2.1.

Laser Selection

Important considerations for laser selection are the wavelength, divergence, and the pulse length and repetition frequency. The most common wavelength for marine lidar is 532 nm, owing to the wide availability of rugged, small, and inexpensive lasers, and favorable absorption characteristics in natural waters. While the absorption of light in pure water has a minimum at $\sim 420\mathrm{nm}$,³⁶ the absorption minimum shifts to longer wavelengths as the concentration of dissolved organic matter increases.^1,37 Morel³⁸ developed a model that related the chlorophyll concentration to the attenuation coefficient of downwelling irradiance, $K_d$, which showed that at chlorophyll concentrations above $\sim 0.2{\mathrm{mg}/\mathrm{m}}^3$ the attenuation at 500 nm is less than that at 400 nm. Chlorophyll-a concentrations are well above this level in Flathead Lake³⁹ and Yellowstone Lake,⁴⁰ especially during the summer months. For these reasons, we chose 532 nm as our design wavelength.

The laser pulse width creates a limit on the accuracy of depth information that can be obtained by the lidar. For our fisheries application, we simply need to detect the presence of fish and possibly quantify the biomass of the fish present in a given area.⁴¹ We are not able to distinguish fish species; suspected lake trout spawning sites are identified by consideration of the location and depth of the detected fish in concert with other ecological parameters in a manner similar to what is used with acoustical tracking devices.^28,42 In this case, the loss of precision due to a large pulse width is not an impediment. When profiling plankton layers, precise measurements of depth are more useful, but these measurements can be easily obtained from the surface. Thus, while short pulse width was important, it was not a major requirement.

The pulse repetition frequency (PRF) limits the maximum speed that the aircraft can travel while maintaining overlap between adjacent shots and must be high enough to allow for a reasonable flight speed if continuous coverage along the flight path is desired. Thought must also be given to the laser divergence as it is desirable to match the divergence and the FOV of the receiver. Broadening a narrow laser beam is often easily accomplished with a negative lens.

Based on previous positive experiences with Big Sky Laser products, we chose the air-cooled, diode-pumped, 40 mJ Centurion laser (Quantel, Bozeman, Montana). This laser is similarly robust to lasers we have used in the past and is diode-pumped, which provides better electrical efficiency. The Centurion outputs a 40-mJ pulse at 1064 nm, which is doubled to 532 nm. Any residual energy at 1064 nm is blocked. Pulse energy at 532 nm is 26 mJ, output divergence is 5 mrad, pulse length is 7.2 ns, and maximum PRF is 100 Hz. Our pulse-limited depth resolution is 80 cm in water, and with an 800 mega-samples per second (MSPS) digitizer, the sample-rate limited depth resolution in water is 14 cm.

2.2.

Received Signal and Background Power

FOV and receiver aperture size are crucial considerations as the product of aperture area and FOV projected solid angle gives the radiometric throughput for an optical receiver.⁴³ A wide FOV will reduce the effective attenuation in water by capturing multiply scattered photons but will increase the amount of unwanted background light received. To help choose these parameters, we modeled the signal-to-noise ratio (SNR) and signal-to-background ratio (SBR) for various FOV and receiver aperture sizes.

The received electrical lidar signal power $P_{\text{electrical}}(z)$ in watts at depth $z$ is calculated similarly to Churnside¹

Table 1

Lidar parameters to model received signal, SNR, and SBR for various fields of view and receiver aperture sizes. Laser parameters are from the Quantel Centurion laser. Digitizer parameters are for the GaGe CS148001U USB Digitizer. PMT parameters are for the Hamamatsu H7680. Parameters not used in the simulation are unlisted.

The water surface is assumed to be flat and the reflection at the surface is computed using the Fresnel equations for the lidar tilt angle. The value obtained for the surface transmission of $T_S=0.951$ for this simple model does not differ significantly from a rigorous computation by Mobley⁴⁵ for a polarized sky and various wind speeds.

The lidar attenuation coefficient $\alpha$ is an “effective” attenuation coefficient, which accounts for the effects of multiple scattering in the water. The following equation is from Churnside,¹ which was derived from Monte Carlo simulations of oceanic lidar by Gordon:⁴⁶

By definition, $c=a+b$, where $a$ is the attenuation coefficient and $b$ is the scattering coefficient. Measurements of optical properties of local lakes are lacking, so for simulation we were forced to estimate these parameters. Models from Gallie and Murtha⁴⁹ were used to estimate $a$ and $b$ given chlorophyll-a concentration, suspended mineral concentration, and colored dissolved organic matter (CDOM, referred to as “yellow substance” by Gallie). The chlorophyll-a concentration of $0.75\mu \mathrm{g}/\mathrm{L}$ is a representative number from Yellowstone Lake⁴⁰ while the suspended mineral concentration of $3\mathrm{mg}/\mathrm{L}$ and CDOM value of $0.3{\mathrm{m}}^{-1}$ (at 350 nm) are numbers from Chilko Lake,⁴⁹ an oligotrophic lake in British Columbia similar to Yellowstone Lake, as these data were unavailable for local lakes. These values yielded $a=0.179{\mathrm{m}}^{-1}$ and $b=0.8427{\mathrm{m}}^{-1}$ at 540 nm. Thus, for simulation, the beam attenuation coefficient $c=1.0214{\mathrm{m}}^{-1}$.

To compute the diffuse attenuation coefficient, we used the equation from Lee et al.⁵⁰

To determine the volume scattering coefficient $\beta (\pi ;\lambda )$, we used the definition of the spectral volume scattering phase function $\tilde{\beta }(\varphi ;\lambda )$, where $\tilde{\beta }(\varphi ;\lambda )·b(\lambda )=\beta (\varphi ;\lambda )$. The value of the phase scattering function is again taken from Mobley,⁵¹ $\tilde{\beta }(\pi ;530\mathrm{nm})=3.154·{10}^{-3}{\mathrm{sr}}^{-1}$, which yields $\beta (\pi ;\sim 532\mathrm{nm})=3.9·{10}^{-3}{\mathrm{m}}^{-1}{\mathrm{sr}}^{-1}$.

In computing the SNR, we took into account shot and ideal quantization noise. Shot noise power is defined as $P_{\text{shot noise}}=2qIB{R}_L$, where $q$ is the elementary charge, $I$ is the output current of the PMT (including the background signal and dark current), $B$ is the system bandwidth, and $R_L$ is the load resistance.⁵³ The quantization noise power is defined as $P_{\text{quantization noise}}={\delta }_V^2/12$, where ${\delta }_V$ is the digitizer voltage step size. Thus, SNR is computed in dB as (expressed in decibels)

2.3.

Effects of Varying Receiver Aperture Diameter and Field of View

To determine an optimal receiver configuration, we modeled the effects of varying the receiver aperture diameter and FOV. We first tested aperture diameters from 5 to 15 cm for a 5-mrad FOV, which matches the unexpanded laser beam divergence. The results are shown in Fig. 1. Increasing receiver aperture size improves the SNR (by increasing the received signal power), although because of our high background radiance the lidar remains SBR-limited in all configurations. With less background light, the simulation indicates that for a 5-mrad FOV a 15-cm-diameter telescope is optimal, with maximum depth of penetration at 13 m; however, the gains to be had by increasing aperture diameter are quite modest, especially given the expense of a larger aperture and the difficulty of fitting a large telescope in a small airplane. The results for a 15-mrad FOV are similar to those for the 5-mrad FOV.

Fig. 1

Received power (a) and SNR and SBR for a 5-, 10-, and 15-cm-diameter aperture and 5-mrad FOV [parts (b), (c), and (d), respectively]. Increasing the aperture diameter provides modest improvements in SNR, although the lidar remains SBR-limited in each case.

The same plots were generated for 10-, 15-, and 20-mrad fields of view for a 5-cm-diameter aperture (shown in Fig. 2) and follow the same pattern as increasing the aperture size, but with slightly larger improvements in penetration depth compared to the aperture diameter case. Each configuration is again SBR-limited, although increasing the FOV has improved the performance relative to increasing the aperture diameter. Again considering only the SNR, the simulation indicates that a 5-cm-diameter aperture with a 10-mrad FOV outperforms the 15-cm-diameter aperture with a narrower 5-mrad FOV. These plots demonstrate the importance of the FOV in capturing multiply scattered photons as was noted by Gordon.⁴⁶

Fig. 2

Received power (a) and SNR and SBR for a 5-cm-diameter telescope and 10-, 15-, and 20-mrad FOVs [parts (b), (c), and (d), respectively]. Increasing the FOV limits the loss from multiply scattered light.

Figure 3 shows the effects of varying the aperture diameter and FOV on the received power from 5, 7.5, and 10 m in depth, again emphasizing the advantage of increasing the FOV versus increasing the aperture diameter.

Fig. 3

Received power at 5-, 7.5-, and 10-m depth for (a) 5- to 15-cm aperture diameter and 5-mrad FOV and (b) 5- to 20-mrad FOV and 5-cm aperture diameter.

Eye safety is an important part of FOV calculations. The single pulse exposure limit is $5{\mathrm{mJ}/\mathrm{m}}^2$.⁵⁴ Because it is possible for a stationary observer to view two pulses as the plane passes overhead, we apply a correction factor of $N_p^{-0.25}$, where $N_p=2$ is the number of pulses,¹ yielding an eye safety limit of $4.21\mathrm{mJ}/{\mathrm{m}}^2$. For our laser, the pulse energy is 26.8 mJ and our nominal flight altitude is 300 m. Without expansion, the laser beam divergence is 5 mrad, which gives a spot area of $1.75{\mathrm{m}}^2$ on the water surface and a laser energy of $15\mathrm{mJ}/{\mathrm{m}}^2$, above the eye safety limit calculated above; however, expanding the beam to 15 mrad yields a laser energy of $1.7\mathrm{mJ}/{\mathrm{m}}^2$, below the calculated limit.

Our instrument operates at a 5- and 15-mrad FOV, with matched laser divergences. The narrow FOV is used to study the lidar attenuation coefficient in water as it more closely approximates the beam attenuation coefficient.⁴⁶ The wide FOV is used to study fish and plankton because of its greater depth penetration. Section 2.7 discusses the precautions we take in the narrow FOV configuration when the laser beam is not eye safe.

2.4.

Signal-to-Noise Ratio and Signal-to-Background Ratio for Lake Trout

We wanted to verify that the lidar would be able to detect spawning lake trout in local lakes. During the several week spawning season in the fall, lake trout congregate in large groups at spawning sites close to the surface, at depths of just a few meters. Preferred spawning sites are rocky shoals, devoid of vegetation, and the fish will habitually return to the same site each year.^55–61 This behavior is the key that allows lidar to locate their spawning sites and is also why knowledge of the location of their spawning sites is of such importance in controlling their population.

Churnside⁴¹ performed a detailed study of the lidar backscatter from sardines and developed equations to compute the cross-sectional area $A_f$ and volume backscatter coefficient at angle pi ${\beta }_f$ of fish, which we use here to model the lidar signal from a lake trout.

For lake trout, we chose a Lambertian reflectivity $\rho =0.146$, which is a worst-case number for ocean fish as similar data for freshwater fish are unavailable.⁶² 53 cm was chosen for the length, which is a representative number from Yellowstone Lake.²⁷ Using the model from Churnside, we computed ${\beta }_f=0.0016{\mathrm{m}}^{-1}{\mathrm{sr}}^{-1}$. The lidar signal is again computed using Eq. (1) with ${\beta }_f$ substituted for $\beta (\pi ,z)$.

SNR was defined as

Other parameters were the same as in Table 1. The results for a 5-cm-diameter telescope and 5- and 15-mrad FOVs are displayed in Fig. 4, which again demonstrate the advantages of increasing the FOV.

Fig. 4

Received power (a) and SNR and SBR plots for a single lake trout, 5-cm-diameter telescope, and 5- and 15-mrad FOVs [parts (b) and (c), respectively].

2.5.

Coaxial Receivers

Many dual-polarization lidars use a single optical assembly with some method of separating polarizations, either with a polarizing beamsplitter cube, liquid crystal variable retarder,⁶³ or other method of discriminating co- and cross-polarization.

We chose to use separate co- and cross-polarization receivers mounted side by side. Optically, this makes the receivers simpler but increases the difficulty of aligning and calibrating the lidar. Because of this, alignment is performed on the ground at a test range, and calibration is performed in a lab. Alignment while in the air is not feasible due to variations in the signal from the water surface and because the small size of the plane makes it difficult to adjust the lidar while in flight. This raises the concern of the lidar losing alignment during flight and being unable to correct it; however, this has yet to happen.

Each receiver is calibrated separately using an integrating sphere so we are able to make meaningful comparisons between the co- and cross-polarized signal. The sphere is cycled through a series of radiance values, and at each value, the PMT output is recorded as the PMT gain voltage is varied. We then calculate a fit to a $4\times 1$ calibration polynomial, given below

2.6.

Tilt Angle

Marine lidars are typically operated at a small angle from zenith to reduce the unwanted specular reflection from the water surface, which is often very large and can saturate the copolarized receiver. To determine the optimum tilt angle, we performed a simple simulation where we considered the laser as a single ray pointed at the surface (without divergence). Using the calibration discussed in the previous section, we computed the amount of light at each receiver necessary to saturate the digitizer. We then calculated ${\varphi }_{\mathrm{sat}}$, how far in radians outside the FOV ${\varphi }_{\mathrm{FOV}}$ the laser beam could fall while saturating the receivers.

To model the distribution of wave slope angles, we used the Gram Charlier distribution from Cox and Munk.⁶⁴ Shaw and Churnside⁶⁵ showed that the Cox and Munk distribution is valid for near-neutral conditions (i.e., equal air and water temperatures), but that it underestimates surface roughness with negative stability (water warmer than air). We assumed the worst-case scenario where the receiver tilt is aligned with the wind direction. ${\sigma }_u^2$ was calculated using the “clean surface” equations, as were the skewness and peakedness coefficients. We then computed the probability that a wave slope falls within the saturation angle

Fig. 5

The probability of the copolarized receiver at 4-V gain voltage not saturating in 5 min at wind speeds from 1 to $20\mathrm{m}/\mathrm{s}$ and tilt angles from 5 deg to 30 deg. In the final design, we chose 15 deg as our tilt angle.

From the simulation, we chose 15 deg as our lidar tilt angle, but the system was designed so that this angle is adjustable. Increasing the angle beyond 15 deg would lessen the probability of saturation but could possibly eliminate the surface return altogether, in which case our surface detection algorithm would fail. At a $5\text{-}\mathrm{m}/\mathrm{s}$ wind speed and 4-V gain voltage, the probability of the copolarized receiver not saturating in 5 min is 0.94 (min/max radiance is 0.02 and $710\mathrm{W}{\mathrm{cm}}^{-2}{\mathrm{sr}}^{-1}{\mathrm{nm}}^{-1}$, respectively) and the probability of the cross-polarized receiver at a 3.5-V gain voltage not saturating is 0.91 (min/max radiance is 0.02 and $465\mathrm{W}{\mathrm{cm}}^{-2}{\mathrm{sr}}^{-1}{\mathrm{nm}}^{-1}$, respectively), which was acceptable for our purposes. We have not experienced significant problems with saturation at 15 deg in practice. Due to safety concerns, we do not fly if surface wind speeds exceed $7\mathrm{m}/\mathrm{s}$.

2.7.

Final Optical Design

Initially, the lidar was designed with a 5-cm-diameter copolarized aperture and 5-mrad “narrow” FOV (e.g., undiverged laser beam). The cross-polarized aperture diameter was increased to 7.5 cm to better capture the typically weaker cross-polarized signal. After simulation and field studies proved the narrow FOV was inadequate, the capability to operate at a “wide” 15-mrad FOV was added. This is achieved by placing a negative diverging lens in front of the laser and changing out the receiver telescopes. The optical system was designed so that this can be accomplished without adjusting the alignment, and calibrations are performed for both FOVs. A FOV “swap” can be performed on the ground in $\sim 30\min$.

Because the narrow-FOV configuration is not eye safe it is not operated near people or animals. During most flights, this does not present a significant impediment, as the lakes we study are remote and typically have little to no human activity. During flight, the pilot constantly monitors for people/animals and other hazards on the surface, which are easily identified and avoided because of the low flight altitude. These precautions are not necessary for the wide-FOV configuration.

The current system is not scanned, and the receivers and laser are held in a fixed orientation to the plane. This first system was intended as a proof-of-concept to investigate the possibility of studying freshwater ecosystems with lidar. Adding a scanner system would increase the complexity, cost, and size of the system but could be useful in the future.

2.8.

Dynamic Range and Digitizer Considerations

Dynamic range is an important consideration in lidar design. Older designs typically used either a logarithmic amplifier or two separate digitizers to achieve an acceptable dynamic range as high-speed digitizers were limited to eight bits. Designs using logarithmic amplifiers suffer from the challenge of calibrating the amplifiers and large quantization noise for larger signals. Using multiple digitizers also requires careful calibration and attention to matching the phase, frequency, and amplitude responses of each digitizer.

Modern digitizers are just becoming available with high sample rates and larger bit depths. For our project, we chose to use a GaGe CS148001U 14-bit, 800 MSPS USB digitizer from GaGe Applied (Lachine, Quebec, Canada). This digitizer has an ideal dynamic range of 86 dB, but when the effective number of bits (ENOB) is considered the actual dynamic range is only 69 dB, corresponding to an ENOB of 11.2, which provides penetration depth to close to the SNR-limit of the 5-cm-diameter aperture, 15-mrad FOV optical design.

2.9.

Trigger Generation, Computer Interface, and Power Supply

A custom-built trigger generator using a Xilinx (San Jose, California) Spartan-6 field-programmable gate array (FPGA) allowed a USB-programmable variable delay to gate the PMTs and trigger the digitizers. Careful attention was paid during FPGA design to ensure a worst-case timing skew between trigger outputs of 171 ps. A 64-MHz clock frequency provides a delay resolution (in air) of 4.7 m, with a minimum delay of 65 m. Because the trigger delay is programmable, we minimize extraneous data captured by the lidar and enable it to be easily adjusted for different flight altitudes.

All the hardware was designed to interface with the computer via USB, and the entire lidar was controlled from a laptop with one USB cable. This minimizes the amount of cabling in the aircraft cabin and simplified installation. We have, however, experienced some difficulties with the limited data bandwidth of USB 2.0. If the laser was operated at the full 100 Hz PRF, we missed lidar shots because the samples could not be transferred quickly enough to the computer. To avoid this, the laser was operated at a reduced 50 Hz PRF, which still provides sufficient shot overlap at a $44\text{-}\mathrm{m}/\mathrm{s}$ flight speed. Upgrading to USB 3.0 would solve this problem and allow us to fly at a greater speed, but USB 3.0 digitizers were not available when the system was designed. Figure 6 is a block diagram that illustrates the major electronic components of the lidar system.

Fig. 6

Block diagram of the major electronic components of the lidar system.

Despite the higher electrical efficiency of the diode-pumped laser the power requirements for our lidar still exceed what has been available from our small planes. To power the lidar, we used a 12-V, 92 AH deep-cycle battery and a 600-W, pure sine-wave, regulated AC inverter. This configuration was able to power the lidar while collecting data for $\sim 2\mathrm{h}$.

2.10.

Synchronization

A major task was synchronizing each piece of hardware and software because each component was designed to operate asynchronously. The digitizers were synchronized to each other using an Abracon SYNC-10 portable 10 MHz frequency reference (Irvine, California) and a $-3\text{-}\mathrm{dB}$ splitter, with matched cables feeding each digitizer.

The computer was synchronized to global positioning system (GPS) time using a Time Machines TM1000A GPS Time Server (Lincoln, Nebraska). Each incoming piece of data was then timestamped by the computer as it arrived so that it could later be matched with the corresponding GPS location.

To synchronize the digitizers to the computer time, a feature of the GaGe digitizers was enabled that timestamped each shot from a given “epoch,” which is set by the computer. Each shot could then be associated with a matching shot from the other digitizer and timestamped by the computer.

2.11.

Operating Software Design

The software is divided into two major pieces: the application software, which runs the lidar in the air, and the postprocessing software, which generates the images for analysis after a flight.

The application software allows the operator to troubleshoot errors and monitor the operation of the lidar during flight but does not perform any analysis of the data. During the hardware selection, we took note of the programming libraries available for each component and selected C#.NET as the development language for this software program as all the hardware had libraries in this language.

The software enables the operator to adjust the laser PRF, PMT gains, and trigger altitude. Both single shots and an “echosound” plot are displayed, as well as the laser status, temperature, and the GPS location.

Data were stored on the fly in a SQLite database. SQLite was chosen over a “flat-file” storage scheme due to the ease of programmatic access and implementation, with minimal overhead. The application stored the raw data, PMT gains, trigger altitude, and the time for each shot. Laser PRF, sample rate, and laser head tilt angle along with remarks for each run were stored in a separate configuration table. A third table stored the calibration parameters; however, data were not stored calibrated to prevent a mistake in the calibration parameters from ruining data from a run. Each shot had a cross-reference to the related entry in the configuration and calibration table. GPS data were stored in a separate table with both a computer and GPS timestamp, to guard against errors in either corrupting a data run and for comparison.

2.12.

Postprocessing Software Design

After completing a lidar run, the data stored in the database were processed using a Python application that converted the digital number to radiance, calculated the exact location and altitude of each shot, and also computed the location of the water surface and the depth increment for each sample.

The water surface was identified using a basic algorithm that located the maximum signal peak in the copolarized channel and then walked “backward” in the direction of the lidar to 1% of this maximum value, which we called the “surface.” While this algorithm may fail when the surface return is weaker than the volumetric scattering from the water immediately below the surface,⁶⁶ our lidar is not intended to perform high-accuracy bathymetry, and a low-cost solution was preferable to other proposed solutions to this problem, such as a separate infrared or Raman channel requiring an extra receiver and associated hardware.² This is a capability that could be added in the future by unblocking the 1064-nm output of the laser.

Each shot location was calculated using coordinates from a commercial GPS receiver with wide area augmentation system capability. The location of shots taken between position fixes was interpolated.

Shots were assembled into false-color images, an example of which is shown in Fig. 10 in Sec. 4. These images were examined qualitatively for the presence of fish or plankton; no automated algorithms to detect these organisms in freshwater are known by us to currently exist.⁶⁷