser links have garnered significant interest as they may provide several orders of magnitude more bandwidth than acoustic technologies can provide. However, compared to acoustics, optical links are limited to much shorter link ranges, and vary from approximately 100 m in clear open ocean waters, to just a few meters in more turbid littoral waters. Clearly, the propagation of light in the ocean is tied closely to water optical properties. In particular, optical propagation is complicated by absorption and scattering of light by ocean particulates. Combined, these two processes represent the total attenuation coefficient . The attenuation of the remaining nonscattered and nonabsorbed light is given as Beer’s law: where is the received power, is the transmitted power, and the argument is the attenuation length, where is the Manuscript received November 01, 2012; revised March 07, 2013; accepted March 25, 2013. Date of publication July 25, 2013; date of current version October 09, 2013. Guest Editor: M. Porter. B. Cochenour and L. Mullen are with the Naval Air Systems Command, Patuxent River, MD 20670 USA (e-mail: [email protected]). J. Muth is with the Electrical Engineering Department, North Carolina State University, Raleigh, NC 27607 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JOE.2013.2255811

physical range. Absorption is the dominant source of loss in the clear waters of the deep open ocean. These links are typically characterized as “photon limited.” Absorption can be minimized by operating in the blue/green portion of the spectrum. Longer ranges [or better signal-to-noise ratio (SNR)] may be achieved with higher powered optical sources or photodetectors with high responsivity. However, photon-limited links are ultimately limited by the exponential attenuation of the channel. In turbid littoral waters, scattering is the dominant source of attenuation. These environments are classified as “dispersion-limited” links. Two types of dispersion exist. The first type is spatial dispersion, where photons are scattered away from the initial beam path. Spatial dispersion is observed by noting changes in the average [or direct current (dc)] received intensity. For the application of wireless underwater optical links, information is encoded by changes in intensity (pulsed or modulated). Depending on the extent of spatial dispersion, as well as link geometry or other system variables, path length differences between scattered photons may arise. These path length differences between scattered photons, or between scattered and nonscattered photons, result in temporal dispersion. Temporal dispersion can be thought of as a form of intersymbol interference as the time-varying [or alternating current (ac)] intensity is received with less fidelity. Clearly, both spatial and temporal dispersions stand to limit link range and bandwidth. It is crucial to recognize that, unlike the photon-limited link, the dispersion-limited link cannot be improved by higher transmit powers or more efficient photoreceivers. Temporal dispersion fundamentally bandlimits the underwater optical communications channel. Historically, experimental measurements investigating forward scattering of optical beams underwater have favored spatial dispersion. The 1960s and 1970s produced the widely cited works of Duntley [1], Petzold [2], and Jerlov [3], all of whom presented comprehensive measurements of light attenuation undersea as functions of range, turbidity, geometry, and system variables, such as receiver field of view (FOV) or transmit intensity distribution. Limitations in source and receiver technology limited temporal dispersion measurements, particularly underwater. Few measurements that were reported were made mostly in the atmospheric channel (through fog, clouds, and rain), but were also technology limited in either dynamic range or temporal resolution. Snow et al. [4] and Longacre et al. [5] reported on some of the first experimental measurements on the temporal dispersion of forward-scattered light underwater in the early

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COCHENOUR et al.: TEMPORAL RESPONSE OF THE UNDERWATER OPTICAL CHANNEL FOR HIGH-BANDWIDTH WIRELESS LASER COMMUNICATIONS

1990s. Their work showed that tens of megabits per second were possible, even in turbid waters in line-of-sight (LoS) configurations. However, the speed of the photoreceiver limited investigation to 100 MHz. Hanson and Radic used a laser source derived from a continuous-wave (CW) laser at 1064 nm, which was intensity modulated using a high-speed telecom Mach–Zender modulator, and then frequency doubled to 532 nm [6]. This provided channel measurements up to 1 GHz (limited by the photoreceiver response). Their experiments (and subsequent Monte Carlo simulations) showed error-free transmission of 1 Gb/s pseudorandom data over . Unfortunately, the experimental setup was “geometry limited” in that their medium was a 2-m-long, 4-in-wide, water pipe with windows on opposite ends. This meant that only on-axis phenomenon could be measured, and that the narrow pipe diameter may have influenced the spatial (and, hence, temporal) dispersion observed. Cochenour et al. have studied temporal dispersion at frequencies 100 MHz over short ranges and very high turbidities [7], [8], as well as spatial dispersion and overall attenuation [9], [10] as a function of range and pointing accuracy. Dalgleish et al. [18] recently studied temporal dispersion using a 500-ps pulsed laser. Experiments were conducted in a test tank measuring 12.48 m in length, with turbidity controlled via calibrated laboratory scattering agents. These experiments utilized a high-gain/high-bandwidth photoreceiver in the form of a microchannel plate photomultiplier tube (PMT). Dalgleish et al. also made measurements of pulse spreading at distances up to 1 m away from the beam axis (approximately 3 ). Pulse spreading was observed with a full-width half-max of 700 ps ( 1.4 GHz) with 0.4/m and 2 ns (500 MHz) at 2.0/m . The experimental results found good agreement to a Monte Carlo model, except at high turbidities, possibly due to the inclusion of extra scattering contributions of the tank walls in the experiment. Mullen et al. described an experimental technique to measure the frequency response of modulated light in turbid waters out to 1 GHz [11]–[14] in a LoS geometry. The experimental results have also been used to validate a Monte Carlo model by Li et al. [15], [16]. Measurements were performed in experimental test tanks of 3.66 and 7.6 m, using calibrated laboratory scattering agents to increase water turbidity up to . The experiments utilized a high bandwidth PMT, which provided gains of 10 , a 25-mm aperture, and electrical bandwidths out to 1 GHz. Mullen’s laboratory measurements have included investigations with polarization as well as the effect of water optical properties such as scattering albedo and volume scattering function. However, they did not include a study of system variables (such as receiver field of view) or geometry (measurements were only made along the beam axis, LoS). Using a similar technique, the frequency response of diffuse light was presented in [17]. In this paper, we aim to expand these previous LoS measurements to study what effect off-axis viewing (transmitter/receiver pointing accuracy), receiver FOV, and scattering particle have on temporal dispersion. A review of the measurement technique used by Mullen (borrowed from Gloge et al. [19] and Helkey et al. [20]) is presented first. This method provides a large measurement dynamic range and excellent sensitivity over a large

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frequency bandwidth out to 1 GHz. A large dynamic range is needed to fully characterize the channel over a wide range of water turbidities (in this work, out to attenuation lengths). It is believed that the experimental results presented here will be of great use to the link designers, communication engineers, and theoretical modelers who are involved with underwater optical wireless communications. II. EXPERIMENTAL TECHNIQUE A. Broadband Signal Generation A common technique in acoustic channel sounding is to create a wideband signal by modulating a pseudorandom code onto an acoustic carrier, and to then perform a correlation between the received signal and a local copy. However, “wideband” for acoustic channels can be a few megahertz or less. For an optical link, which may provide bandwidths out to 1 GHz under certain conditions, the term “wideband” has a decidedly different meaning. Unfortunately, due to limitations in laser and/or modulator technologies, it is difficult, if not impossible, to develop a high power blue/green laser source that can be continuously modulated using a pseudorandom code with the speeds necessary ( GHz) to perform measurements analogous to the acoustic technique. To synthesize a wide-bandwidth signal for optical channel sounding, we borrow a technique from [19] and [20], which has been used with prior success for underwater optical measurements in [11]–[14]. This technique uses a mode-locked laser (MLL) source which outputs a Gaussian pulse train given by

(1) where is the average optical power, is the pulse repetition period, and is the Gaussian pulse time constant. Recall that the Fourier relationship between a train of Gaussian pulses in the time domain is itself a train of pulses in the frequency domain, where the frequency impulses are spaced at harmonics of the laser repetition rate . After photodetection, the frequency spectrum of the received electrical signal is given as (2) where is the electrical power at frequency , is the load resistance, and is the detector responsivity. The average, or dc component is . For a narrow pulse width (on the order of 10 ps), the exponential term on the righthand side is approximately unity for 1 GHz. Expressing (2) then in terms of voltages results in (3) Hence, the MLL pulse train (1) can be used to generate a signal with a broad frequency content (2) where the ac harmonics have amplitude equal to the root mean square (RMS) voltage (3). Observation of the dc (i.e., time average) component provides insight into the spatial dispersion of the channel. Observation of the ac (i.e., time varying) component describes the degree of

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temporal dispersion. In a dispersive medium, both the dc and ac components will attenuate due to absorption and scattering. However, the ac component may experience additional attenuation as the path length differences between multiple-scattered photons result in a loss of coherence. Recall that we speak not of optical coherence, but rather the coherence of the time-varying intensity modulation placed upon the optical carrier. Shorter modulation wavelengths will be more susceptible to destructive interference arising from the path length differences between nonscattered, single-scattered, and multiple-scattered light. The modulation depth is defined as the ratio between the average received signal and that which has retained modulation. In terms of the received voltages in (3) (4) This relationship between the modulated (i.e., the information bearing) component and the average component provides a straightforward way of measuring the frequency response of the channel.

Fig. 1. Experimental setup. The transmitter and the receiver are placed behind opposite facing windows. Tank geometry allows for the beam to be deflected up 30 . to

B. Experimental Setup A diagram of the experimental setup is shown in Fig. 1. The test tank is 7.62 m in diameter and 3.65 m in height. A transmissometer is used to measure the beam attenuation coefficient at 532 nm. In this study, one of two scattering agents is used to vary the turbidity: magnesium hydroxide [Mg(OH) ], and Coarse Arizona Test Dust (ISO 12103-1, A4 Coarse Test Dust, or ATD). The scattering albedo, or ratio between the scattering coefficient and overall attenuation, is large for each agent . The scattering phase function of each agent is measured in the near forward direction with a LISST-100 (Sequoia Scientific, Bellevue, WA, USA), and is shown in Fig. 2, along with Petzold’s turbid water phase function [2]. The scattering phase function is a common inherent optical property which describes the probability of light scattering into a particular angle given a single-scattering event. Note that Fig. 2 illustrates that, for the large particle scattering that occurs in seawater, scattering events favor very small angles near the beam axis. Understanding the preference of individual scattering events provides insight into the nature of spatial and temporal dispersion over many scattering events. Section IV will explicitly show how certain properties of the phase function influence each type of dispersion. The laser source is a diode pumped solid-state MLL frequency doubled to 532 nm with an average power of 4 W at 532 nm. The pulse width is 10 ps with a repetition period of 10 ns. This results in frequency harmonics spaced evenly at 100 MHz. A small mirror placed on a motorized rotation stage is situated at the tank input window, which allows for the beam to be scanned 30 (in water) off alignment with the photoreceiver. The photodetector, a Photonis 37303 five-stage, high-speed, PMT is placed behind a window on the opposite side of the tank. The PMT has a 25-mm aperture, but has been specifically designed to achieve 3-dB bandwidths out to 1 GHz. An optical front end consisting of a 50-mm #f/2 lens and iris are used to control the FOV between 1 and 7 (measured

Fig. 2. The scattering phase functions of Mg(OH) , ATD, and Petzold’s turbid water. The phase function can be interpreted as the probability distribution of a single-scattering event.

in air). A 532-nm optical interference filter is used to reject ambient light. Dynamic range is controlled by adjusting transmit power, or by using neutral density filters at the receiver. A bias tee placed after the PMT separates the ac and dc components of the received signal. The dc component is measured with a multimeter, while a microwave spectrum analyzer is used to measure the ac component at the individual frequency harmonics of the mode-locked pulse train. The resolution bandwidth (RBW) of the spectrum analyzer is normally set at 5 kHz, but can be lowered to 1 kHz in turbid waters where the signal level is low. The ability to narrow the measurement bandwidth while still making measurements at high frequencies is a benefit to such frequency domain measurements. Capturing the ac and dc components simultaneously allows for easy calculation of the modulation depth as a function turbidity, FOV, Tx/Rx alignment, and scattering agent. The ac response on-axis in clear water is used as a system calibration, and accounts for any slight variations


Fig. 3. The amplitude and modulation depth as a function of Tx/Rx alignment for (a)–(b) , (c)–(d) point in the modulation depth plots. dotted line represents the dc signal level in the amplitude plots, and the

in the frequency response of the PMT, microwave components, cables, etc. Since the on-axis clear water response is unaffected by any scattering, this serves as an appropriate way to subtract out the system response from the rest of the data. It also means that any subsequent changes in are solely due to the environment.

, and (e)–(f)

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. The

All ac and dc voltages are also normalized relative to this clear water response according to

(5)

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Fig. 4. The dc and ac amplitudes and modulation depth as a function of attenuation length for several frequencies at (a)–(b) 10 , and (g)–(h) 30 .

where ac or dc. The first term on the right-hand side of (5) normalizes all the amplitudes to the clearest water investigated in this study . The second term

0 , (c)–(d)

1 , (e)–(f)

simply accounts for Beer’s law, since the transmitted signal experiences a small amount of loss even in clear waters .


III. SPATIAL AND TEMPORAL DISPERSION OF A COLLIMATED BEAM FOR A SINGLE-SCATTERING AGENT AND RECEIVER FOV This section presents results for a collimated beam, where Mg(OH) is used as the scattering agent. The receiver FOV is 7 , full angle. The scattering function of Mg(OH) has been previously shown in Fig. 2. A. Results as a Function of Tx/Rx Geometry The amplitudes of the dc and ac components (at 100 MHz, 300 MHz, 500 MHz, 700 MHz, and 1 GHz) and modulation depths versus pointing angle at , and are shown in Fig. 3. The dc component includes the factor of as per (4). The dotted horizontal line in the modulation depth plots represents , a metric that describes where the modulation depth is reduced by half (equivalent to a 3-dB point). In clear waters [Fig. 3(a)], the amplitude distribution of both dc and ac components is very sensitive to . As turbidity increases [Fig. 3(c) and (e)], changes in amplitude as a function of position decrease, as the multiple scattering makes the beam more diffuse. There is also a loss of ac amplitude at these turbidities. For , the frequency dependence occurs mainly at distances away from the main beam 0 , while for , the frequency dependence is observed over all positions (even on-axis). This loss of ac signal relative to the dc average results in a loss of modulation depth [Fig. 3(d) and (f)]. The modulation depth decreases as a function of increasing frequency and increasing distance from the beam axis. These results are a direct consequence of the scattering phase function, which favors scattering events at small angles. In clear water , there is a significant drop in amplitude away from the beam axis, since the probability of scattering at large angles is low and there is little multiple scattering. This means that the modulation depth is fairly well maintained despite the large amplitude variations. At a higher turbidity such as , the modulation depth is maintained near the beam axis, since even in multiple-scattering environments, a peaked phase function results in little appreciable path length differences between small-angle multiple-scattered photons. However, far from the beam axis, the collection of large-angle, multiple-scattered light introduces temporal dispersion and a subsequent loss of modulation. At , the high turbidity causes multiple-scattered light to dominate in all positions, even on-axis. This results in temporal dispersion and a loss of modulation depth at all locations. B. Results as a Function of Attenuation Length It is also useful to examine the results as a function of attenuation length. Fig. 4 shows the dc and ac amplitudes as well as the modulation depth as a function of attenuation length for several frequencies at a specific . Each graph is a different receiver angle . The discussion is segmented to focus on two regions: on-axis 0 , and off-axis 0 . 1) On-Axis 0 : The amplitude of the dc and ac components as a function of attenuation length at the beam axis 0 is shown in Fig. 4(a). Also shown is the attenuation predicted by Beer’s law (dotted line). Note that attenuation of both dc and ac components follows Beer’s law (an attenuation

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of approximately 4.34 dB/ ), until (as noted in the plot). Additionally, Fig. 4(b) shows that no modulation depth is lost for . Both results suggest that, for these attenuation lengths, the received signal is dominated by nonscattered light. For , the dc component in Fig. 4(a) attenuates at a lower rate of 1.4 dB/ . Here, the amplitude attenuates slower than predicted by Beer’s law due to the additional collection of multiple-scattered light that scatters back into the receiver FOV. This transition between nonscattered attenuation and multiple-scattered attenuation has previously been observed in the study of optical communications through fog in the atmosphere [21]. However, those prior investigations considered only the average (dc) behavior. Fig. 4(a) also shows the attenuation of each of the ac components, and represents a new result relative to the prior knowledge regarding how multiple scattering affects the time-varying (and information bearing) portion of the optical signal. Note that as the frequency increases, the rate of attenuation approaches that predicted by Beer’s law. This indicates that, at high frequencies, any modulated light that is received (i.e., that has retained its modulation) is also that which has been minimally scattered. It is also observed that, for , modulation depth is lost, but at different rates depending on the frequency. This is a direct result of the behavior of the rate of attenuation of the individual radio-frequency (RF) amplitude components in Fig. 4(a) in the same region. The location of this transition is not arbitrary and can be predicted based on the optical properties of the water. More specifically, the diffusion length has been used by researchers as a convenient way to describe different scattering regimes [22]–[24]. The diffusion length is an average physical distance (projected onto the axis of initial direction) that an average amount of photons travel before a “forward trajectory” is lost due to multiple scattering. It is given by (6) Recall that is the scattering coefficient ( is the scattering length), and is the average cosine of the scattering phase function, given as (7) The average cosine essentially describes the prolated nature of the scattering phase function . It may also be convenient to express (6) in terms of the scattering albedo (or ratio of the scattering coefficient to the total attenuation) (8) Despite its name, the reader is cautioned that the diffusion length does not imply a total isotropic scattering condition, particularly underwater. Lerner and Summers [24] found via Monte Carlo simulations that, at one diffusion length, while many photons are multiple scattered, a majority still have a forward trajectory. Additionally, Bucher [23] found that it took two to three diffusion lengths before propagation behaved in a truly diffuse manner underwater. Each conclusion is the result of a highly

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Fig. 5. The dc and ac amplitudes, and modulation depth, as a function of attenuation length for several positions at (a)–(b) 100 MHz, (c)–(d) 500 MHz, and point in the modulation depth plots. (e)–(f) 1 GHz. The dotted line represents the dc signal level in the amplitude plots, and the

peaked phase function which tends to keep scattering events close to the beam axis. To determine the number of attenuation lengths at which the diffusion length condition is reached, all that is needed is the scattering albedo and average cosine. The scattering albedo of Mg(OH) is . Calculation of the average cosine of Mg(OH) , however, is more difficult as the LISST-100 provides only the first 10 of the phase function, resulting in the inte-

gral calculation in (7) to be overestimated. As an alternative, the average cosine of Mg(OH) was estimated using the similarly peaked turbid water phase function from Petzold [2], which has been measured over the full 180 . This results in an average cosine of . Substituting these values into the above equation and rearranging terms results in , which shows excellent agreement to the transition noted in the data. In other words,


Fig. 6. The modulation depth as a function of position . (c)

for two different scattering agents, MgOH (solid) and ATD (dashed), at (a)

for , nonscattered and minimally scattered light is expected to dominate. For , multiple-scattered light can be expected to dominate. This suggests that appears to be a useful metric in determining not only a change in behavior of average attenuation (i.e., spatial dispersion), but also for describing attenuation of modulated light and modulation depth (i.e., temporal dispersion). Finally, we note that estimating the average cosine of the MgOH phase function using Petzold’s turbid water phase function appears valid despite differences in shape between their forward peaks (see Fig. 2). This is not to say that the specific shape of the phase function does not matter (Section IV will examine this more). Rather, it only suggests that for the simple purpose of determining the transition between nonscattered dominated and multiple-scattered dominated propagation, it is sufficient to simply assume that the phase function is highly peaked (i.e., has a large average cosine). The interested reader may be further convinced of this fact by noting that the three disparate water types measured by Petzold (open ocean, coastal, and turbid harbor) all have relatively similar average cosines [2]. The scattering albedos, however, are quite different. While scattering albedo was not a variable in this work, the authors have previously examined the impact of this variable on temporal dispersion in [14]. 2) Off-Axis 0 : At the off-axis positions in Fig. 4(c)–(h), the behavior is markedly different. Clearly, Beer’s law is not valid off-axis. Note that differences between the ac and dc components begin to occur at shorter attenuation lengths with increasing distance from the beam axis. A corresponding change in the transition between and is also observed. This is because off-axis, multiply scattered light is likely to have undergone at least one large-angle scattering event, and several other small-angle multiple scattering events. Therefore, fewer scattering events are needed to accumulate the path length differences necessary for modulation loss. These trends are also summarized in Fig. 5, where the amplitudes and modulation depth at 0 , 1 , 10 , and 30 are plotted versus attenuation length for 100 MHz [Fig. 5(a)–(b)], 500 MHz [Fig. 5(c)–(d)], and 1 GHz [Fig. 5(e)–(f)]. Note how the transition attenuation length (and subsequent rate of modulation loss versus ) at each position varies with increasing frequency.

, (b)

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, and

C. Summary This section presented some basic relationships between the propagation of modulated and nonmodulated light in turbid environments. Section III-A showed that, in clear waters, there is little or no temporal dispersion, even though there is a significant amplitude variation with transmitter/receiver alignment. As turbidity increases, the amplitude is less sensitive to position, but more sensitive to temporal dispersion (i.e., modulation loss). As a result of the peaked scattering phase function, modulation is well preserved for moderate turbidities near the beam axis, while away from the beam axis, modulation depth loss is frequency dependent due to the collection of multiple-scattered light. At extreme turbidities, modulation loss is observed at all positions since the light field is composed of mainly multiple-scattered light. Section III-B quantified this behavior as a function of attenuation length. On-axis, nonscattered light dominates for , which was defined as a function of inherent optical properties. For , multiple-scattered light dominates, as evidenced by a slower rate of attenuation in the dc component and a loss of modulation depth for the ac components. High-frequency components (approaching 1 GHz) are found to attenuate at a rate similar to Beer’s law, suggesting that, on-axis, any modulated light remaining at high turbidities is likely to be minimally scattered. At large , the behavior can be quite different, as Beer’s law is not valid in any sense. Away from the beam axis, the collection of multiple-scattered light results in a higher probability of modulation depth loss. It was also shown that the transition between minimally scattered and multiple-scattered photon dominated regimes moves to lower attenuation lengths as the angle between the receiver and main beam is increased. This makes intuitive sense since multiple-scattered light is more likely to dominate at lower attenuation lengths as the distance from the main beam increases. Regardless of , the frequency response of multiple-forward-scattered light exhibits a lowpass response as a function of frequency, since shorter modulation wavelengths are more susceptible to the path length differences associated with the time spread of multiple-scattered light. Finally, it should be mentioned, particularly in the case of the large attenuation lengths studied in these experiments, that the

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Fig. 7. The modulation depth as a function of attenuation length for ATD (solid) and Mg(OH) (dashed) at 100 MHz (red), 500 MHz (blue), and 1 GHz (black) 0 , (b) 1 , (c) 10 , and (d) 30 . The dotted horizontal line represents . at (a)

scattering albedo (i.e., ratio of scattering to total attenuation) of Mg(OH) is rather high . In real ocean environments, higher levels of absorption are usually observed. Therefore, for an equivalent attenuation length, additional absorption (and less scattering) will likely lead to less temporal dispersion. Previous work by the authors at short ranges, examining only on-axis propagation, has shown that, for the same attenuation length, a decrease in scattering albedo (i.e., an increase in absorption relative to scattering) suppresses scattered light [10] and ultimately results in less temporal dispersion [14]. One may expect the same to be true off-axis as well. IV. INFLUENCE OF SCATTERING PARTICLE Section III has shown how temporal dispersion in underwater optical links is closely tied to geometry and turbidity. In general, light collected in a LoS geometry is resilient to temporal dispersion up to a diffusion length, at which point multiple-scattered light dominates. Moving away from the beam axis results in greater sensitivity to temporal dispersion depending upon the distance and the amount of multiple scattering. These are all di-

rect consequences of the shape scattering phase function, which has been shown to favor scattering events at near forward angles. It is worthwhile then to investigate to what extent small changes in the shape of the phase function shape at small forward angles influence these previous results. In this section, two different scattering agents, Mg(OH) and ATD, are investigated. The phase functions of each agent were measured with a LISST-100 scattering instrument between 0 and 10 , and were shown in Fig. 2. Recall that the phase function is an inherent optical property that can be interpreted as a probability distribution of a single photon scattering event into a given angle. Note then that the ATD particles tend to scatter light into near forward angles more than MgOH . This would suggest that, for a given geometry and turbidity, received light collected after propagating in ATD waters should be more resilient to temporal dispersion, since more scattering will be contained closer to the beam axis than MgOH . Indeed, the results show that this is true. Fig. 6 shows the modulation depth as a function of at , and . These turbidities are shown as they represent measurements


Fig. 8. The dc and ac amplitudes for the nFOV (solid lines) and wFOV (dashed lines) as a function of position

for (a)

and (b)

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agent at 100 MHz, 500 MHz, and 1 GHz. Each subgraph is a different pointing angle . Fig. 7(a) shows the results at 0 . Note that for each scattering agent occurs at approximately the same location . The results also confirm that modulation depth is maintained better in ATD enhanced waters due to the more highly peaked phase function. A. Discussion

Fig. 9. The frequency at which the modulation depth is reduced by half, , plotted as a function of position for wFOV (dashed) and nFOV 0 1 10 , and 30 are shown. MgOH is the (solid). The results at scattering agent.

made at turbidities lower than a diffusion length, at a diffusion length, and greater than a diffusion length. The modulation depth versus pointing angle is shown for 100 MHz, 500 MHz, and 1 GHz for both ATD (dashed lines) and Mg(OH) (solid lines). In all cases, ATD enhanced waters maintain modulation depth better than Mg(OH) enhanced waters. This indicates that subtle variations in the shape of the forward peak of the scattering phase function do indeed influence temporal dispersion, as originally posited. Additional insight is gained in Fig. 7 by plotting the modulation depths as a function of attenuation length for each scattering

We can now make several assertions regarding the influence of scattering function on temporal dispersion. It was previously shown that the diffusion length , which is itself a function of the scattering albedo and the average cosine , can be used to predict the transition between nonscattered and multiple-scattering regimes. In this case, it was not necessary to know the exact phase function shape, as the average cosine can be estimated by simply assuming that the phase function is sufficiently peaked in the forward direction. It is further suggested that this transition is likely to be more sensitive to the scattering albedo. It is of little surprise then that Fig. 7 also shows that, regardless of the scattering agent (i.e., scattering phase function), the attenuation length at which the modulation depth begins to decrease from unity is similar between scattering agents. However, the new information that this section illustrates is that, once the multiple-scattering regime is reached, the forward shape of the phase function does in fact influence the rate at which modulation depth is lost. Therefore, we can conclude that the degree at which the link designer must characterize the scattering function is dependent upon the level of detail at which temporal dispersion is important. If the link designer is only concerned with determining at what attenuation lengths (i.e., what turbidities or physical ranges) the link may be able to operate “dispersion-free,” then it is sufficient to only obtain the scattering albedo and a coarse estimate of the average cosine. However, if the operation in multiple-scattering regimes is anticipated, then the designer must be cognizant of the extent of temporal dispersion, since it will ultimately change the channel bandwidth. This section has shown that to determine the rate at which the modulation depth at a

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specific frequency will then be lost, a more detailed characterization regarding the forward peak in the phase function shape is required. V. INFLUENCE OF RECEIVER FOV This section examines the impact of a receiver FOV on spatial and temporal dispersion. The test geometry remains the same, and MgOH is used as the scattering agent. The results are compared for a wide field of view (wFOV) of 7 and a narrow field of view (nFOV) of 1 . Varying the FOV can have two impacts with regards to dispersion. It can raise or lower the signal level as more or less light is collected with the acceptance angle. Additionally, widening or restricting the FOV can change the amount of temporal dispersion in the received signal, depending on the extent of multiple scattering. This section will show that there are only certain cases where this conventional thinking is valid. Fig. 8 shows the dc and ac amplitudes (at 100 MHz, 500 MHz, and 1 GHz) for each FOV as a function of position. Fig. 8(a) shows the results at , while Fig. 8(b) shows the results at . Note that widening the FOV has no impact on-axis 0 , but raises the signal level off-axis 0 . This suggests that, regarding the amplitude, widening the FOV only results in a signal level increase when multiple-scattered light dominates. On-axis, where nonscattered light dominates, the addition of minimally scattered light with increasing FOV does not appreciably change the signal level. This is not a surprising result, since each graph in Fig. 8 is for . For , where multiple-scattered light makes significant contributions, the on-axis amplitude is expected to be sensitive to FOV. Next, the influence of FOV on temporal dispersion is explored. Fig. 9 plots as a function of attenuation length for several pointing angles. In showing the attenuation length at which the modulation depth is reduced by half, we have arrived at a qualitative measure of channel response, similar to a “ 3-dB point” or “corner frequency.” The data reveal several interesting behaviors, namely that the point (i.e., temporal dispersion) is only sensitive to FOV near the beam axis, and only then at very high turbidities. It is only at very large attenuation lengths that the nonscattered, minimally scattered, and multiple-scattered components become comparable in amplitude, leading to a sensitivity of temporal dispersion to receiver FOV. Moving away from the beam axis, the point for a given frequency occurs at lower attenuation lengths, which is consistent with previous results describing the behavior of multiple-scattered light. However, it is also observed that the sensitivity of temporal dispersion to FOV decreases with larger . For example, at 30 , there is very little change between the curves for each FOV. This is an interesting, albeit counterintuitive, result as common thought suggests that collecting more scattered light with a larger FOV should reduce the temporal fidelity. The results show, however, that there is a strong directional dependence that one must consider. For example, at distances farther from the beam axis, there exists a “temporal homogeneity” of multiple-scattered light, which causes the modulation depth to be insensitive to the receiver acceptance angle. By “temporal homogeneity,” we mean that all of the photons collected within

the FOV at large distances from the beam axis have similar temporal properties, since all scattered photons have scattered approximately the same number of times to reach the off-axis location. VI. IMPACT ON THE LINK DESIGNER It is worthwhile to consider in totality how the results presented in this paper will impact the link design. In general, we have shown that spatial and temporal dispersions are linked through water optical properties, link geometry, and system variables. This section attempts to quantify some of the previously illustrated trends. Fig. 9, which showed the frequency as a function of attenuation length for various pointing regimes, can be a useful tool in managing the trade space that the link designer has available. Consider the plane of Fig. 9 as the entire trade space of modulation frequencies available over the range of all attenuation lengths. The curves of at a given pointing accuracy serve to partition this trade space into regions where reception is or is not influenced by temporal dispersion. If a transceiver has a pointing accuracy of 10 , then the region below and to the left of the curve represents all conditions where temporal dispersion does not play a role. (In other words, 100 MHz is supported for all , 300 MHz for all , 500 MHz for all , etc.). Conversely, the region above and to the right of a given curve represents the conditions where temporal dispersion will have considerable impact on the given pointing accuracy. If higher bandwidths, longer ranges, or the operation in more turbid waters is desired, then one must improve the pointing accuracy (which thereby makes more of the trade space available). Naturally, the best frequency response in the most turbid waters is achieved when the transmitter and the receiver are precisely aligned 0 , which is where nonscattered collection is most likely to occur. These curves represent a bound where the greatest amount of the trade space is available. Of course, Fig. 9 describes only the temporal behavior for a given condition. Even if the designer has determined that temporal dispersion will not be an issue, they must still verify that enough photons have been collected to achieve the desired SNR. To this end, Fig. 10 plots the dc (average) signal level at the attenuation length where occurs for each frequency (i.e., at each point in the curves of Fig. 9). Fig. 10 can be interpreted as the dynamic range required by a transceiver to achieve the widest range of attenuation lengths for a given bandwidth and pointing angle as indicated by Fig. 9. As a reminder, the amplitude is a measure of the received voltage (or received optical intensity). The top portion of Fig. 10 shows the signal levels for the wFOV, while the bottom portion shows the nFOV. The individual markers represent the signal levels when each of the individual frequencies has reached the point. The line joining them represents the trends for a given pointing accuracy. Results show that for a given pointing accuracy, the average signal level at the condition is larger at high frequencies than at lower frequencies. This is to be expected as higher frequencies experience temporal dispersion at lower attenuation lengths. A lower attenuation length results in less amplitude loss. Lower frequencies, however, are not susceptible to


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to block out ambient light in the laboratory, solar ambient in real ocean environments may place additional requirements on system dynamic range and sensitivity. Of course, another way to increase the SNR can also be seen in Fig. 10, where both the wide and narrow FOVs are shown. Note that widening the receiver FOV results, on average, in a 15-dB increase in the received signal, which from a link budget viewpoint is highly desirable. Recall that Fig. 9 illustrated that widening the FOV is only detrimental near the beam axis. The response is neutral to FOV changes far from the beam axis. This is a rather important and novel result, as it suggests that under loose pointing conditions, the link operator can increase the FOV to improve the SNR without worrying about a simultaneous loss of temporal fidelity, even in multiple-scattering regimes. Near the beam axis, however, a careful tradeoff must be made between link bandwidth and SNR. VII. CONCLUSION

Fig. 10. The dc (average) signal level for each frequency at as a function of attenuation length. Several pointing angles are shown for both wFOV (dashed) and nFOV (solid). MgOH is the scattering agent.

temporal dispersion until much higher attenuation lengths, and, therefore, undergo more amplitude attenuation before reaching the condition. These results are consistent with Fig. 4. To illustrate the utility of Figs. 9 and 10, consider the following example. A transceiver with 10 pointing and tracking accuracy is used to implement a link. The link is to support a maximum frequency of 500 MHz. Assuming a wFOV, the longest number of attenuation lengths that the link can traverse and still support this frequency is 9–10, as per Fig. 9. While this establishes a bound for dispersion-free transmission, Fig. 10 can be used to determine the dynamic range needed to achieve it. Fig. 10 indicates that the average signal level for this condition is 63.5 dB (relative to perfectly clear water with no loss). In other words, for this example, if the designer intends for the link to operate over the widest range of water clarities possible, then the transceiver must have a dynamic range sufficient to accommodate an optical signal that will vary over six orders of magnitude. If this amount of dynamic range is not available, then the link would still support the given bandwidth, but it would be limited in terms of the number of attenuation lengths it could operate over. From a practical point of view, increasing the system dynamic range can be accomplished by increasing the laser power (to a certain extent), increasing the photoreceiver efficiency, or, as Fig. 10 suggests, improving the pointing accuracy. It is important to understand that while increasing the laser power or photoreceiver efficiency may allow the link engineer to buyback SNR, this has no impact on temporal dispersion itself. Additionally, while a 532-nm optical filter was used in the experiments

We have described a method for measuring the frequency response of the underwater optical laser communications channel out to 1 GHz. By performing the measurement in the frequency domain, we are afforded superior measurement dynamic range and sensitivity that allows measurements up to attenuation lengths, and at transmitter/receiver pointing differences up to 30 . The influence of receiver FOV and scattering particle was also studied. Link designers will take note that the convenience of Beer’s law has narrow application only for LoS links when the transmitter and the receiver are accurately aligned. Even in this geometry, Beer’s law fails in highly multiple-scattering regimes. Link designers should also now recognize that knowledge of the received average power (whether predicted via Beer’s law, determined empirically through an experiment, or theoretically through modeling) only provides a portion of the information needed to predict system performance, since additional losses may be incurred via temporal dispersion. This work has shown that temporal dispersion is highly dependent upon link geometry, water optical properties, and the behavior of spatial dispersion. While the scattering phase functions of ocean waters are highly peaked in the forward direction, subtle differences in the shape of the forward peak can have large influence on the temporal dispersion observed. With regards to the receiver FOV, widening the FOV can increase the signal level only in conditions where scattered light dominates (at all attenuation lengths for 0 or at for 0 ). With regard to temporal dispersion, widening the FOV significantly alters the available bandwidth at 0 , and only at high turbidities . Off-axis, temporal dispersion is largely insensitive to changes in FOV. Fig. 9 presented, for a given pointing accuracy, the attenuation length bounds by which a specific frequency can be transmitted without the consequence of temporal dispersion. With the aid of Fig. 10, the necessary dynamic range needed to achieve this bound can also be determined. Finally, we have shown that under loose pointing and tracking, temporal dispersion does not increase with increased receiver FOV, however, there are large gains to be had in terms of signal level and dynamic range improvement.

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While beyond the scope of this paper, future work will examine how the relationships uncovered in this study impact underwater optical communication links in a quantitative manner (link range, bandwidth, error rate, etc.). Additionally, given the challenges presented in the past for obtaining temporal measurements of the underwater channel, we expect this data set to be useful for the validation of theoretical models.

[18] F. Dalgleish, F. Caimi, and A. Vuorenkoski, “Efficient laser pulse dispersion codes for turbid undersea imaging and communications applications,” Proc. SPIE, vol. 7678, 2010, DOI: 10.1117/12.854775. [19] D. Gloge, E. L. Chinnock, and D. H. Ring, “Direct measurement of the (baseband) frequency response of multimode fibers,” Appl. Opt., vol. 11, pp. 1534–1538, Jul. 1972. [20] R. Helkey, D. Derickson, A. Mar, J. Wasserbauer, and J. Bowers, “Millimeter-wave signal generation using semiconductor diode lasers,” Microw. Opt. Technol. Lett., vol. 6, no. 1, pp. 1–5, Jan. 1993. [21] G. Mooradian, M. Geller, L. B. Stotts, D. H. Stephens, and R. A. Krautwald, “Blue-green pulsed propagation through fog,” Appl. Opt., vol. 18, pp. 429–441, Feb. 1979. [22] V. Weisskopf, The Science and Engineering of Nuclear Power. Reading, MA, USA: Addison-Wesley, 1947. [23] E. Bucher, “Computer simulation of light pulse propagation for communication through thick clouds,” Appl. Opt., vol. 12, pp. 2391–2400, Oct. 1973. [24] R. Lerner and J. Summers, “Monte Carlo description of time-and space-resolved multiple forward scatter in natural water,” Appl. Opt., vol. 21, pp. 861–869, Mar. 1982.

ACKNOWLEDGMENT The authors would like to thank Y. Agrawal at Sequoia Scientific (Bellevue, WA, USA) for the LISST measurements of the scattering phase functions. REFERENCES [1] S. Duntley, “Underwater lighting by submerged lasers and incandescent sources,” Scripps Inst. Oceanogr. Visibility Lab., San Diego, CA, USA, Tech. Rep., 1971. [2] T. Petzold, “Volume scattering functions for selected ocean waters,” Scripps Inst. Oceanogr. Visibility Lab., San Diego, CA, USA, Tech. Rep., 1972. [3] N. Jerlov, “Marine optics,” Elsevier Scientific, Amsterdam, The Netherlands, Tech. Rep., 1976. [4] J. Snow, J. Flatley, D. Freeman, M. Landry, C. Lindstrom, J. Longacre, and J. Schwartz, “Underwater propagation of high-data-rate laser communications pulses,” Proc. SPIE—Ocean Opt. XI, vol. 1750, pp. 419–427, 1992. [5] J. Longacre, D. Freeman, and J. Snow, “High-data-rate underwater laser communications,” Proc. SPIE—Ocean Opt. X, pp. 433–439, 1990. [6] F. Hanson and S. Radic, “High bandwidth underwater optical communication,” Appl. Opt., vol. 47, no. 2, pp. 277–283, 2008. [7] B. Cochenour, L. Mullen, A. Laux, and T. Curran, “Effects of multiple scattering on the implementation of an underwater wireless optical communications link,” in Proc. IEEE OCEANS Conf., 2006, DOI: 10.1109/OCEANS.2006.306863. [8] B. Cochenour, L. Mullen, and A. Laux, “Phase coherent digital communications for wireless optical links in turbid underwater environments,” in Proc. IEEE OCEANS Conf., 2007, DOI: 10.1109/OCEANS. 2007.4449173. [9] B. Cochenour, L. Mullen, and A. Laux, “Characterization of the beam-spread function for underwater wireless optical communications links,” IEEE J. Ocean. Eng., vol. 33, no. 4, pp. 513–521, Oct. 2008. [10] B. Cochenour, L. Mullen, and J. Muth, “Effect of scattering albedo on attenuation and polarization of light underwater,” Opt. Lett., vol. 35, no. 12, pp. 2088–2090, 2010. [11] L. Mullen, A. Laux, and B. Cochenour, “Time-dependent underwater optical propagation measurements using modulated light fields,” Proc. SPIE—Ocean Sens. Monitor., vol. 7317, 2009, DOI: 10.1117/12.818588. [12] L. Mullen, A. Laux, and B. Cochenour, “Propagation of modulated light in water: Implications for imaging and communications systems,” Appl. Opt., vol. 48, no. 14, pp. 2607–2612, 2009. [13] L. Mullen, B. Cochenour, A. Laux, and D. Alley, “Optical modulation techniques for underwater detection, ranging, and imaging,” Proc. SPIE—Ocean Sens. Monitor. III, vol. 8030, 2011, DOI: 10.1117/12. 883493. [14] L. Mullen, D. Alley, and B. Cochenour, “Investigation of the effect of scattering agent and scattering albedo on modulated light propagation in water,” Appl. Opt., vol. 50, pp. 1396–1404, Apr. 2011. [15] J. Li, Y. Ma, Q. Zhou, B. Zhou, and H. Wang, “Monte Carlo study on pulse response of underwater optical channel,” Opt. Eng., vol. 51, no. 6, 2012, 066001. [16] J. Li, Y. Ma, Q. Zhou, B. Zhou, and H. Wang, “Channel capacity study of underwater wireless optical communications links based on Monte Carlo simulation,” J. Opt., vol. 14, Dec. 2011, 015403. [17] B. Cochenour and L. Mullen, “Channel response measurements for diffuse non-line-of-sight (NLOS) optical communication links underwater,” in Proc. IEEE OCEANS Conf., 2011, pp. 1–5.

Brandon Cochenour (M’00) received the B.S. degree in electrical and computer engineering from Lafayette College, Easton, PA, USA, in 2003, the M.S. degree in electrical and computer engineering from Johns Hopkins University, Baltimore, MD, USA, in 2008, and the Ph.D. degree in electrical and computer engineering from North Carolina State University, Raleigh, NC, USA, in 2012. He has worked at the Naval Air Warfare Center, Patuxent River, MD, USA, since 2004, where his research focuses on underwater laser communications, underwater laser imaging, oceanographic LIDAR systems, and STEM outreach. Dr. Cochenour was awarded as a Department of the Navy “Top Scientist and Engineer of the Year” in the Emerging Investigator category in 2006. In 2009, he was named “Outstanding Young Engineer of the Year” by the Maryland Academy of Sciences. He was a recipient of the Science, Mathematics, and Research for Transformation (SMART) Scholarship, sponsored by the U.S. Department of Defense (DoD) and the American Society for Engineering Education (ASEE).

Linda Mullen (M’88–SM’02) received the B.S. degree in electrical engineering from Trenton State College, Ewing, NJ, USA, in 1992 and the M.S. and Ph.D. degrees in electrical engineering from Drexel University, Philadelphia, PA, USA, in 1993 and 1996, respectively. She has been a Researcher at the Naval Air Warfare Center, Patuxent River, MD, USA, since 1996, leading research efforts in underwater laser detection, ranging, and imaging.

John Muth (M’07) received the B.Sc. degree in applied engineering physics from Cornell University, Ithaca, NY, USA, in 1988. After serving as submarine officer in the U.S. Navy he received the Ph.D. degree in solid state physics from North Carolina State University, Raleigh, NC, USA, in 1998. He is a Professor of Electrical and Computer Engineering at North Carolina State University. His research interests include growth and fabrication of novel photonics materials and devices as well as underwater optical communications. He has over 100 peer-reviewed publications and seven awarded patents. Dr. Muth has received several awards including the U.S. Office of Naval Research Young Investigator Award (2003), the National Academy of Engineers Frontiers of Science Award (2004), and a Bronze Star for meritorious service while on active duty in Iraq (2008).