Active Triangulation in the Outdoors: A Photometric Analysis

David Ilstrup and Roberto ManduchiUniversity of California

at Santa Cruzdavei@soe.ucsc.edu, manduchi@soe.ucsc.edu

Abstract

Active triangulation is a well established technique forcollecting range points. This work performs a photomet-ric analysis of relative irradiance expected at the camerasensor as a result of intended operating conditions and de-vice parameters including laser power. The limiting effectsof eye safety compliance, minimum realizable shutter timesand pixel bit depth for linear response cameras are con-sidered. Quantitative results are established determiningdynamic range requirements on the camera, when exposurecontrol is needed, and when laser return can be expected toproduce the brightest pixels in the image.

1. IntroductionActive triangulation is a well-established technique for

measuring distance (range) to surfaces. Applications in-clude mobile robotics [10, 9], 3-D photography [2], and as-sistive technology [14, 6]. An active triangulation system iscomprised of a light source and a camera placed at a certainlateral distance (baseline) from the source. It is commonpractice to add narrow-band optical filtering in front of thecamera, to suppress ambient light energy outside the laserwavelength.

In this work we consider systems using a laser striper,which emits a “fan” of radiant energy with a wide spread inone direction and a narrow spread in the orthogonal direc-tion. These systems measure distance to all surface pointswithin the angular sector in the slicing plane determined bythe laser fan geometry. For a number of applications (e.g.curb detection [11]), measuring range within the spread ofthe laser fan is sufficient. By rotating the system around anaxis parallel to the laser fan, it is possible to obtain a full3-D measurement of the environment.

The main challenge with active triangulation is the de-tection of the laser return in the camera image. Ideally, thebrightest pixels in the image would correspond to the laserreturn. Unfortunately, this is not always the case, especiallyin the case of outdoor scenes, where the sun light may add

a non-negligible contribution to the irradiance induced bythe laser at a surface element. The simplest strategy to in-crease rejection of ambient light is to increase the powerof the laser. However, eye safety considerations pose clearlimits to the amount of energy in a laser pulse. In particular,ANSI regulations dictate that the duration of a laser pulseshould be reduced when the power is increased. For rela-tively powerful lasers (with power exceeding 1 Watt), themaximum allowable pulse duration can be on the order of 1microsecond.

Light reflected by a surface element is integrated by thecamera over a certain period of time (shutter time). Theshutter time should be kept to a value no larger than thelaser pulse, in order to avoid integration of useless ambientlight. Unfortunately, typical commercial cameras 1 cannotprovide shutter times smaller than a few microseconds. Thislimits the benefits of using very powerful lasers, with pulsedurations smaller than the achievable shutter time.

This paper provides a thorough photometric analysis ofactive triangulation in the outdoors. Specifically, we ad-dress three important questions:

1. What are the dynamic range requirements of the camera?The imaging system must cope with the dynamic range ofthe light reflected by surface elements. This can be done viaa combination of shutter time, amplification gain, iris, andthe sensor’s ability to map irradiance on a pixel into bright-ness levels. We give a quantitative theoretical expressionfor the expected dynamic range at a pixel for a triangula-tion system in the outdoors, which directly translates intorequirements placed on the camera.

2. When is exposure control necessary? Exposure controlinvolves setting the camera’s shutter time, gain and iris toensure that all pixels with a laser return are correctly ex-posed. This typically results in a delay of a few frames dueto a “settling” period of the exposure control algorithm. Ex-posure control, though, is only necessary when the dynamicrange of the light from the scene exceeds the camera’s own

1 Recent consumer cameras with high ‘megapixel’ counts have longerminimum shutter times.

dynamic range. Based on our quantitative analysis of theexpected range of irradiances at a surface point, one caneasily determine when exposure control is necessary.

3. What are the brightest pixels in the image? The pixelswith a laser return are not necessarily the brightest ones inthe image, even when powerful lasers are used. We providea quantitative analysis of pixel brightness as due to laserreturn and ambient light as a function of laser power anddistance.

2. Related Work

Other works exist modeling the surface irradiance in-duced by a laser stripe, but using a smooth 1D Gaussianprofile [3, 8]. While the authors of [3] consider scene sur-face geometry and reflectance changes in detail, no consid-eration is given to interfering ambient light. The authors of[8] rely on a static camera and scene so that image differ-encing can be used to remove the effect of ambient light.

In [4], the authors attempt to determine the amount oflaser power required for an active triangulation applicationto insure that return is brighter than areas illuminated bysun, yet neglect the effects of illumination angle and surfacereflectivity resulting in estimates that are generally too low.

In [9], a fixed exposure setting is calculated based on es-timated sensor irradiance, typical surface albedo, and theratio between delivered laser power and (Martian) solar ir-radiance. The system is designed so that the laser is severaltimes brighter than the ambient illumination.

In [11], the ANSI standard [1] is applied to demonstratethe eye-safety of an active triangulation device. It is alsonoted that there are some cases falling within intended op-erating conditions where the laser return does not create thebrightest pixel values in the image.

3. Geometric and Photometric Analysis

This section provides an expression of the irradiance at agiven pixel as a function of both laser and sun light and ofthe geometry of the surface being illuminated.

3.1. Surface Irradiance

We begin by deriving the expression of the irradianceon a surface element induced by the laser light. Let’s firstconsider a simplified model of the fanning laser beam ge-ometry. For a laser with divergence γ, minimum beamwidth w and lens with fanning angle β about the opticalcenter, it can be shown that at range R from the center,Ω(R) = β(γ + w/R) is a good model of the solid anglesubtended by the laser. Assuming the power Wl emittedby the laser is uniformly distributed through this solid an-

R

!s

!l"

#

Figure 1. A representation of the active triangulation system witha fanning laser.

gle 2, the radiant intensity Il of the laser is Il = Wl/Ω(R).Consider a small surface element of area dA completely il-luminated by the laser. The apparent area of the patch seenfrom the laser is approximately dA cos θl, where θl is theangle between the surface normal and the line joining thesurface patch to the optical center of the laser. The solidangle subtended by the patch is then dΩ = dA cos θl/R2.Thus the irradiance induced at any point inside the patch bythe laser light is Elsr = IldΩ/dA, or:

Elsr =Wl cos θlΩ(R)R2

(1)

If the surface element is also lit by the sun, then there isa component Esun to the total irradiance on the pixel equalto E⊥sun cos θs, where θs is the angle between the surfacenormal and the direction to the sun. Values for E⊥sun can beobtained, for example, from tables for spectral irradiancefrom the sun (ASTM Standard Tables [7]). Other irradiancecomponents due to diffuse ambient light are usually negli-gible 3, as they are much smaller than direct sun or laserlight.

In conclusion, the total irradiance on a surface elementilluminated by laser and sun light is:

Etot = Elsr + Esun =Wl cos θlΩ(R)R2

+ E⊥sun cos θs (2)

3.2. From Surface Irradiance to Pixel Values

We model the radiance L from a surface patch resultingfrom irradiance by the laser and the sun using the Lamber-

2Typical lasers have Gaussian intensity profiles. For the simple modelhere, extents can be determined by e.g. the full width at half maximum(FWHM) intensity.

3 An important exception occurs when laser light at maximum rangeapproaches the same order of magnitude as diffuse ambient light.

2

tian reflectance model:

L =ρ

πEtot (3)

where ρ is the surface albedo.Consider a pixel that ‘sees’ the surface patch. The irra-

diance on the pixel Epix is equal to [5]:

Epix = Lπ

4

(D

f

)2

A(α) (4)

where D is the diameter of the lens, f is the focal length,and α is the off-axis angle that a ray from the pixel throughthe center of the lens makes with the principal axis. A(α) isa monotonically decreasing function (with A(0) = 1) thataccounts for the cos4(α) attenuation [5] as well as othervignetting effects.

The equation above assumes a flat spectral response ofthe sensor element. In fact, in order to reject ambientlight, it is customary to apply an optical filter in front ofthe sensor, with narrow band-pass spectral transmittance.We approximate the filter’s spectral transmittance as beingconstant and equal to H within the interval [λmin, λmax]with ∆λ = λmax − λmin. We also assume that the laseris monochromatic: Wl(λ) = Wlδ(λ − λl) (with λl ∈[λmin, λmax]) and assume that within [λmin, λmax] the sur-face reflectance spectrum ρ(λ) is constant and equal to ρλl

.Let Esun,λl represent irradiance contributed to Epix by thesun that is not completely removed by the filter. Esun,λl canbe approximated by summing table values [7] for solar irra-diance over the range [λmin, λmax]. These assumptions arejustified since filters used in these systems are narrow band-width, with ∆λ equal to 10 nm not uncommon. Thus, theirradiance on the pixel is equal to:

Epix = Epix,lsr + Epix,sun (5)

=π

4

(D

f

)2

A(α)∫ ∞−∞

L(λ)H(λ) dλ

= Hρλl

4

(D

f

)2

A(α)(Wl cos θlΩ(R)R2

+ E⊥sun,λlcos θs

)For a camera with a linear response function, the measuredpixel value M is equal to:

M = ΓEpix (6)

where Γ represents an abstract representation of camera ex-posure setting. In practice, Γ is the product of the shuttertime, Tsht, the linear amplifier gain, and the lens aperturearea (when iris control is available). Of particular impor-tance in this work is the minimum value that the shutter timeTsht,min can take. Commercial cameras are widely availablewith Tsht,min as low as 10 µs.

10−2 10−1 100 101 10210−3

10−2

10−1

100

101

102

103

LASER POWER Wl (Watts)

MAX

PUL

SE D

UR. T

lsr,m

ax (m

s)

min viewing dist. = 10cm

min viewing dist. = 60cm

Figure 2. Maximum pulse duration Tlsr,max vs. power Wl for anIR (λl=908 nm) laser according to the ANSI eye safety standard[1], assuming a minimum viewing distance of 10 cm and 60 cmfor different frame rates (solid line: 30 fps; dashed line: 15 fps;dashed-dotted line: 5 fps; dotted line: 1 fps). The laser fan pa-rameters are: β = 60, γ=1.5 mrad, w=1 mm.

Note that we don’t consider specular reflection in thiswork. Specular reflection of sun light from metallic or glasssurfaces can produce very high values of irradiance at apixel, which are not modeled by (5). However, these situ-ations usually manifest themselves as isolated bright spots,and can often be detected and ruled out by suitable imageprocessing.

3.3. Laser Power Considerations

3-D measurements are obtained by precisely measuringthe location of laser return on the image. This requires thatthe pixels receiving reflected laser light be reliably identi-fied. In order to facilitate this operation, it is useful to max-imize the power Wl of the laser, so that the pixels corre-sponding to a laser return will be brighter than the pixelsthat only receive ambient light.

There are of course constraints on laser power, the needfor eye safety being perhaps the most limiting. The ANSIZ.136 standard [1] specifies maximum permissible expo-sures to laser radiation, establishing the relationship be-tween power Wl, maximum pulse duration Tlsr,max, puls-ing rate, wavelength, beam characteristics, and minimumviewing distance. For example, Fig. 2 shows Tlsr,max as afunction of powerWl for a particular choice of beam geom-etry and for different pulsing rates and minimum viewingdistances. Note that smaller minimum viewing distancesrequire shorter pulse durations Tlsr,max for the same powerWl.

In order to facilitate rejection of ambient light, the cam-era’s shutter time Tsht should be set to a value no larger thanthe laser pulse duration Tlsr,max. Indeed, if Tsht > Tlsr,max,

3

10!2 10!1 100 101 10210!2

10!1

100

101

$%&'( P+W'( Wl (wa11s)

'456

7%$'

8T P

+W

'( W

l:e< (w

a11s

)

Figure 3. The equivalent power Wl,eq vs. laser power Wl as de-fined in (8) assuming Tsht,min = 10µs. Using same laser param-eters as figure 2 at 30 fps. Green lines: green (λl=532 nm) laser;Red lines: infrared (λl=908 nm) laser. Solid lines: min. viewingdistance = 10 cm; Dashed lines: min. viewing distance= 60 cm.

the sensor integrates useless non-laser light for a period oflength Tsht − Tlsr,max. However, as shown by Fig. 2, largevalues for the laser power require very short pulse durations(less than 10 µs for laser power above 100 mW), and thus itis not always possible to ensure Tsht is less than or equal toTlsr,max. In general, we can rewrite (6) as:

M ∝ Epix,lsr ·Tlsr,max +Epix,sun ·max (Tlsr,max, Tsht,min)(7)

where Tsht,min is the minimum shutter time that the cam-era can realize. This equation accounts for the fact that, ifTlsr,max < Tsht,min, ambient light is integrated by the sen-sor for a longer period than laser light. We define the equiv-alent laser powerWl,eq as the average irradiance from laserreturn over the exposure time:

Wl,eq = Wl ·Tlsr,max

max (Tlsr,max, Tsht,min)(8)

Note from Fig. 3 that, beyond a certain value of power Wl,the equivalent power Wl,eq remains constant.

4. Dynamic Range Considerations4.1. Estimating the Required Dynamic Range

The range of irradiance values onto a pixel receiving re-flected laser light from a surface can be computed as fol-lows. The minimum irradiance Epix,min is achieved whenno ambient light is present (e.g., indoors in a dark room),the surface is at the maximum considered distance Rmax,at the maximum considered incidence angle θl,max and atthe maximum off-axis angle αmax, and for a surface withthe minimum expected albedo ρλl,min. The maximum ir-radiance, Epix,max, is achieved at the minimum considered

distance Rmin for θl = θs = α = 0, and for a surface withthe maximum expected albedo ρλl,max which is also illu-minated by the sun. The ratio of Epix,max and Epix,min isthe full dynamic range of irradiances incident on the sensorDRE :

DRE =Epix,max

Epix,min(9)

=ρλl,max

ρλl,min

K1(Rmin, Rmax) +K2(Wl,eq, Rmax)cos θl,maxA(αmax)

where

K1(Rmin, Rmax) =Ω(Rmax)Ω(Rmin)

R2max

R2min

(10)

K2(Wl,eq, Rmax) =E⊥sun,λl

R2maxΩ(Rmax)Wl,eq

The presence of ambient light (term E⊥sun,λlin (10)) con-

tributes to the dynamic range through K2(Wl,eq, Rmax), al-though its effect can be mitigated by increased equivalentlaser power. The minimum and maximum operating dis-tances (Rmin and Rmax) are application-specific. It is im-portant to note that (Rmax/Rmin)2 strongly affects the dy-namic range and cannot be mitigated by increased equiv-alent laser power. The maximum incidence angle (θl,max)and extremes of albedo (ρλl,min and ρλl,min) depend on theoperating environment. For example, snow or bright whitesynthetic surfaces may have albedo as high as 0.9 while newasphalt or black matte painted surfaces may have albedo aslow as 0.05 [13], giving a ‘surface term’ ρλl,max/ρλl,min ofabout 20. Fig. 4 (a) shows DRE (conveniently expressedin bits, by taking its logarithm base 2) as a function of thelaser powerWl for specific choices of parameters, assumingthat Tsht,min = 10µs. Note that for large values of Wl thedynamic range DRE flattens out to a constant value. It isalso worth noting that Ω(Rmax)/Ω(Rmin) does not dependon β and is close to one for typical values of γ, w, Rmax

and Rmin).

4.2. Matching the Dynamic Range

In order to produce a usable image, the camera needs tomatch the expected dynamic range. Let Γmin and Γmax bethe minimum and maximum values for the camera’s expo-sure settings (as defined in Sec. 3.2), and let Pmin and Pmax

be the minimum and maximum pixel values in the linear re-sponse range of the camera. For example, we could choosePmin = 1 and Pmax = 254 for a typical 8-bit camera. Fol-lowing [12], we define the camera’s dynamic range as

DRP =Pmax

Pmin(11)

A given value of pixel irradiance Epix will be called com-pliant if it can be linearly mapped onto a pixel value be-

4

tween Pmin and Pmax. In other words, Epix is compli-ant if there exists a value Γ ∈ [Γmin,Γmax] such thatPmin ≤ ΓEpix ≤ Pmax. This condition can be re-writtenas:

Pmin

Γmax≤ Epix ≤

Pmax

Γmin(12)

4.2.1 Matching the Dynamic Range of a Pixel

The compliance of an irradiance value is determined bothby the camera’s dynamic range Pmax/Pmin and by theavailability of a suitable exposure setting Γ4. The balancebetween these two camera properties is examined in detailin the following.

Let Epix,min and Epix,max be the minimum and maxi-mum compliant irradiance values at a pixel receiving laserreturn, as defined in Sec. 4.1. From (12) we derive the con-dition for all irradiances between Epix,min and Epix,max tobe compliant:

Pmax

Pmin≥ Γmin

Γmax

Epix,max

Epix,min=

Γmin

ΓmaxDRE (13)

We will concentrate in the following on the shutter time Tsht

component of Γ, assuming that the other parameters (gain,iris) are kept fixed. This translates into

Γmin

Γmax=Tsht,min

Tsht,max(14)

Based on the discussion in Sec. 3.3, Tsht,max should beset to max(Tlsr,max, Tsht,min): increasing Tsht beyond thisvalue simply increases the amount of useless ambient lightbeing integrated. We thus obtain the following condition forthe camera’s dynamic range:

DRP =Pmax

Pmin≥ Tsht,min

max(Tlsr,max, Tsht,min)DRE (15)

This result states that if the camera enables arbitrarily smallshutter time, the required dynamic range DRP can be arbi-trarily small: all of the variations of irradiance at a pixel canbe accounted for by properly choosing the shutter time. Thefact that the shutter time cannot take arbitrarily small valuesimplies that the variations of irradiance at a pixel must alsobe accounted for by the each pixel’s dynamic range.

Fig. 4 (b) shows the required dynamic range DRP as afunction of the laser power Wl for a particular choice ofparameters. Note that Tlsr,max increases as the laser powerincreases. For large enough values of Wl, the first term inthe rhs of (15) becomes equal to 1, and thus DRP becomesequal to DRE (shown in Fig. 4 (a)).

4Note that selecting an appropriate value for Γ requires some mecha-nism of exposure control.

When the amplifier gain and/or the iris are allowed tochange, then term Γmin/Γmax in (14) may take smaller val-ues. Fig. 4 can be easily modified to account for this, by“lowering” all curves by a constant amount. Gain and/oriris control are especially effective when Tsht has reachedits minimum value. However, use of iris or gain controlcannot change the fact that when Tlsr,max < Tsht,min, thecamera integrates more ambient light, thus decreasing thesystem’s ability to detect the laser return.

4.2.2 Matching the Dynamic Range Matching of anImage

Within a single frame, the exposure setting Γ is constant.We will say that an image is compliant if all pixels in theimage receiving laser return are compliant for a given Γ.It is easy to see that the ratio between the maximum andminimum compliant irradiances for fixed Γ is equal to thecamera’s dynamic range DRP . Hence, a sufficient condi-tion for image compliance is the following:

DRP ≥ DRE (16)

Note that the requirement in (16) is very conservative. Itmay well be (and often is the case) that all pixels in an imageare compliant, even though the camera does not satisfy (16).In fact, the importance of (16) is in that it highlights thefact that if a camera does match the dynamic range at apixel, then exposure control is not necessary (see for exam-ple Fig. 5). If this is not the case, a suitable control settingΓ can maximize the number of pixels that are correctly ex-posed. If the image is non-compliant (as in the case shownin Fig. 6), no exposure setting is able to correctly expose allof the laser return points.

4.2.3 Allowing for Saturation

Our compliance requirement can be relaxed if pixels withlaser return are allowed to saturate (e.g. Fig. 7). If suchpixels are safely expected to be the brightest ones in theimage, saturation for these pixels can be tolerated (but seeSec 4.3 for limitations of this assumption). This translatesinto a different expression for the dynamic range at a pixel,which can be substituted for DRE in (15) and (16). K2 isdefined as in (10):

DRE,sat =ρλl,max

ρλl,min

K2(Wl,eq, Rmax)cos θl,maxA(αmax)

(17)

As seen in Fig. 4 (a) and (b), allowing for saturation has thedesirable effect of significantly reducing the dynamic rangerequirements. However, it is critical that values of pixelsthat do not correspond to laser return be not saturated. En-forcing this condition via exposure control is a non-trivialproblem, since the control algorithm would have to know in

5

10−2 10−1 100 101 1020

2

4

6

8

10

12

LASER POWER Wl (watts)

DYNA

MIC

RAN

GE

DRE (b

its)

(a)

10!2

10!1

100

101

102

0

2

4

6

8

10

12

LASER POWER Wl (watts)

RE

Q’D

DY

NA

MIC

RA

NG

E D

Rp (

bits)

(b)Figure 4. Full dynamic range at a pixel DRE (a) and requiredcamera dynamic range DRP in order to insure pixel compliance(b) as a function of the laser power Wl. It is assumed that onlythe shutter time T component of Γ is allowed to vary, and thatTsht,min = 10µs. In all plots, the laser is fanned over β = 60

with divergence equal to γ = 1.5 mrad and minimum line widthequal to w = 1 mm. The maximum considered incidence angleis θl,max = 60. The sun light Esun(λ) is modeled using ASTMStandard Tables [7] for full sun at sea-level. The bandwidth of theoptical filter is 10 nm. It is assumed that ρλl,max/ρλl,min = 20.A frame rate of 30 fps is assumed. The plots refer to the pixel atthe principal point, i.e. α = 0. Green lines: green (λl = 532 nm)laser; Red lines: infrared (λl = 908 nm) laser. Lines with circlemarkers: Rmax= 6 m; Lines without circle marker: Rmax= 3 m.Thin lines: saturation not allowed; Thick lines: saturation allowed(see Sec. 4.2.3). Solid lines: min. viewing distance = 10 cm;Dashed lines (hollow markers): min. viewing distance = 60 cm.Points with DRP = 0 bits indicate situations where the laser re-turn can be mapped to Pmin by a suitable shutter time T .

advance which pixels correspond to a laser return and whichdon’t. A natural use of (17) then is to determine that expo-sure control is not needed and perform a brightness calibra-

Figure 5. An example of a compliant image. All pixels with a laserreturn are well exposed.

Figure 6. Example of a non-compliant image. The two imagesof the same scene have been taken with very different exposureparameters. In the first one, the laser return from the nearby lightsurface is well exposed, but the laser return from the far away darksurface is not visible. In the second case, the situation is reversed:the first return is saturated and indistinguishable from the saturatedbackground, while the laser return from the far away dark surfaceis visible. There is no exposure setting that makes both returnscorrectly exposed.

6

tion to a fixed exposure control value so that the brightestnon-laser returns are just below saturation.

Figure 7. An example image where much of the laser return issaturated, yet can be clearly distinguished from the bright (non-saturated) surrounding background. Saturated pixels are markedred in the right image.

4.3. What is the Brightest Pixel in the Image?

In an active triangulation system, it would be very desir-able that the brightest pixels in an image correspond to laserreturn, as it would simplify laser return detection. Severalfactor contribute to the balance between the irradiance com-ponent due to the laser return and that due to ambient light.We can consider a worst-case scenario, by comparing themaximum irradiance at a pixel as a function of sun lightonly (which occurs for θs = 0 and high albedo) with theminimum usable irradiance from laser return (for incidenceangle equal to θl,max and low albedo) as a function of thedistance R:

Msun,max

Mlsr,min(R)=ρλl,min

ρλl,max

K2(Wl,eq, R)cos θl,maxA(αmax)

(18)

We define by Rthr the value of distance such thatMsun,max/Mlsr,min(Rthr) = 1. Only when R < Rthr arethe pixels with laser return certain to be the brightest ones inthe image. This means that ifRmax > Rthr, one cannot relyon brightness alone to identify the laser return on an image,and other detection mechanisms should be employed. Forexample, one may turn the laser on for one frame and offat the next frame, and compute the difference between thetwo images to reject stationary background pixels. One mayalso exploit the characteristic shape of the laser return, andonly consider conforming brightness ridges in the image aspossible candidates.

Fig. 8 shows plots ofRthr vs. laser powerWl for a greenand an IR laser, with minimum viewing distance of 10 cmand 60 cm. The IR laser allows larger Rthr since sun lighthas more power in the green spectrum than in the IR spec-trum. Rthr becomes constant beyond a certain value of Wl

because the shutter time cannot take arbitrarily low values.Fig. 9 shows a case in which all pixels with a laser returntake lower values than pixels in a region of strong sun light.

10−2 10−1 100 101 1020

0.2

0.4

0.6

0.8

1

1.2

1.4

LASER POWER Wl (Watts)

DIST

ANCE

Rth

r (met

ers)

Figure 8. The maximum distance Rthr at which a pixel with laserreturn is certain to be brighter than any other pixel receiving onlyambient light, as a function of the laser power Wl,eq. Green lines:green (λl=532 nm) laser; Red lines: infrared (λl=908 nm) laser.Solid lines: min. viewing distance = 10 cm; Dashed lines: min.viewing distance= 60 cm. See caption of Fig. 4 for the parametersof the system considered for these plots.

Laser light M=76

Sun lightM=253

Laser light M=14

Figure 9. An example of an image in which the pixels receivinglaser return are not the brightest ones.

5. Conclusions

Perhaps the most obvious conclusion from our analysisis that although increasing the laser power in an active trian-gulation system can improve rejection of ambient light (andthus detection of the laser return), this improvement is lim-ited by the fact that cameras cannot accommodate arbitrar-ily small shutter times. Indeed, even with powerful lasers,ambient light may generate higher values of pixel bright-ness than laser return from surfaces after a certain distance.Furthermore, we have shown that increasing the laser powerleads to higher requirements in terms of camera’s dynamicrange for correct exposure, as the range of realizable shut-

7

ter times is decreased. Our analysis has also highlighted thedynamic range requirements of a camera in order to avoidthe need for exposure control.

6. AcknowledgementsThis material is based upon work supported by the Na-

tional Science Foundation under Grant No. BES-0529435.

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