74 4. Static <strong>Laser</strong> Scanning4.1.2 Mixed PixelDue to beam divergence, the laser beam is spread out during propagation.Depending on the range <strong>and</strong>the beam divergence, the laser beam creates a characteristic footprint when hitting objects.to be scanned <strong>and</strong> the deflection <strong>of</strong> the laser beam maycause the footprintbelong to only one object but to two or more objectssituated at different distances. Thecannot be identified with one <strong>of</strong> these objects since the range is measured by integratingThe situationto hit a surface that does notreflected energyover the entirefootprint, as characterized by the projected spot. This phenomenon is referred to as mixed pixels, whichcan be anywhere along the line <strong>of</strong> sight [Hebert <strong>and</strong> Krotkov, 1992]. The detected ranges from such mixedpixels are somewhere in between, behind or in front <strong>of</strong> the surfaces.The interpretation for the existence <strong>of</strong> such mixed pixels is described by [Hebert <strong>and</strong> Krotkov, 1992]. If onesurface occludes a second surface, the laser beam is reflected by both objects. The geometricallocation <strong>of</strong>the resulting mixed pixel is obtained according to a description <strong>of</strong> the range <strong>and</strong> the intensity as a complexnumber with the vector componentsv I+4>i (4.3)=where I is the intensity or magnitude, which depends on several parameters, e.g.the reflectivity<strong>of</strong> thematerial, the range, <strong>and</strong> the angle <strong>of</strong> incidence, <strong>and</strong> is the phase, which is proportional to the range. Theresulting elements <strong>of</strong> a mixed pixel caused by two reflections v\ <strong>and</strong> v2 is calculated byv = vi + V2 = h + h + (i + 2)*- (4.4)The addition <strong>of</strong> two vectors results in a new vector, with a phase that can be anywhere, dependingon theratio <strong>of</strong> the lengths <strong>and</strong> depending on the phase angles. Considering the difference in the phase angles A<strong>of</strong> the two objects,a distinction can be made between(1)=A (f>2 -4>1< 7T(2)=A (f>2 -4>1> 7TThe first one results in a mixed pixel with a phase, i.e. the range, between the phase<strong>of</strong> the individualcomponents. The second one produces a mixed pixel with a phase that is either greater than or less than thephase <strong>of</strong> both individual components, depending on the ratio <strong>of</strong> the intensity values. Figure4.1 visualizesthe effects <strong>of</strong> mixed pixels with respect to phase angles <strong>and</strong> intensity values. The left part shows case (1)<strong>and</strong> the right one shows case (2). For (2) a case differentiation is necessary to decide whether the mixedpixel is closer or farther than the object.object.The right figure shows the mixed pixel,which is closer than theThe elimination <strong>of</strong> mixed pixels is proposed to be carried out by applying a median filter to the rangeimage [Hebert <strong>and</strong> Krotkov, 1992]. Most <strong>of</strong> the pixels should be detected since they appear only along thedirection <strong>of</strong> edges. The mixed pixels are <strong>of</strong>ten isolated pixels in 3D space<strong>and</strong> thus, can be removed easierin 3D space than in 2D images, e.g. range images. The elimination <strong>of</strong> mixed pixels is onlysuccessful ifthese pixels are far from objects. In contrast, if mixed pixels occur cumulatively near the vicinity <strong>of</strong> objects,they can rarely be removed automatically.elimination <strong>of</strong> such mixed pixels can be improved.However, in combination with images,The appearance <strong>of</strong> mixed pixels can be avoided with a small beam divergence.the identification <strong>and</strong>The smaller the beamdivergence, the less the probability that more than one object will be hit by the laser beam. Furthermore,the problem <strong>of</strong> mixed pixels is related to laser measurement systems using AMCW technique<strong>and</strong> cannot be
'.4.1 Data Processing 75v=\ j—V2=(l,2)original signal'v2=(h^2lFigure 4.1: Geometrical interpretation <strong>of</strong> mixed pixels for two surfaces. The leftfigure shows a phase difference <strong>of</strong> lessthan n, the right figure shows a phase difference <strong>of</strong>greater than n, adaptedfrom [Hancock, 1999].completely avoided but can be minimized. In case <strong>of</strong> the direct time-<strong>of</strong>-flight principles,the measurementsystem can separate the incoming signals in first <strong>and</strong> last pulses. Thus, the problem <strong>of</strong> mixed pixels shouldnot be <strong>of</strong> interest if a first pulse <strong>and</strong> a last pulseis detectable.Figure 4.2 shows the presence <strong>of</strong> mixed pixels, which are either between two objectsthan the objects. In the figure, a sphere is placed in front <strong>of</strong> a wall. The mixed pixelssphere <strong>and</strong> between the sphere<strong>and</strong> the wall.or farther or closerare both in front <strong>of</strong> theFigure 4.2: Mixed pixels occurred near objects: A sphere is positioned in front <strong>of</strong> a wall. The mixed pixels<strong>of</strong> the sphere are either in front <strong>of</strong> the sphere or between the sphere<strong>and</strong> the wall.seen at the4.1.3 Range/Intensity CrosstalkThe distance measurement system does not operate independently from the received intensityintensity value <strong>of</strong> the reflected laser beam influences not only the noise <strong>of</strong> the rangedistance value.Objects, which differ in reflectivity, measured at the same range,value. Thebut also the absoluteshould have identicaldetected ranges. Unfortunately, reflectivity causes different values for the distance to the objectsintensity <strong>of</strong> the laser beam varies. Thus, the less the intensity, the more biased the rangesince thedata. This is calledcrosstalk between range <strong>and</strong> intensity. This can be distinguished between electronic crosstalk, caused by theimplementation <strong>of</strong> detection electronics, <strong>and</strong> optical crosstalk, caused by the sensor opticsreflections.due to internalThe receiver electronic is limited to function only within a specific intensity range.Measurements derivedfrom intensity values outside the intensity range are noisy or erroneous, cf. Figure 3.44. Ideally, the operat¬ing range should be adjusted dynamically according to the intensity,as it is done in modern total stations.