A new approach to shallow depth measurement (<2 m) using polarization lidar is presented. The transmitter consists of a 532-nm linearly polarized laser coupled with conditioning and polarization optics. The prototype lidar evaluates the differing polarization attributes of signals scattered from semitransparent media surfaces, simultaneously receiving signals polarized in the planes parallel and perpendicular to the transmitted laser signal via dual photomultiplier tubes. In the event the first surface nearly preserves the incident polarization and the second surface depolarizes the incident energy, signals scattered from the second surface are isolated from the first by a polarization analyzer in the receiver. This approach translates depth measurements into the conditions of single surface range measurements, giving the ability to resolve extremely shallow depths (e.g., 1 cm) independent of laser or detector pulse widths. This approach can circumvent dead time issues in photon-counting systems and can be applied to extremely shallow and deeper waters for depth determination. Furthermore, the approach provides an estimate of the first surface linear depolarization ratio, enabling differentiation between surfaces with variable scattering properties. Using this technique to acquire range-resolved observations through shallow semitransparent media to measure depth removes the dependency on sophisticated and, subsequently, costly lidar components by becoming independent of system bandwidth. The limiting factor in-depth resolution is driven only by the timing resolution of the time-to-digital converter. This approach allows for the use of common lasers, optics, and detector equipment, making it comparatively cheaper and less complex while achieving vast improvement in the accuracy and precision of shallow depth measurements.
The development of laser ranging has enabled a variety of remote sensing distance measurements, including observation of hard targets such as bare terrain and satellite reflectors (Abshire et al. 2005; Degnan 2001; Degnan et al. 2002) and distributed targets such as vegetation canopies (Blair et al. 1999; Harding and Carabajal 2005). Range-resolved observations through semitransparent targets are enabled by the lidar technique, which has been used to profile the distribution and structure of media, such as clouds and aerosols (McGill et al. 2002; Spinhirne 1993). Airborne lidar bathymetry has developed in recent years to provide range-resolved observations through semitransparent media, such as coastal waters, and to enable media depth measurements (Guenther et al. 2000a; Guenther and Maune 2007). Lidar bathymetry systems routinely operate on board platforms such as helicopters and fixed-wing aircraft, collecting bathymetric measurements of water volume and subsurface terrain for use in coastal engineering and resource management, nautical charting, and reconnaissance efforts (Churnside et al. 2001; Guenther et al. 2000b; Irish and Lillycrop 1999).
The typical lidar bathymetry system consists of a pulsed laser transmitter operating at 532 nm, near the spectral absorption minimum of most natural waters (Smith and Baker 1981), coupled with a receiver telescope and optical detector (see Table 1 for lidar parameters). As illustrated in Fig. 1, a laser pulse of temporal width τ is transmitted from the instrument at time t0 through air with refractive index n0 toward the target water body. The pulse intercepts the water surface S, shown here as smooth water for illustrative purposes, at time t1. A portion of the laser pulse is reflected at the air–water interface back to the instrument. The remaining portion of the laser pulse is transmitted into the water, where the energy is subject to increased extinction along the refracted optical path through the water column. A portion of the transmitted energy reflects off the bottom B of the water body at time t2 and propagates back to the receiver. Depth measurement is based on the differential arrival times of the range-resolved received signals 1 and 2, accounting for differences in the refractive index along the optical path and the laser pointing angle relative to the water surface normal.
Conventional lidar bathymetry systems employ an analog detection scheme, transmitting modest laser pulse energies (mJ) and using high detection thresholds to resolve unambiguous measurement of surface and bottom returns with few false alarms in the presence of noise from detector dark counts and background solar illumination (Guenther and Thomas 1983; Harding 2009). These systems are designed to receive hundreds, even thousands, of reflected photons for each transmitted laser pulse in order to exceed the detector noise floor and to enable monopulse detection. Laser energy is of particular demand for these systems in the deep water regime, where optical signals scattered from the bottom are subject to maximum extinction along the optical path. Because of the demand for high peak power, conventional lidar bathymetry systems use lasers with pulse widths on the order of 1–3 ns (Feygels et al. 2013; Irish and White 1998; Nayegandhi et al. 2009).
Degnan et al. (2002) and Degnan (2002) demonstrated theoretically that the conventional high signal-to-noise approach to laser ranging does not efficiently use available laser photons. Building upon this theory, the depth sounding rate of a lidar bathymeter can be increased for a given laser output power by transmitting the available photons in a high-frequency train of low-energy (μJ) pulses and employing a photon-counting detection approach. Significant scientific interest exists in the potential to increase sounding density, particularly in the study of rapidly developing water bodies, such as areas of coastal flooding and dynamic supraglacial melt ponds that form on the Greenland Ice Sheet (Das et al. 2008; Tedesco and Steiner 2011; Zwally et al. 2002).
Additional limitations on sounding density are manifested for both analog and photon-counting lidar bathymeters in the shallow water regime (typically <2 m) due to the inability of the lidar system to distinguish between signals scattered from the surface and the bottom (Peeri et al. 2011). The limit to achieving a shallow water depth measurement is related to the applied lidar technique and the governing time responsivity of the lidar, which defines the capacity of the system to distinguish between two surfaces along the same optical path but separated in range. The time responsivity is governed by the slowest timing element in the lidar system, such as the laser pulse width, the detector pulse width, or the speed of the acquisition electronics. Invariably, modern techniques for determining shallow depth in semitransparent media are constrained by the governing time responsivity of the system, resulting in ambiguities between overlapping returns from sequential media surfaces and rendering depth indeterminable. As a result, modern bathymetry lidars ranging through shallow waters are typically limited to meter-level depth measurements (Guenther and Maune 2007), with sophisticated systems working to achieve submeter resolution (Feygels et al. 2013; Nayegandhi et al. 2009). Enhanced performance of the lidar in the shallow regime demands a reduction of the governing time responsivity, often at the expense of increased complexity and cost associated with high-performance components, such as picosecond pulse width lasers and fast detectors.
Polarimetry of scattered light exploits the relationship between incident polarized light and the polarization of diffusely and specularly reflected light by objects or surfaces to obtain additional information about the target. Polarization lidars have been applied to ocean waters to study, for example, suspended particulate matter whose polarization scattering attributes lead to an improved characterization of scattering layers (Vasilkov et al. 2001) and water optical properties (Churnside 2008). Building upon this work and scatter polarimetry of surfaces (DeBoo et al. 2005), this paper details a new approach to shallow depth measurement by evaluating the differing polarization attributes of signals scattered from sequential media surfaces. Although generally applicable to any semitransparent medium, the technique is applied to shallow water depths given the known limitations of most lidar bathymetry systems to resolve water depths below 1 m (Klemas 2011).
The prototype lidar described here simultaneously receives optical signals polarized in the planes parallel and perpendicular to the transmitted linearly polarized laser signal via a photon-counting approach. In the event the first surface of the media nearly preserves the incident polarization state and the second surface depolarizes the incident energy, returns from the second surface are isolated from the first surface by a polarization analyzer in the receiver. This approach enables measurement of shallow depths at subgoverning pulse width resolution, overcoming conventional instrument timing limitations. Furthermore, the approach provides an estimate of the first surface linear depolarization ratio, enabling differentiation between surfaces with variable scattering properties. Range-resolved observations through shallow semitransparent media to obtain a depth measurement are no longer limited by the governing time responsivity of the lidar, but by the timing resolution of the time-to-digital converter.
2. Instrument overview
The prototype lidar described here has been developed at the University of Colorado Boulder, in concert with other ongoing lidar research. A block diagram of the polarization lidar is presented in Fig. 2. The laser transmitter consists of a continuous-wave diode-pumped passively Q-switched frequency-doubled Nd:YAG microchip laser. The laser outputs 2.45 μJ of linearly polarized 532-nm light at a repetition rate of 14.3 kHz and a pulse width of 450 ps (6.75-cm equivalent range in air). The transmitted beam passes through a 5-times beam expander to achieve a divergence of 1.8 mrad. A half-wave plate aligns the laser polarization to the transmission plane of a 532-nm Glan–Thompson polarizer to ensure maximum linearly polarized output with a measured degree of polarization (DOP) greater than 99.99%. Light exiting the polarizer is transmitted through a pair of Risley prisms configured to steer the transmitted light into alignment with the biaxial receiver. Optical leakage from the outgoing laser pulse is sampled by a fast photodiode, which time tags the start pulse with a SensL HRMTime time-to-digital converter (TDC).
The receiver consists of an F/13.9 Maksutov–Cassegrain telescope with a 1250-mm focal length and a 90-mm aperture. An iris is located at the focal point of the telescope and is adjusted to control the receiver field of view. The collected light is collimated by a 25-mm positive lens and passed through an interference filter (1-nm bandwidth) and a Glan–Taylor polarizer. The halfwave plate and the Glan–Thompson polarizer in the transmitter are oriented to align the laser polarization plane with the reflection axis of the Glan–Taylor polarizer in the receiver. The Glan–Taylor functions as a polarization analyzer in the receiver, reflecting scattered signals oriented parallel to the transmitted polarization plane and passing perpendicular signals. All components within the receiver optical path have been selected and evaluated with negligible capacity to rotate or depolarize incident polarized light.
Received signals scattered from semitransparent media are collected by dual dynode-chain photomultiplier tubes (PMT), Hamamatsu model H7422PA-40. Each PMT operates with a 1-ns rise time of a 2.5-ns full width at half maximum (FWHM) pulse (37.5-cm equivalent range in air). The detectors operate with known timing jitters of 290 and 270 ps in the parallel and perpendicular channels, respectively. The output of each PMT is input to independent channels of a dual-channel constant fraction discriminator (CFD), which determines the PMT signal apex independently of the signal pulse height. The CFD operates with an intrinsic timing jitter of 3.2 ps, outputting a transistor–transistor logic (TTL)-level pulse of 270-ns duration (4050-cm equivalent range in air). Each CFD output pulse is passed to and stored on board the TDC, operating with a 27-ps bin width (±0.4-cm equivalent range in air), one bin entry per laser firing, and 190-ns dead time between consecutive events (2850-cm equivalent range in air). Time-of-flight (TOF) measurements are performed by an onboard processor, determined by differencing the TDC time tags of the laser fire (“start”) event sampled by the fast photodiode in the transmitter and the photon return (“stop”) events from each PMT.
A block diagram of the CFD circuit is provided in Fig. 3. Electrical output from each PMT in the parallel and perpendicular detection channels is input into independent channels of the CFD. Each PMT pulse is amplified and split into two components. The component passed through the top portion of the circuit is fed into a comparator that compares the PMT signal to a programmable threshold voltage, set to a level that defines when a useful real signal is arriving. The output of this comparator serves as an enable signal to qualify the output of the bottom section of the CFD. The component passed through the bottom portion of the circuit is split a second time, fractioned and delayed, and input into a second comparator. Providing suitable fractions and delays are chosen for the PMT output characteristics, the delayed signal will cross through the fractioned signal at the same point in time, regardless of the amplitude of the PMT output.
A flip-flop with a delayed clear fixes the pulse width of the TTL-level output, which can be programmed by the user to either 8 or 270 ns. For a 450-ps laser pulse width, 2.5-ns PMT output pulse width, and a 190-ns TDC dead time, the CFD ouput is configured to 270 ns for the measurements presented in the following sections in order to define the governing time responsivity of the lidar; this is referred to as the dead time of the system. For each PMT output pulse (noise or signal) of sufficient amplitude to enable the CFD, an event is recorded by the TDC and the lidar is subject to a 270-ns dead time before recovering to record the next event.
3. Ranging through semitransparent media: Polarization indiscriminate detection
To demonstrate the assortment of depth measurement regimes possible using a photon-counting lidar system, timing data were acquired during reception of signals backscattered from the experimental setup of Fig. 4. The experiment is to represent fundamental timing issues when trying to delineate top and bottom surfaces in time-of-flight measurements. The experiment consists of a glass panel separated for select distances from a rough, opaque surface with air as the intervening propagation medium. The glass panel represents a still water surface and the rough, opaque surface represents the water bottom. Although a basic configuration, the experiment helps elucidate the important considerations of resolving range to separated targets in time. More sophisticated experiments using water bodies of various depths have been carried out using the approaches presented here.
The first measurement regime considers targets separated by time-of-flight distances more than the dead time of the acquisition system. An opaque surface was mounted at a known distance d0 of 5100 cm from the lidar (340-ns TOF) to simulate the floor of an arbitrary body of water. Timing data were acquired in the parallel-detection channel, as illustrated in Fig. 5, to replicate the performance of a conventional lidar bathymeter using no polarization discrimination in the receiver. The timing histogram results from the integration of scattered pulses for 4 s with at most one entry per bin per laser fire at the laser pulse repetition frequency of 14.3 kHz, or a 70-μs interpulse period. In this experiment, the CFD enable threshold voltage was raised above the operational noise level, resulting in the lack of background counts (a high-signal-to-noise condition). The histogram is centered around the 340-ns TOF and has a 290-ps width dominated by pulse jitter in the parallel channel PMT. For each PMT output pulse of sufficient amplitude to enable the CFD, an event is recorded in the TDC; however, the CFD requires 270 ns to recover and thus defines the dead time of the system.
Timing data were then acquired with the lidar ranging through a glass panel, used to simulate a still water surface, mounted between the lidar and the opaque surface. The glass surface was initially mounted at depth A of 4252.5 cm from d0, corresponding to 847.5 cm from the lidar (56.5-ns TOF). The TOF between signals scattered from the sequential surfaces in this configuration was 283.5 ns. The lidar discriminates and records returns from the semitransparent surface and is subject to the governing 270-ns dead time, depicted spatially as dCFD in Fig. 4. With the glass mounted at depth A, the lidar recovers from the dead time to discriminate and record returns from the opaque surface, as illustrated in Fig. 6. The differing histogram amplitudes are related to the different backscattered properties of each surface and subsequent probability of discrimination by the CFD. Thus, targets separated by more than the dead time of the system can be detected and their depth determined.
The second measurement regime considers targets separated by distances that are less than the system dead time. The glass surface was translated and mounted at depth B of 3651 cm from d0, corresponding to 1449 cm from the lidar (96.6-ns TOF). The TOF between signals scattered from the sequential surfaces in this configuration was 243.4 ns. As illustrated in Fig. 7, the lidar discriminates and records returns from the glass surface. The lidar is unable to recover from the governing 270-ns dead time and no longer records events from the opaque surface. Consequently, a lidar system employing photon counting must consider its limiting dead time in resolving targets in a manner similar to sampling rates for waveform generation in lidar systems using analog detection. However, we will illustrate in the next subsection a means of enabling depth between closer separated targets to be resolved by actually lowering the signal-to-noise ratio (SNR) of the system.
a. Considerations: Noise
The histograms of Figs. 5–7 demonstrate timing data for backscattered signals that generate PMT output amplitudes greater than the CFD enable threshold voltage, configured above the operational noise level to ensure the TDC records only desired signal returns (a high SNR condition). However, the high SNR condition limits the system’s ability to resolve targets closer than the dead time of 270 ns because it guarantees a detection of the stronger first target effectively blinding the system to targets with TOF within the dead time, as shown in Fig. 7. This limitation to the range measurement is eliminated in the case where signal and noise (e.g., solar background, detector dark counts) events are of similar amplitude. It remains that any PMT output pulse of sufficient amplitude to enable the CFD will subject the lidar to the governing 270-ns dead time. Thus, for a deterministic signal return from a fixed surface, such as the glass panel, the dead time is initiated at that distance, within the pulse jitter of the PMT. However, with the lowered SNR voltage threshold, noise events randomly distributed in time can occasionally trigger the CFD, resulting in a random distribution of dead time intervals lasting 270 ns.
Consequently, given sufficient integration time, the random occurrence of the governing CFD dead time permits the TDC to record returns from sequential surfaces with differential TOF less than the system dead time. This capability is demonstrated in Fig. 8. Here, the glass surface remains mounted at depth B—that is, inside the system dead time. The CFD enable threshold voltage is lowered to enable registration of noise events, and timing data are integrated over a 20-s integration period. The effect of random noise events occasionally prohibits the instrument from recording events from the glass surface, permitting detection of returns from the opaque bottom surface. As the lidar integrates over the extended 20-s period, timing histograms are acquired from both surfaces and depths inside the dead time of the CFD can be resolved. This represents an improvement in depth resolution but at the expense of longer integration periods to achieve the same detection precision as in the first measurement regime, where targets are separated by more than the system dead time.
Severe noise levels can statistically render the lidar blind to both surfaces and therefore must be characterized for a given measurement environment in order to configure the CFD enable threshold appropriately. Adequate control of receiver field of view and spectral filtering can be implemented to help control the amount of sky noise on the detectors (Degnan et al. 2002; Degnan 2002).
b. Considerations: Laser/detector pulse width
A third measurement regime remains for sequential media surfaces with separation distance less than the spatial width of the combined laser/detector pulse. In this optical regime, returns from sequential surfaces are contained within the envelope of the laser/detector pulse width and is an issue for photon-counting or digitizing lidar bathymetry systems. For the lidar described here, in the event sequential surface returns are contained within the envelope of the laser/detector pulse, the CFD will determine the signal apex of the resulting PMT output and generate a single output pulse to be recorded by the TDC. While discrimination of noise events provides a means to reduce the severity of the governing system dead time, operation in this more shallow measurement regime remains limited in this prescribed configuration for returns enveloped by the combined pulse width of the laser and detector. The next section removes this limitation by introducing a novel scheme by using a polarization lidar and exploiting the polarization attributes of the scattering domain.
4. Ranging through semitransparent media: Polarization discriminate detection
The lidar configuration described in this section utilizes dual detection channels and optical polarization discrimination to overcome the governing limit on time responsivity imposed by the laser/detector pulse width. To demonstrate the capacity of the dual-channel polarization approach to achieve high-resolution ranging through semitransparent media, the experimental setup of section 3 is revisited and new measurements are made within the three different depth regimes.
a. Overcoming the limitation imposed by CFD dead time
To demonstrate the capability of the lidar to measure depth between sequential surfaces located within the governing CFD dead time, additional timing histograms were acquired with the CFD enable threshold voltage configured above the operational noise level, identical to the high SNR configuration utilized for acquisition of the data shown in Fig. 7. Here, the glass surface remained mounted at depth B from d0. However, unlike the single polarization indiscriminate detection channel measurement, timing histograms were simultaneously integrated by two separate detection channels in the receiver, with one channel receiving scattered signals parallel to the transmitted polarization plane and the other receiving perpendicular signals.
When incident upon the glass surface, a portion of the transmitted linearly polarized light reflects back to the receiver in a nearly preserved orientation and with a high degree of polarization. The result is a linearly polarized light incident upon the receiver and is reflected by the Glan–Taylor polarizer to the PMT for detection of the scattered parallel polarized signal. The CFD in the parallel detection channel discriminates the PMT voltage output and is subject to the 270-ns dead time. Energy scattered from the surface into the perpendicularly polarized plane is of insufficient intensity to enable the CFD in the perpendicular detection channel.
A portion of the laser light transmits through the semitransparent glass surface and incidents the opaque surface. This light depolarizes upon reflection due to the rough topography of the opaque surface. Returning to the lidar receiver, the parallel and perpendicular components of the now partially polarized scattered light are selectively isolated by the Glan–Taylor polarizer into their respective PMT detection channels. Reception of scattered light from the polarization-preserving glass surface previously enabled the CFD in the parallel channel; therefore, no event is recorded from the depolarizing surface in the parallel detection channel. The CFD in the perpendicular detection channel discriminates the PMT output pulse and is subject to the 270-ns dead time.
This capability to overcome the limitation on range measurement imposed by the governing CFD dead time is illustrated in Fig. 9. By discriminating the polarization orientation of scattered signals for each transmitted laser pulse, the lidar simultaneously acquires timing histograms from the sequential surfaces. This translates the shallow media range measurement into two surface altimetry measurements, where target selection is dictated by the propensity of the surface to couple energy into the perpendicular polarization plane. The polarization-preserving surface is effectively removed from the measurement in the perpendicular detection channel, enabling the depolarizing surface signals to be isolated for analysis. Thus, a benefit of the polarization lidar approach is the capacity of the sensor to overcome the governing electrical dead time via isolation of optical signals, reducing the integration time required by the single-channel approach outlined in section 3a, where the dead time limitation was mitigated through the occurrence of randomly occurring noise events.
b. Overcoming the limitation imposed by laser/detector pulse width
To demonstrate the capability of the lidar to measure depth between sequential surfaces limited by the laser/detector pulse width, timing data were acquired during the reception of signals scattered from the glass surface mounted at depth C of 2.4 cm from d0. Note here that the glass panel is physically measured to 0.95-cm thickness, placing the front surface of the glass 3.35 cm from the opaque surface. With a laser of 450-ps pulse width (13.5-cm spatial equivalent), scattered optical signals from the sequential surfaces overlap within the envelope of the laser pulse, depicted spatially as dLASER in Fig. 4. Lidars performing the range measurement with a polarization-indiscriminate detection approach are subject to this intrapulse ambiguity, even in the presence of noise.
Two measurements were conducted with the glass mounted at depth C. First, timing histograms from the opaque surface were simultaneously integrated over 30 s in the parallel and perpendicular detection channels in the absence of the glass surface, providing a baseline range measurement to the depolarizing surface. This measurement is indicative of a typical range calibration routine performed with the lidar in the laboratory prior to acquisition of water depth measurements in the field. The semitransparent glass surface was then reinserted into the optical path and timing histograms were integrated into both channels to demonstrate the capability of the lidar to measure the depth between sequential surfaces at sublaser pulse width resolution.
Figure 10 illustrates the envelope of the timing histograms, the width of which corresponds to the respective jitter of each PMT. To remove discrepancies in integrated counts per bin between channels and to highlight the timing resolution of the lidar, the histograms were integrated over 30 s and normalized to their respective maximum count value. Range to the opaque surface registers 5409.6 cm (360.64-ns TOF) in both detection channels, measured at the apex of the timing histograms. Inserting the semitransparent surface into the optical path physically reduces the range to the first surface by a distance l of 3.35 cm. As a result, it is expected that the peak of the semitransparent surface timing histogram tsemi will advance in time to
which agrees with the TDC measurement of 5406.8 cm (360.45-ns TOF) to within the precision of a ±0.4-cm bin width.
Contrasting the setup between experiments, light scattered from the opaque surface is subject to a transit distance l of 0.95 cm of glass compared to 0.95 cm of air. Given the refractive index n = 1.7 of the glass, inserting the panel into the optical path is expected to delay the opaque surface return topaq in time by
solely due to the change in n from air to glass over the 2l round-trip distance. The expected apparent shift to 5410.2 cm (360.68-ns TOF) agrees closely with the range measurement of 5410.8 cm (360.72-ns TOF).
The polarized dual detection-channel approach and results illustrate unique aspects of the polarization technique. First, the technique enables sublaser/detector pulse width depth resolution that is limited only by the timing resolution of the TDC. For the lidar described here, the precision of the measurement is established by the 27-ps bin resolution of the TDC. Second, the technique removes the dependency on short laser pulses and fast detectors, allowing for increased flexibility in laser selection criteria and enabling more affordable and less complex lidar components to be employed while still achieving significant improvements in shallow water depth measurements. Multiple surfaces in sequence can be resolved at high resolution but would require longer integrations. Further investment in reducing the dead time of the CFD would reduce the necessary integration time.
c. Linear depolarization estimate
The polarization lidar described here overcomes several depth measurement limitations through simultaneous detection of signals scattered in the polarization planes parallel and perpendicular to the transmitted laser light. In addition to timing information, the detected signals also contain polarization information about the scattering properties of the surface. This information can be evaluated to differentiate between surface types, such as water and ice (Rodier et al. 2012), by measuring the propensity of the surface to depolarize incident light into the perpendicular polarization plane.
Linear depolarization may be characterized by ratioing the parallel and perpendicular polarization components of the backscattered light. The resulting linear depolarization ratio is defined as (Gimmestad 2008)
where N⊥ and N∥ are the components of the detected signal polarized perpendicular and parallel to the transmitted beam, respectively. Ratioing the integrated timing histograms from a single surface in both detection channels leads to the generation of a depolarization ratio δ for the surface.
The expectation of a weak perpendicularly polarized signal from the bottom surface was a driving requirement for the optical layout of the lidar. Consequently, the optical design of the system was optimized for maximum SNR of the perpendicular optical path. Providing an accurate measurement of the surface depolarization ratio requires calibration of the lidar, including a parameterization of gain offsets induced by the Glan–Taylor polarizing beamsplitter, PMT detectors, and cross talk between the two receiver channels due to receiver and transmitter misalignment in polarization. Hayman and Thayer (2009) describe a generalized approach to calibrate a lidar system for depolarization estimates, particularly when significant optical retardance is present. Building upon this work, the lidar presented here has been designed with minimal reflecting elements that effectively eliminated any optical retardance. This allows the methods of Alvarez et al. (2006) and Hunt et al. (2009) to be applied for the gain calibration of the depolarized signals. In this case, the digitized signals stored in the TDC are proportional to the observed photon counts at the detector faces, . Here,
where G is a constant and accounts for the electrooptic gain offset between receiver channels, including PMT quantum efficiencies, amplifier gains, and line losses through the PMT, CFD, and TDC electrical paths. Misalignment between the transmitter and receiver polarization planes by an angle θ introduces a degree of polarization cross talk into the measured depolarization ratio. In this condition, a fraction of the parallel signal is leaked into the perpendicular channel, or vice versa. Without properly calibrating the lidar, these effects contaminate the measurements from which the depolarization ratio δ is derived.
The range-resolved depolarization ratio m observed by the lidar is a function of the gain ratio G, the misalignment angle θ, and the depolarization ratio δ of the scattering surface. The observed ratio takes the form
To calibrate the lidar, a halfwave plate was inserted into the transmit path and timing histograms were acquired from the target surface over a sequence of controlled halfwave plate calibration angles ϕj. For each timing histogram acquired at each calibration angle, the effective offset angle is the sum of the misalignment angle θ between the transmit and receive planes and the calibration angle ϕ. Acquiring timing histograms for a range of halfwave plate calibration angles generates a dataset with controlled amounts of polarization cross talk between detection channels. For the jth calibration angle ϕj the range-resolved observed depolarization ratio is now defined as
where mj(r) and ϕj are measured and δ(r), G, and θ are evaluated during the calibration process.
As illustrated in Fig. 11, timing histograms were integrated in the parallel and perpendicular detection channels for signals scattered from the opaque surface for calibration angles ϕj = 0°, 10°, …, 90°, as well as ϕj = 45° for reference. Observed depolarization ratios mj were generated for each calibration angle ϕj by summing the histogram counts in the parallel and perpendicular detection channels and taking their ratio. Evaluating Eq. (6) via the observed ratios and a nonlinear least squares algorithm resulted in values of G = 1.67 and θ = 2.53° for the systematic gain and misalignment angle of the lidar, respectively; and a δ = 0.52 of the opaque surface.
Thus, an added benefit of the polarization technique beyond improved ranging through semitransparent media is the ability to characterize the depolarization ratio of the scattering first surface. This can be used to classify differing media surfaces, owing to their relative roughness and propensity to decouple the incident polarized signal (DeBoo et al. 2005). For example, the δ of sand and still water, typical bathymetric surfaces, were measured with the instrument to 0.55 and 0.01, respectively, using Eq. (5) and the systematic values of G and θ. In addition to providing depth measurements of shallow coastal waters, the approach can therefore be used to identify land–water transitions and provide an estimate of relative surface water roughness due to wave activity caused by surface winds.
5. Lidar system design
The timing histograms in Figs. 9 and 10 demonstrate the elimination of conventional governing pulse width limitations through exploitation of the variability between the polarization orientation of optical signals scattered from different surfaces. In this lidar system, the 2.5-ns PMT pulse width limits the conventional single detection-channel approach to a shallow depth measurement between sequential surfaces to tens of centimeters, even in the presence of randomly initiated noise events. However, by isolating the detection of intrapulse surface and bottom returns through polarization discrimination in the lidar receiver, the dual surface depth measurement is transformed into two single surface altimetry measurements, each now ultimately limited only by the 27-ps resolution of the TDC.
Optimization of instrument performance using polarization is achieved through application of the Stokes vector lidar equation (SVLE), which relates the Stokes vector of the transmitted light to the received photon counts in each observed polarization channel, accounting for all polarization effects along the optical path (Hayman and Thayer 2012). A complete description of polarization through the lidar is expressed in terms of Stokes vectors and Mueller matrices along the optical path. Following this description, the SVLE takes the form of
where is a vector of the photon counts in each observed detection channel, defined as
and is the output projection matrix corresponding to the measurements, written as
The matrix denotes that only the S0 (intensity) element of the received Stokes vector is directly measured by the PMT; RX is the lidar receiver Mueller matrix; atm is the Mueller matrix accounting for atmospheric transmission and is represented by a scaled identity; is the scattering phase matrix of the semitransparent media surface for the incident and scattered wavenumbers and , respectively, at range R; TX is the Mueller matrix of the lidar transmitter; is the Stokes vector describing the laser polarization state; and is the Stokes vector of the background at the input of the receiver.
Particular emphasis has been focused on the design and implementation of TX and RX, as the lidar is configured to interrogate linear depolarization, since most natural and man-made media exhibit depolarization (DeBoo et al. 2005) and prior work has demonstrated success exploiting depolarization in bathymetric laser ranging (Churnside 2008; Mitchell et al. 2010). Assuming the surfaces of the semitransparent media do not cause diattenuation or retardance, the scattering phase matrix assumes the form of a normalized depolarization matrix in the backscattered direction as (Lu and Chipman 1996; Flynn et al. 2007; Gimmestad 2008)
where the magnitude of a, b, and c are all approximately 1 for polarization-preserving surfaces and <1 for depolarizing surfaces.
The timing diagram of Fig. 1 is revisited and reconfigured in Fig. 12 to demonstrate the advantage of the approach in the shallow water regime. At time t0, and TX are configured to effectively code the transmitted laser pulse with an electric field oriented linearly. The linearly polarized pulse intercepts the air–water interface S at time t1. For a polarization-preserving S, a portion of the pulse 1 reflects back to the receiver with a nearly preserved linear code. The remaining portion of the pulse is transmitted into and refracted along the water column and reflects off the bottom B of the water body at time t2. Scatterers defined within the depolarization matrix B modify the linearly coded pulse, effectively scrambling the polarization state of the pulse returning to the receiver 2. The polarization analyzer RX is configured to decode the information contained within each return pulse. In the event the depth between S and B is less than cτ/n1, the receiver discriminates the codes of each return signal at subpulse width resolution.
The ability of the instrument to range to sequential surfaces in the shallow media regime requires transmission of linearly polarized light to a polarization-preserving penetrable first surface followed by a depolarizing second surface. Instrument performance can be limited by the scattering matrix defining each surface. If the scattering matrix of the first surface couples sufficient energy into the perpendicular polarization plane to enable the CFD in both detection channels—for example, in the case of ice floating atop the water surface—then the TDC is unable to record events from the second surface and the depth measurement is unobtainable. Furthermore, the lidar is configured to minimize systematic coupling of energy into the perpendicular polarization plane that may prematurely enable the CFD in the perpendicular detection channel (Hayman and Thayer 2009). The Stokes vector describing the laser polarization state has been chosen for maximum degree of linearity and DOP. The Mueller matrices of the transmitter and receiver paths TX and RX, respectively, avoid the use of reflective components and have been evaluated with negligible capacity to rotate or depolarize incident polarized light. As detailed, the misalignment of the transmit and receive polarization planes has been calibrated for cross talk.
Although the dual-channel approach provides an estimate of first surface linear depolarization, as described in section 4, estimating the depolarization of the second surface in the shallow water regime is challenging. For light incident upon a polarization-preserving first surface and depolarizing second surface, the CFD in the parallel detection channel will be enabled initially by the first surface statistically. In the shallow regime, the CFD in the parallel channel is unable to recover from the 270-ns dead time to discriminate returns from the depolarizing second surface. As a result, the estimate from the second surface is biased toward an increased depolarization ratio δ. A relative change in intensity of the second surface can be evaluated, but an observed depolarization ratio cannot be measured without accounting for the parallel-polarized signal scattered by the second surface but not detected due to the statistics of first surface detection.
Both detection channels were calibrated in the time domain to account for differences in optical and electrical pathlengths. Because of the physical setup of the instrument, the optical pathlength between the Glan–Taylor polarizer and the detector face in the perpendicular channel is 9.5 cm longer than the parallel channel. Additional timing offsets exist due to the variability of cabling used to connect the PMT, CFD, and TDC electrical paths in each channel. Timing calibration was accomplished by ranging to the depolarizing opaque surface in the absence of the glass panel. Timing histograms were acquired over a 30-s integration period in the parallel and perpendicular channels and then normalized to their maximum respective count values. The histogram acquired in the perpendicular channel was shifted forward in time 56 TDC bins (1.512 ns) to match the peak bin to that of the parallel channel, as demonstrated in Fig. 10, left panel. The resulting error in range measurements between the detection channels is defined as one-half of a TDC bin width, or 0.4 cm (in air).
The lidar system, experimental setup, and approach, as thus far described, have direct application to measuring extremely shallow water depths. The basic configuration described here does not address the complexity of various water conditions associated with the littoral zones of natural waterways, but the polarization lidar approach does provide a solution to ambiguous shallow-water bathymetry that plagues existing systems even in the clearest, calmest waters. We have applied the described lidar system and technique to prescribed shallow-water conditions in the laboratory and have achieved the same high-resolution success as shown by the experimental setup presented in section 4 (Mitchell et al. 2010). Field deployments are a future direction for the system and undoubtedly issues will arise that may limit the capability of this particular instrument, but the approach is robust and applicable to digitizing and photon-counting bathymetric lidar systems.
It is worthwhile to address some of the potential aspects of employing a polarization lidar for shallow water depth determination in natural environments. Lidars for shallow water bathymetry are increasingly utilized in coastal water research, as evidenced by the recent special issues in the Journal of Coastal Research focusing on lidar (Brock and Purkis 2009; Pe’eri and Long 2011), and have also been used in combination with other remote sensing techniques to map riverbed topologies (Feurer et al. 2008). The polarization lidar approach described in this paper has direct application to these environments, and consideration of the trades between technique and environment is worthwhile. The requirement for polarization-maintained scattering from the water surface will be compromised if debris located on the water surface, such as leaves, snow, foam, etc., significantly modifies the original polarization state or inhibits transmission to the bottom. However, as mentioned previously, the surface condition can still be characterized by estimating its depolarization ratio. In addition, the roughness of the water surface may cause depolarization if surface facets are on scales of the order of the transmit wavelength, so highly turbulent waters may limit the applicability of the approach. Both situations will depend on conditions, as higher thresholds in the cross-polarized channel could be employed to eliminate the cross-polarized signals from the first surface return while still observing the bottom return. Surface winds will also disturb the water; however, Churnside (2008) demonstrated that the amount of depolarization induced under nominal wind conditions was negligible.
Working in shallow waters of less than a few meters does have its benefits, as the level of attenuation by the water along the optical path is significantly reduced. Particulates suspended in the water can add to the attenuation as their number density increases, leading to levels of turbidity that may prohibit signals from reaching the bottom or returning to the lidar. Furthermore, with an adequate level of particulate matter, return signals from this scattering layer may be sufficiently depolarized to cross the detection threshold of the cross-polarized channel and be interpreted as a bottom surface. Interestingly, the high-resolution capability of the approach would allow for the depth of a turbid scattering layer in shallow water to be determined. Again, the ability to detect multiple surfaces in the water along with a bottom surface is feasible with the techniques described in section 4, but it would be system and situation dependent.
An additional issue in polarization detection is that aspherical particles suspended in the water will cause depolarization of the signal. Some level of aspherical particulate matter may be a benefit to the technique, as scattering by micron-sized particles lies within the Mie regime and most of the scattered light will be concentrated in the forward-propagation direction. Consequently, the degree of polarization of the optical signals would decrease along the optical path containing suspended Mie-scattering particles, making the signal more cross polarized while experiencing lesser attenuation by scattering preferentially in the forward direction. This more depolarized signal will scatter from the bottom and forward scatter back to the detector where the cross-polarized signal from the bottom can be detected. Thus, the bottom surface return signal in the cross-polarized channel is composed of three components: the scattering of the signal by aspherical particles before reaching the bottom, surface scattering off of the rough bottom, and aspherical particle scattering along the return path. Thus far, single scattering has been assumed but multiple scattering can also be a factor in the attenuation (Gordon 1982) and depolarization (Churnside 2008) of the laser signal propagating through the water. Although the influence of multiple scattering on the signal depends on the field of view of the lidar and becomes more significant with deeper waters, Churnside (2008) has identified multiple forward scattering as a contributor to the cross-polarized signals in the manner similarly described for the single-scatter aspherical particles. This also appears to be the case for turbulent water flow where preferentially forward-scattered depolarized signals will occur due to refractive index fluctuations caused by turbulence in the flow (Woods et al. 2010).
The technique can function throughout the transition from the extremely shallow water environment to the deep water environment. Once the range overlap ambiguity is no longer an issue, the lidar system can use either one or both polarization channels, depending on signal behavior, to estimate depth. Several polarization bathymetric lidars have demonstrated their applicability in waters deeper than a few meters to tens of meters and have shown bottom return signals and interesting behavior between the copolarized and cross-polarized signals (e.g., Vasilkov et al. 2001; Churnside 2008). Our technique will experience the same type of signal behavior, with the actual depth of detection dependent on the system specifications of the lidar.
Transmission of linearly polarized light and simultaneous detection of the scattered parallel and perpendicular polarized signals enhances the fidelity of range-resolved observations through shallow semitransparent media beyond the conventional polarization indiscriminate approach. By exploiting the variability between polarization orientations of optical signals scattered from sequential surfaces, governing pulse width limitations imposed in the shallow regime are removed. As a result, the traditional depth measurement is effectively transformed into two single surface range measurements. The time responsivity of traditional lidar bathymeters, previously confined by the governing pulse width of the system, are now limited only by the resolution of the time-to-digital converter.
Success of the approach is constrained by the scattering matrices defining the semitransparent media surfaces. The capacity to overcome conventional governing pulse width limitations requires ranging through media bound by a polarization-preserving first surface and depolarizing second surface. Incorporation of additional depolarizing elements along the optical path, such as increased water turbidity, will diminish instrument performance. Emphasis must be placed on performance of optical components within the transmit and receive Mueller matrices in an effort to minimize systematic coupling of energy between detection channels.
The lidar presented here has demonstrated measurement of sequential semitransparent media surfaces of sublaser pulse width depth. By removing the demand for narrow optical and electrical pulse widths, components with other favorable performance attributes can be incorporated into the lidar. For example, lasers of longer pulse width can transmit more energy per pulse and improve the SNR performance of the system, lasers of more favorable transmission wavelengths can be utilized, and less expensive lasers and detectors can be used. The approach can be equally applied to continuous range measurements from extremely shallow to deep semitransparent media.
Evaluation of the linear depolarization ratio can provide information regarding the material properties and physical state of the semitransparent media for use in applications such as identification of land–water interfaces and surface water roughness due to turbulence. Using the polarization approach described here for depth measurement of semitransparent media on targets such as supraglacial lakes can provide estimates of the water volume available to support ice sheet fracture and subsequent lake drainage in the Arctic (Das et al. 2008), with enhanced resolution beyond existing techniques such as passive satellite imagery (Sneed and Hamilton 2011). In the case of Atlantic coastal waters (Parson et al. 1997), evaluation of depth and depolarization can provide information regarding water surface roughness and subsurface topography of the ocean floor in support of nautical charting activities.
S. E. Mitchell was supported by the NASA Earth and Space Science Fellowship Project 154-5064 and the 2008 CIRES Innovative Research Program Project 10652. J. P. Thayer was supported by National Science Foundation (NSF) Grant AGS-1135446. Discussions with SensL Technologies representative Steven Buckley have been instrumental. A patent application has been filed, PCT/US2012/045038 (Mitchell et al. 2012), that includes the details presented in Mitchell et al. (2010). An exclusive license of the innovative technology has been established between the University of Colorado Boulder and ASTRA LiTe, Inc.