International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
    
   
RESEARCH ON THE THREE ANGULAR RESOLUTION 
OF TERRESTRIAL LASER SCANNING 
Ronghua Yang ^^*, Xianghong Hua”, Junning Liu*, Hao Wu* 
? School of Civil Engineering, Chongqing University, No.174, Shazheng Street, Chongqing City, P.R.China - 
yrh2009@gmail.com 
? School of Geodesy & Geomatics, Wuhan University, No.129, Luoyu Road, Wuhan City, Hubei Prov, P.R.China - 
xhhua@sgg.whu.edu.cn, njuil@whu.edu.cn 
* School of Resources and Environmental Engineering, Wuhan University of Technology, No.129, Luoshi Road, 
Wuhan City, Hubei Prov, P.R.China - haowu2010@gmail.com 
Commission III, WG III/2 
KEY WORDS: Terrestrial Laser Scanning, Angular Resolution, AMTF Model, EIFOV Model, Beamwidth, Sampling Interval 
ABSTRACT: 
Terrestrial laser scanning technology has been applied more and more widely in the field of Surveying and mapping. Although 
requirements of the accuracy for different laser scanner survey may differ considerably, spatial resolution is an important aspect, 
which can be divided into range and angular components. The latter is a focus of this paper and is governed primarily by scanning 
interval, laser beam width and angle quantisation. An ultimate goal of this research is to derive the relationship and simplified 
formula between scanning interval and the angular quantisation when the EIFOV(Effective Instantaneous Field of View) is equal to 
the scanning interval; the relationship and simplified formula of scanning interval and the angular quantisation when the EIFOV is 
equal to the laser beam width, and the relationship and simplified formula of the theoretical minimum EIFOV and the angular 
quantisation. Firstly, this paper introduces the EIFOV model and the AMTF(Average Modulation Transfer Function) model. 
Secondly, the dimensionless AMTF and EIFOV generic model are proposed. Thirdly, the above relathionships are deduced, which 
are ellipse or hyperbola, and the three simplified formulas are proposed. The simplified formulas have direct significance on the 
angular resolution's calculation and the scanning interval setting. 
1. INTRODUCTION 
The emergence of the terrestrial laser scanning technology has 
broken the traditional mode of surveying data acquisition and 
processing, and has promoted the development of the objective 
surface characteristics' recovery techinque which is based on the 
measurement model of point cloud(Reshetyuk, 2009; Zhang Yi, 
2008). Recovery degree of the objective surface minuitiae 
feature is described generally by the spatial resolution. In terms 
of terrestrial laser scanning technology, the spatial resolution 
designates the range and angular resolution of point cloud. The 
latter is the main factor to determine the objective details' 
recognition capability of point cloud (Lichti, 2006; Zhu Ling, 
2008), which is governed primarily by scanning interval, laser 
beam width and angle quantisation. At present, Professor 
Lichi’s EIFOV(Effective Instantaneous Field of View)model, 
which was deduced from AMTF(Average Modulation Transfer 
Function) model, is the only one involving above three aspects. 
In practical, the angle quantisation can be changed only by 
selecting different scanner. Scanning interval and laser 
beamwidth are usually required to determine in advance 
through the formula of beam width, the relationship of the 
  
EIFOV and the scanning interval, and the EIFOV of the point 
cloud can be obtained. But no manufacturer of scanner provide 
the formula of the beam width and the range, meanwhile the 
relationship model among the EIFOV, scanning interval, and 
the angular quantisation is very complicated, so that we need to 
develop a simple method to calcuate the magnitude of scanning 
interval on the angular quantisation knowned. Furthermore, the 
magnitude of theoretical minimum angular resolution can be 
used to evaluate the instrument performance. However the 
theoretical minimum angular resolution is unavailable. 
In order to resolve the above problems,Related research would 
be focused on the formulas of differenct scanner in detail: 
1) The relationship and simplified formula of scanning interval 
and the angular quantisation when the EIFOV is equal to the 
scanning interval; 
2) The relationship and simplified formula of scanning interval 
and the angular quantisation when the EIFOV is equal to the 
laser beam width; 
3) The relationship and simplified formula of the theoretical 
minimum E/FOV and the angular quantisation. 
* Yang Ronghua, Ph.D, majors in the theory and application of terrestrial laser scanning technology, yrh2009@gmail.com. 
Project source: National Natural Science Foundation of China(NO.41174010 and No.40901214) 
The Ministry of Land and Resources Sponsorship (NO.1212010914015) 
This paper is a further research with some addition of more introduction of theories, on the base of my Ph.D dissertation 
Research on Point Cloud Angular Resolution And Processing Model of Terrestrial Laser Scanning and an early paper in Chinese 
Research on the point cloud angular resolution of terrestrial laser scanners, which was accepted by Geomatics and Information 
Science of Wuhan University and is in publication plan.