polarization lidar for shallow water depth measurement

Polarization lidar for shallow water depth measurement

Steven Mitchell,1,* Jeffrey P. Thayer,1 and Matthew Hayman2

1University of Colorado, Department of Aerospace Engineering Sciences, Boulder, Colorado, 80309, USA2University of Colorado, Department of Electrical, Computer and Energy Engineering, Boulder, Colorado, 80309, USA

*Corresponding author: [email protected]

Received 24 August 2010; accepted 18 October 2010;posted 9 November 2010 (Doc. ID 133497); published 15 December 2010

A bathymetric, polarization lidar system transmitting at 532 nm and using a single photomultiplier tubeis employed for applications of shallow water depth measurement. The technique exploits polarizationattributes of the probed water body to isolate surface and floor returns, enabling constant fraction detec-tion schemes to determine depth. The minimum resolvable water depth is no longer dictated by the sys-tem’s laser or detector pulse width and can achieve better than 1 order of magnitude improvement overcurrent water depth determination techniques. In laboratory tests, an Nd:YAG microchip laser coupledwith polarization optics, a photomultiplier tube, a constant fraction discriminator, and a time-to-digitalconverter are used to target various water depths with an ice floor to simulate a glacial meltpond. Mea-surement of 1 cm water depths with an uncertainty of �3 mm are demonstrated using the technique.This novel approach enables new approaches to designing laser bathymetry systems for shallow depthdetermination from remote platforms while not compromising deep water depth measurement. © 2010Optical Society of AmericaOCIS codes: 010.3640, 120.0280, 280.1355, 280.3640.

1. Introduction

Advancements in light detection and ranging (lidar)have enabled measurement of increasingly shallowwater depths (<2 m) for collection of bathymetricdata [1,2]. Present day bathymetry lidar systemsare capable of depth measurements down to tensof centimeters [3–5]. The limit to achieving shallowerdepth measurements is related to the applied techni-que and the imposed demands for short laser pulsewidths and rapid detector response times. Additionallimits occur when analyzing analog-to-digital con-verted waveforms. A demonstration of such wave-form analysis under shallow water conditions usingsignal returns generated by Raman scattering in thewater column is presented in [6]. The signal returnwaveform is the convolution of backscattered nano-second laser pulses from the water with detectorresponse times that, together, constitute the instru-ment bandwidth. Invariably, current techniques for

determining shallow water depth are inhibited bythe overall instrument bandwidth. For shallowwaters, such as those often found along the shorelineof glacial meltponds, limited instrument bandwidthresults in ambiguities among surface reflections, vol-ume backscatter, and floor returns, making waterdepth indeterminable. Future developments of pico-second pulse width lasers and fast detectors canfurther improve shallow water measurement capa-bilities, but at greater cost and complexity. Ulti-mately, these techniques will be limited by pulsebroadening caused by the dispersive properties ofair and water.

This paper introduces a new approach to shallowwater depth determination by exploiting the differ-ing polarization attributes of scattered signals fromthe water surface, volume, and floor. The polarizationpreserving nature of the water surface and volume,as well as the depolarizing nature of rough floor to-pographies, has been demonstrated [7]. Thus signalreturns from the depolarizing floor can be isolatedfrom surface and volume returns through polariza-tion discrimination at sub-pulse-width resolution.

0003-6935/10/366995-06$15.00/0© 2010 Optical Society of America

20 December 2010 / Vol. 49, No. 36 / APPLIED OPTICS 6995

Laboratory experiments performed by the authorsalso demonstrate a significant amount of depolariza-tion produced by ice, suggesting glacial meltponddepths can be determined using this technique.

By using this approach, minimum depth resolutionis no longer limited by laser or detector pulse widthand instead places the demand on the timing electro-nics. For this purpose, we use constant fraction detec-tion of separated surface and floor signals to produceboth accurate and precise timing of lidar histograms.This approach enables better than 1 order of magni-tude improvement in shallow water depth measure-ment. The technique of discriminating polarizedlidar return signals within the pulse width providesa single wavelength solution to shallow water bathy-metric ambiguities. These attributes facilitate mea-surement of water depth down to single centimetersand less.

2. Technique

The fundamental instrument setup for the techniquedescribed here is illustrated in Fig. 1. The transmit-ter consists of a 532 nm linearly polarized laser. Ahalf-wave plate is used to rotate the linearly polar-ized light exiting the laser head into alignment withthe vertical transmission axis of a 532 nm polarizingbeam splitter (PBS) cube. The vertically copolarizedlaser light exiting the PBS passes through a quarter-wave plate that is free to rotate about the opticalaxis. When the fast axis of the quarter-wave plateis oriented 45° to the linear polarization output ofthe cube, the quarter-wave plate retards the linearslow polarization component relative to the fast po-larization component by 90°, emitting left-hand cir-cularly polarized light toward the target water body.

When incident upon the water surface and column,the transmitted circularly polarized light reflectsback to the receiver in a nearly preserving, but oppo-site, circular polarization state. This polarization,180° out of phase from the transmitted state, is re-tarded again by the 45° oriented quarter-wave plate.The result is linearly polarized light incident uponthe PBS, rotated about the optical axis by 90° (hor-izontal) into the reflection axis of the PBS to a photo-multiplier tube (PMT) for detection.

When the quarter-wave plate fast and slow axesare aligned to the PBS transmission plane, no rela-tive phase shift is imposed by the quarter-wave plate.As a result, vertically polarized laser light is trans-mitted to the water. The surface and column arepolarization preserving, reflecting light that isprimarily in the vertical plane. This linearly polar-

ized light passes through the quarter-wave plate un-modified so that the PBS does not reflect the lightinto the receiving channel. However, when incidentupon the floor, the linearly polarized light depo-larizes upon reflection due to the rough topography.The quarter-wave plate has no impact on the back-scattered unpolarized light, of which half is reflectedby the PBS to the detector in the receiver.

Through discrimination of the reflected signalpolarization state between laser firings, the lidartransitions between reception of water and floorbackscatter. This translates the shallow water depthmeasurement problem into two independent altime-try measurements, where target selection is dictatedby the orientation of the quarter-wave plate. Rota-tion of the quarter-wave plate permits the receiverto transition between detection of either state, evenwhen surface and floor returns are contained withineach return pulse. As such, the body of water can beeffectively removed from the return signal, enablingthe depolarized floor signals to be isolated for analy-sis. This can either be performed on a predeterminedpulse-to-pulse basis, as applicable to the presentlydescribed compact single telescope and detector sys-tem, or simultaneously by including a separate re-ceiving telescope with two detectors. In an effort togenerate the most compact and inexpensive instru-ment design for potential use onboard a remote plat-form, such as an unmanned aerial vehicle, thepolarization discrimination between signals is per-formed in this paper on a pulse-to-pulse basis usinga single telescope and detector.

A. Simulation

Shallow water bathymetry using the setup in Fig. 1is dictated by the quarter-wave plate orientation andsubsequent modification of transmitted and receivedpolarization states. An analytical description of thetechnique begins by defining the associated Stokesvector of the linearly polarized laser pulse, ~STx, or-iented using a half-wave plate for maximum trans-mission through the polarizing beam splitter cube:

~STx ¼

264

1−100

375: ð1Þ

An arbitrary wave plate of phase shift γ andfast axis orientation θ is described using Muellermatrices as

VWPðθ;γÞ ¼

26641 0 0 00 cos2ð2θÞþ cosðγÞsin2ð2θÞ cosð2θÞsinð2θÞ− cosð2θÞsinð2θÞcosðγÞ −sinð2θÞsinðγÞ0 cosð2θÞsinð2θÞ− cosð2θÞsinð2θÞcosðγÞ cosðγÞcos2ð2θÞþ sin2ð2θÞ cosð2θÞsinðγÞ0 sinð2θÞsinðγÞ −cosð2θÞsinðγÞ cosðγÞ

3775;

ð2Þ

6996 APPLIED OPTICS / Vol. 49, No. 36 / 20 December 2010

with a half-wave plate γ of π rad oriented to θH andquarter-wave plate γ of π=2 rad oriented to θQ.

The PBS is modeled as a polarizer oriented to θP of0° for transmission along the vertical axis in the in-strument transmitter and oriented to θP þ 90° forhorizontal transmission in the receiver:

PolðθÞ ¼

26664

0:5 0:5 cosð2θÞ −0:5 sinð2θÞ 00:5 cosð2θÞ 0:5cos2ð2θÞ −0:5ðcosð2θÞ sinð2θÞÞ 00:5 sinð2θÞ 0:5ðcosð2θÞ sinð2θÞÞ −0:5sin2ð2θÞ 0

0 0 0 0

37775: ð3Þ

During acquisition of bathymetric measurements,the quarter-wave plate is initially oriented to θQ of45° for transmission of circularly polarized light to-ward the target. After an arbitrary number of laserfirings in this orientation, the quarter-wave plate isrotated to θQ of 0° for transmission of vertical linearpolarization during a second set of laser firings. Inboth orientations, the backscattered light propagatesin the opposite direction from the transmit path,such that the quarter-wave plate is expressed withorientation of −θQ during signal reception.

Combining the transmitted Stokes vector in Eq. (1)with the appropriate Mueller matrices described inEqs. (2) and (3), as depicted by the system layoutin Fig. 1, produces the received Stokes vector:

~SRx ¼ ½PolðθP þ 90Þ · VWPð−θQ; π=2Þ ·Mtarget

· VWPðθQ; π=2Þ · PolðθPÞ · VWPðθH ; πÞ�~STx; ð4Þ

with the intensity measured by the PMT defined as

IRx ¼ ½ 1 0 0 0 �~SRx: ð5Þ

The Mueller matrix Mtarget represents the scatteringphase function of the water target. In these simula-tions, and in the design of our measurements, the de-polarizing components of the scattering matrix willbe the main focus. This is attributed to the observa-tion of significant depolarization caused by coastalshorelines [7] and the authors’ observations of strongdepolarization by ice. As such, the scattering matrix

takes the form of a normalized depolarizationmatrix given by [8] as

Mtarget ¼

26641 0 0 00 a 0 00 0 b 00 0 0 c

3775: ð6Þ

For water surface and volume returns, the magni-tude of a, b, and c are all approximately 1. In thisway the targets are polarization maintaining. How-ever, for rough floor topographies, these terms aregenerally of magnitude less than 1.

Simulation of the normalized received intensity fortargets of varying degrees of vertical linear depolar-ization, represented as element a in Eq. (6), is

illustrated in Fig. 2. Light from a polarization-maintaining target (a ¼ 1) appears sinusoidal, whilea completely depolarizing target (a ¼ 0) produces aconstant intensity of 0.5. By rotating the quarter-wave plate between orientations θQ of 45° and 0° dur-ing bathymetric measurements, received signalstransition between polarized water surface and vol-ume returns and depolarized floor returns.

3. Measurements

Bathymetric measurements were made at the Uni-versity of Colorado, Boulder, using the instrumentconfiguration in Fig. 1. The transmitter consisted of

Fig. 1. Foundational setup of polarization lidar for shallow waterbathymetry.

Fig. 2. Simulation of normalized received intensity for a range ofquarter-wave plate orientations for targets of varying degrees ofvertical linear depolarization.


a cw-diode-pumped passively Q-switched frequency-doubled Nd:YAG microchip laser. The laser outputs2:45 μJ of linearly polarized 532 nm light at a repeti-tion rate of 14 kHz and pulse width of 450 ps. Ahalf-wave plate aligned the laser polarization to thevertical transmission plane of a 532 nm PBS. Lightexiting the PBS was transmitted through a quar-ter-wave plate toward a controlled target consistingof a column of water on top of a depolarizing floor sub-strate. In this case, ice was used as the floor substrateto replicate expected conditions for depth determina-tion of glacial meltponds.

Backscattered laser light received by the instru-ment was collected with a PMT, Hamamatsu modelH7422P, in photon counting mode. The detectiontechnique employs photon counting due to the lowlight levels from the floor return signals during theexperiment, although analog detectors could be usedin the instance where the return signal is sufficientlystrong without compromising the technique. ThePMT operates with a 1 ns rise time and 350 ps tim-ing jitter during output of a 2:5 ns FWHM pulse.Each PMT pulse is passed through a constant frac-tion discriminator (CFD), which determines thePMT signal apex independently of the signal pulseheight. The CFD operates with an intrinsic timingjitter of 3:2 ps, outputting a 2:4 V TTL-level pulsethat is passed to and stored onboard a time-to-digitalconverter (TDC) with 27 ps timing resolution.

For demonstration of depth determination, timingdata were acquired during reception of backscatteredsignals from known water depths of 3 and 1 cm overice in an effort to simulate a glacial meltpond shore-line. The transmitted laser pulse was orientedslightly off nadir for collection of water surface andfloor returns during each run. In the first data set,the quarter-wave plate was oriented to θQ of 45°for reception of polarized surface signals. The seconddata set was then acquired with the quarter-waveplate oriented to 0° to collect backscatter from thedepolarizing floor. Upon completion of each experi-

ment, the timing data were offloaded to a laptopcomputer for analysis.

The TDC produces a histogram with a 27 ps binwidth and one bin entry per laser firing, allowingfor determination of the average time at which thedetector pulses are registered. Figure 3 illustratesthe surface and floor constant fraction detection his-tograms for each depth experiment. Visible in Fig. 3is an initial histogram of timing counts extractedfrom the water surface returns measured over multi-ple laser pulses with the quarter-wave plate orientedto θQ of 45°. The second histogram is from the floorreturns measured over multiple laser pulses with thequarter-wave plate oriented to θQ of 0°. Each histo-gram was normalized to its maximum count value.

The histograms shown in Fig. 3 have a width thatis dictated by pulse jitter from the PMTand the laserpulse width. Generally, these distributions are ex-pected to appear Gaussian; however, the histogramsshown here have an asymmetric shape due to opera-tion of the CFD and TDC modules. The CFD is set toan initial voltage discrimination threshold to passsignals from surface and floor returns and suppressconstant fraction discrimination of noise signals. TheTDC is operated in multichannel scalar mode andinitiates counting when the laser is fired. At thequarter-wave plate orientation θQ of 45°, the surfacereturn is the first photon detected by the CFD andrecorded by the counter. Subsequent return signalsfrom the propagating laser pulse are not countedin shallow waters due to dead time of the electronics.At this point, the TDC waits for another laser pulseto fire and a histogram of surface returns is pro-duced, as illustrated in Fig. 3 (left). Upon rotatingthe quarter-wave plate to θQ of 0°, the detected signaloriginates from the floor and a second, distinct histo-gram is produced, as in Fig. 3 (right). The histo-grams, therefore, represent detection of the firstcounted photon from each pulse. If the probabilityof detecting a photon at time t is given by PdðtÞ,the timing probability distribution function (PDF)

Fig. 3. Normalized digital timing histograms of constant fraction detection for surface and floor returns at 3:0 cm (dashed curves) and1:0 cm (solid curves) water depths.


for counting a photon in first count mode (FCM) isgiven by

PFCMðtÞ ¼ PdðtÞZ

t

0ð1 − PdðτÞÞdτ; ð7Þ

which is the probability of detecting the photon attime t multiplied by the probability that no photonswere previously detected. Thus, in instances wherethe photon detection probability from a single pulseapproaches 1, the PDF appears Gaussian for smallvalues of t. As t increases, the integral term domi-nates and causes the PDF to fall sharply. This resultsin the histogram asymmetry visible in Fig. 3. Addi-tionally, at times where the integral term dominates,uncertainty due to shot noise is minimized. This is adirect result of the integration and supports theclaim that the trailing edge of the timing histogramprovides the most stable reference for calculatingtiming delays for water depth measurement.

Taking into account the refractive index n changeof water relative to air (1.33), the water depth h iscalculated as

h ¼ cΔt2n

; ð8Þ

where the time delay Δt is evaluated by differencingthe half-maximum of the trailing edge timing pointsof the constant fraction histogram for the surface re-turns and the constant fraction histogram for thefloor returns. The results presented in Fig. 3 producetime delays of 247 and 52 ps, corresponding to depthmeasurements h of 2.7 and 0:6 cm, respectively. The27 ps resolution of the TDC imposes a �3 mm uncer-tainty on the water depth estimate, placing theobserved depths within the uncertainty of the physi-cally measured depths of 3.0 and 1:0 cm, which pos-sess a �1 mm uncertainty.

4. Discussion

The results presented in Fig. 3 demonstrate the re-duction of system bandwidth limitations through ex-ploitation of target polarization states. If moretraditional bathymetric techniques were employed,given the 450 ps laser pulse width and 2:5 ns detec-tor response width, water depths less than tens ofcentimeters could not be resolved. By isolating detec-tion of surface and floor returns using polarizationdiscrimination, water depth measurements are lim-ited only by the 27 ps resolution of the timing unit.By removing the need for short laser pulses and fastdetectors, lasers and detectors with other favorableperformance attributes can be used. For instance, la-sers of longer pulse width can transmit more energyper pulse and improve the signal-to-noise aspects ofthe system, lasers of more favorable transmissionwavelengths can be utilized, and less expensive la-sers and detectors can be employed.

To demonstrate independently the extent of thedepth capability of the system, the experiment carriedout in the measurement section is revisited. For thisexperiment, the floor distance remained fixed while 1and 3 cm water depth experiments were performed.Contrasting the setup between measurements, eachfloor return in the 3 cm water experiment is subjectto a transit distance l of 2 cm of water compared tofloor returns traveling through 2 cm of air before en-tering the 1 cm water depth experiment. In thissense, it is expected that the floor return for 3 cmof water would be delayed from the floor return for1 cm by a factor Δ, where

Δ ¼ 2nlc

−

2lc¼ 2ð1:33Þð0:02Þ

ð3 × 108Þ −

2ð0:02Þð3 × 108Þ ¼ 44 ps:

ð9Þ

This is due solely to the change in n from water to airover the 2l round-trip distance.

The floor results of each water depth experimentare plotted together in Fig. 4. The inset is a zoomed-in viewof thehalf-maximumtimingpoints of the trail-ing edges for the floor return curves corresponding towater depths of 3 and 1 cm. Trailing edge values wereused due to their accuracy, repeatability, and reducedshot noise levels, as explained in Section 3. At an ex-pected Δ of 44 ps, the floor returns for each experi-ment would be separated by one 27 ps timing binin the digital timing unit.

Differencing the FWHM timing points of the Fig. 4inset demonstrates the returns from the floor of 3and 1 cm water depths are located in neighboringbins, although the timing unit cannot determinetheir location better than within its 27 ps resolution.This measurement comparison demonstrates thatthe ultimate timing resolution of the technique is dic-tated by the timing bin width and presently indicatesdepths could be determined to within millimeters.

Fig. 4. Overlay of normalized surface and floor histograms fromFig. 3 along with inset of timing differences between the two de-termined floor returns.


5. Conclusions

A novel bathymetry lidar technique employing polar-ization discrimination has been demonstrated, lead-ing to an improvement in shallow water depthdetermination. By transmitting vertical linearly po-larized light through a polarization beam splitterand alternating orientations of a quarter-wave plate,received signals transitioning between polarizedwater surface returns and depolarized floor returnscan be isolated at sub-pulse-width resolution. By ex-ploiting the polarization states of water and floor re-turns, traditional bathymetry instrument bandwidthlimitations are mitigated. The performance of bathy-metric lidars, once confined by laser or detector pulsewidths, are now limited only by the resolution of tim-ing electronics. Constant fraction discrimination and27 ps timing resolution are used in the detectionscheme to ensure accurate timing independent ofthe expectedPMTpulseheight distribution. The tech-nique presented here has demonstrated 1 cm waterdepth with �3 mm uncertainty, more than 1 orderof magnitude improvement over previous approachesto bathymetry lidar, with potential for millimeterdepth measurement. In addition, reduction of tradi-tional system bandwidth limitations decreases theneed for expensive lasers and optical detectors withnarrow pulse widths to measure shallow waters.Longer pulses and more optimal laser wavelengthsmay be used with no consequence on depth determi-nation while potentially improving signal detection.The novel approach can equally be applied to deepwater depth measurements, thus providing a com-plete range of depth determination capabilities.

The first author (S. Mitchell) was supported by theNASA Earth & Space Science Fellowship project 154-

5064 and the 2008 CIRES Innovative Research Pro-gram project 10652. Coauthors (J. P. Thayer and M.Hayman) were supported by National Science Foun-dation (NSF) grant ATM-0454999. Discussions withSensL Technologies representatives Steven Buckleyand David McNally have been instrumental.

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polarization lidar for shallow water depth measurement

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