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When collecting or using LIDAR data, the location of the scanner/sensor relative to the object of interest and the geometry of the object itself can influence the ability to receive returns from laser pulses. These factors can also affect the resulting accuracies of the acquired points. This concept has important implications when selecting the best platform for a particular application. Airborne and helicopter systems will generally have the best look angle for gently sloping topography. Terrestrial systems will have improved results on building facades and cliff faces. An easy way to visually understand the concepts behind grazingincidence angles (how the light hits and reflects from the surface) is to shine a flashlight on a wall and look at the distribution of the light. When you shine it directly orthogonal to the wall, the light pattern is circular. However, when you shine it obliquely, the light produces an ellipse that will become more oblong with increasing obliqueness. Other factors that are important to the effects of grazing are the beam exit diameter and divergence.

Now for the nerdy math to describe what is going on! (We will keep it to 2D derivations for clarity in this article). For the presented derivations, based on scanning a sea cliff, all elevations are relative to the cliff base. Simple geometry can be used to determine the angle of incidence (, angle between the laser beam and surface normal) and grazing angle (, angle between the laser beam and cliff surface). Lower incidence angles and higher grazing angles indicate that the reflection is more direct to the surface.

Figure 1 shows the setup and calculation for airborne LIDAR and Figure 2 shows the setup and calculation for terrestrial laser scanning (TLS). While the geometry and calculations would be the same between the airborne and terrestrial scanners, the equations for each are simplified in a different manner.

First, the general cliff slope can be calculated through trigonometry:

**See PDF for the formulae**

Now that we have discussed the math, let us calculate some values to determine the influence of these parameters on the resulting scanning grazing angles. Figures 3 and 4 show calculated grazing angles based on various configurations of cliff geometry and scanner position. In general, airborne LIDAR has better grazing angles for gentle cliff slopes, while TLS has better grazing angles for steep cliff slopes. Figure 3 shows the grazing angles for the mid-height of the cliff, while Figure 4 shows the worst-case scenario for terrestrial LIDAR at the top of the cliff. Note that for low values of x/h, scanning is performed too close to the cliff, reducing grazing angles. Also, the airborne appears consistent between plots, however, for a fixed airplane position, delta would vary between the mid-height of the cliff and the top, so a different value should be calculated for each position.

Now, why is this important and why go through the math? Ultimately, understanding these fundamentals is important when planning airborne or helicopter LIDAR flight paths or terrestrial scan setup locations to ensure quality data. It is also something important to verify when using a dataset provided by someone else. One of the challenges with LIDAR is the accuracy of every single point varies. Poor scanning geometry can have a much more significant effect on overall accuracy (and resolution) than sensor noise and geo-referencing error. In some cases, you may have no option but to graze because of limited locations you can physically setup at. However, you should be aware of how that will degrade your overall data quality and consider that in your error validation and reporting. When you provide error estimates based on targets and check points that are orthogonal to the scanner, you are not really showing what the quality is in the oblique sections of your data.

To summarize, avoid incidents of poor data by properly planning your surveys so that you can have improved incidence angles!

*Michael Olsen is an Assistant Professor of Geomatics in the School of Civil and Construction Engineering at Oregon State University. He currently chairs the ASCE Geomatics Spatial Data Applications Committee and is on the editorial board for the ASCE Journal of Surveying Engineering. He has BS and MS degrees in Civil Engineering from the University of Utah and a Ph.D. from the University of California, San Diego.*

A 1.037Mb PDF of this article as it appeared in the magazine complete with images is available by clicking **HERE**