To investigate the repeatability of measurements (random error) under static conditions, the variance and the coefficient of variation of the readings were estimated for the short, medium and far measuring ranges. For this purpose the sensor was fixed on a tripod with a horizontal beam orientation. The reflection media were a white sheet of paper, plant leaf and soil (sand). The reference distance was taken in a first step from a tape to adjust the short, medium and far ranges. The systematic error (offset) was not estimated because under real measuring conditions in crops, the height of reflection points is calculated for crop assessment [2]. For this the measuring system is configured in such a way that the ground level reflection height is zero. In this case constant offsets would be eliminated. Differences in sensor height related to the basic vehicle are avoided by the height guidance unit, according to Figure 1.

To investigate the light intensity distribution inside of the spot the sensor was fixed on a tripod with a horizontal axis. A white sheet of paper was placed perpendicular to the beam at three distances. Because laser light with a wavelength of 780 nm and cannot be observed identified by the human eye a digital camera and a ruler were used to indicate the intensity distribution inside the laser beam.

Laser beams have a certain diameter. Because of this feature a beam can produce two or more reflexion levels when targeted on fine structured objects and therefore failure readings can be generated. Hence, the sensitivity inside the beam was investigated. For this purpose the horizontal oriented beam of the sensor investigated was directed on a rear medium distance surface of sandy soil (reflection level B). Then a second reflection surface consisting of a leaf from a ficus plant (reflection level A) was installed in front (Figure 2). The leaf had a straight edge cut with a shear and was fixed in the movable part of a micrometer screw. The fixed part of the micrometer screw was clamped on a tripod. With this arrangement it was possible to move the edge of the leaf forwards and backwards through the laser beam in a stepwise fashion with high accuracy. Because the distances to both reflection surfaces were known, conclusions about the measuring properties were possible.

To investigate how different measuring ranges and target velocities influence the measurement properties, a disc (diameter 380 mm) made from acrylic glass was used (Figure 3). The disc was covered up with green paper and 12 strips made from oilseed rape leaves were stuck on the periphery. The strips were about 38 mm wide and protruded about 30mm from the periphery like the teeth of a gear. Subsequently, the toothed disc was positioned in the laser beam in such a manner that while turning the laser beam alternatively targeted the leaf stripes (reflection level A) and the gaps in a radius of 200 mm. A shell filled with wet sand soil was positioned vertically and perpendicular to the beam to generate the reflection level B. For estimating the ratio from teeth (R_teeth) of oilseed rape leaves to gaps (R_gaps) a specific measurement with a triangulation sensor was performed. The movement of the acrylic glass disc was performed by a small electric drive. The circumferential speed steps were V₁ = 1.67 m s^-1 V₂ = 3.34 m s^-1, and V₃= 6.70 m s^-1 and therefore within the interval of ground speeds of agricultural machines.

To test the measurement properties under real field conditions the laser rangefinder was mounted on a tool carrier together with a swivel drive. In the case of large measuring distances and swivel angles, it is very difficult to investigate the functional relationship between the reflection distance and crop biomass density. An exact site reference to the scanned area can be found only at a high expense. Laser rangefinders can be assessed however in terms of their measuring properties for greater distances by always scanning the same crop plants. Under field conditions, those requirements can be created by a laser sensor mounted on a base vehicle in such a way that its swivel axis is oriented perpendicular to the base vehicle. If the base vehicle is parked in a crop field, for each scan exactly the same crop biomass can be ensured. In this case, the laser sensor should measure the same mean reflection distance for each scan. Based on the variance of the mean reflection distance of each scan it is possible to assess the repeatability of measurements under constant crop conditions.

Another way to assess the sensor properties for larger measuring distance, is to scan characteristics of the crop field as tram lines or stock edges. This should be marked by leaps in reflection distance in the individual scans clearly according to the corresponding swivel angles γ. The sensor was moved with a special swivel body (Figure 4). The swivel axis was arranged perpendicular to the base vehicle and it was swung with a crank arm on a swivel angle of 73 ° and with a frequency of about 1 Hz. The time-synchronous measurement of the swivel angle was performed with a P500A.160 L300 rotation angle sensor (Positek Ltd., UK). As inclination angles φ of the sensor, 45 °, 60 ° and 75 ° were chosen. The crop plots scanned were ripe winter wheat in the summer of 2007 and shooting winter wheat in the Spring of 2008.

Growing and established crop plants have, in contrast to trees, a height in the range of decimetres. Therefore an accuracy at the millimetre level is necessary to measure crop parameters for agricultural production processes. The distance measurements for unmovable target areas like a white sheet of paper, an oilseed rape leaf and sand soil resulted in standard deviations for random errors in the range of millimetres (Table 3). A slight increase was observed for far distances. For most agricultural applications this measuring accuracy is sufficient because roll, pitch and yaw movements of the basic agricultural vehicle cause higher inaccuracies. The exact definition of a tolerable error limit cannot be given with the current state of knowledge.

According to the manufacturers' information the diameter of the laser spot (D_spot) can be calculated approximately: D_spot ≈ 2.5 mm + 0.0005×(measuring range in mm). That means e.g. the spot has a theoretical diameter of about 7.5 mm in the range of 10.00 m. The measurements (Figure 5) confirmed the magnitude of beam cross section given by the manufacturer. Figure 5 demonstrates however that the distribution of light intensity differs from the concentric shape and therefore from the ideal Gauss beam cross section distribution. From this irregular distribution it results that the laser rangefinder has specific beam parameters and therefore specific measuring features. As a consequence of this the theoretical considerations on measuring properties will suffer.

Based on the measuring arrangement in Figure 2 increased standard deviations were observed when the sensitive laser beam targeted two reflection areas (oil seed rape leaf and soil surface) simultaneously. Figure 6 demonstrates this measuring property in the upper measurement range. When the beam targets either the leaf of oilseed rape or the soil surface, the standard deviation was within the range of the readings under static conditions. However, when the beam targets both reflection objects, the standard deviation increased up to 8 mm. Furthermore, from Figure 6 it can be concluded that the sensor readings reflect the relation of illuminated areas resulting from both reflection levels adequately. The influence of movement direction (forwards, backwards) of the leaf on measured distance and standard deviation was marginal. Serious outliers were observed, particularly if the reflection level A was close and reflection level B was further away from the sensor.

For the assessment of measuring properties under dynamic conditions it was necessary to estimate in a first step the ratio from the oilseed rape leaves to the gaps between the leaves (Figure 3). This resulted in R_teeth = 0.365 to R_gaps = 0.635. From this the theoretical resulting measuring distance l_cal was calculated according to eqn. (1): (1) l cal = R teeth l A + R gaps l Bwhere l_A represents the distance from sensor to reflection level A (teeth from oilseed rape), in m, and l_B the distance from the sensor to reflection level B (soil surface), expressed in m (the distances between the sensor and levels A and B were estimated by the rangefinder readings themselves under static conditions.)

Table 4 shows the absolute and relative deviations from the calculated reference distances. The absolute deviations were in the centimetre range and the relative deviations were less than 1 %. Mostly the laser rangefinder measured a slightly higher distance then that calculated according to Eq. (1). An influence of the circumferential speed (equivalent to the vehicle ground speed) in the investigated interval was not recognisable. This can be explained mainly by the ratio for the speed of light (about 3x10⁸ ms^-1) to the speed of target areas in the range of a few ms^-1 and the co-axial arrangement of the transmitter and receiver of the sensor.

To demonstrate exemplarily the conformity of laser readings from the individual scans in visual form, the measured reflection distances and the corresponding swivel angles were combined (Figure 7). The crop was ripe winter wheat immediately before harvest. As Figure 7 expresses, the characteristic patterns of each scan were reflected. Particularly striking are the jumps, caused by the tram lines. In this figure, single points can be observed which obviously cannot result from the crop. Nevertheless, based on the high number of measuring points for each scan, the mean values of scans differ slightly. To assess the scans more quantitatively, the readings for both scanning directions were compared. This comparison, summarized in Table 5, shows that the mean reflection distance of the individual scans has a standard deviation in the range of centimetres for ripe winter wheat and millimetres for green winter wheat. The corresponding coefficients of variation were less than 1 %. An explanation for the reduced standard deviation in green winter wheat results from the used wavelength of 780 nm. At this wavelength green plants reflect the light very intensely.

In agriculture the exploitation of laser rangefinders for optimisation of production processes is just beginning. Resulting from the current state of knowledge laser rangefinders can be used successfully in a site specific technique for application of fertiliser and crop protection agents and also on harvesting machines. In the market-available agricultural machinery sector low cost laser rangefinders are installed on combine harvesters. For example, the agricultural engineering company CLAAS in Bielefeld (Germany) attaches a laser rangefinder (Laser pilot) on Lexion combines harvesters for detection of crop edges. Based on this information the steering mechanism keeps the optimum cutting width constant. A similar solution can be found on the newest CX-combine harvester from the CASE-NEW HOLLAND company (Lake Forest, IL, USA) named Smart-Steer. Besides the optimisation of cutting width the accuracy of yield mapping can be improved.

The laser rangefinders used on combine harvesters are not able to detect detailed crop parameters like, e.g., the crop biomass density. As shown in the introduction, the laser scanner systems used in the field of remote sensing are very cost and labour intensive and therefore not suitable for agricultural practices. In agricultural engineering research only a low cost laser scanner and laser rangefinder with a fixed beam (e.g. those of the SICK AG, company, Waldkirch, Germany and Schmitt Measurement Systems, Inc., USA) were investigated. As discussed in this paper, each sensor system has specific measurement features and generates inconsistent readings, so the comparison of readings gathered under different conditions is very limited.

For both remote sensing with expensive laser scanner systems and low cost laser scanners for agricultural applications it is necessary to discriminate between soil surface and plant material. Because of a lot of modelling experience in remote sensing science the developed methods should be tested and transferred to agriculture for crop assessment.