The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
164 
Wagner et al., 2006), yet many issues require further 
clarification. 
One unresolved problem is that there is not yet a consensus on 
the definition and usage of the involved radiometric and 
reflectance quantities. For example, the echo amplitude 
recorded by topographic lidars is most commonly referred to as 
“intensity” despite the fact that in physical terms it would be 
more natural to associate the intensity with the total energy of 
Being the ratio of infinitesimal quantities, the BRDF cannot be 
measured (Schaepman-Strub et al., 2006). Real measurements 
always involve an average of / over finite intervals, e.g. over 
the solid angle Q. It should also be noted that Equation (1) 
assumes monochromatic, uniform, and isotropic (L is constant, 
independent of 0 and </)) illumination and does not treat 
interference, diffraction, transmission, absorption, fluorescence, 
and polarisation effects (Kavaya et al., 1983). 
one echo, while the amplitude measurement only characterises 
the peak power of the echo. Also, terms like “reflectivity”, 
“reflectance”, or “backscatter” are often used synonymously 
without providing a clear definition of their meaning. 
In this paper we firstly review some definitions of physical 
quantities used for describing the scattering of radiation by 
In lidar applications the basic measurable quantity is the 
biconical reflectance p defined as the ratio of the scattered 
radiant flux P s in the direction (0 S , <p s ) within the cone El s to the 
incident flux Pi in the direction (6*„ <f>) within Q, (Kavaya et al., 
1983): 
objects (Section 2). Then we discuss approaches for the 
radiometric calibration of full-waveform ALS data using 
external reference targets (Section 3) and show some results of 
case studies carried out with full-waveform data acquired with 
the RIEGL LMS-Q560 (Section 4). 
p{a i ,n s )= Ps f s ^ s ' ,Qs ) (5) 
2. SCATTERING THEORIES 
2.1 Biconical Reflectance 
Due to the quasi collinear backscatter geometry 0 S s <9, and <f), = 
<pi+K. Considering that in ALS the solid angles of both the 
illuminating and received radiation are typically small, the 
biconical reflectance can be written as: 
The scattering (reflectance) theory as commonly employed by 
the remote sensing community in the visible and infrared 
p{Çli ,Q S ) = (/(6»,</>■ 9, f + tt))Q s cos0 S (6) 
portion of the electromagnetic spectrum was introduced by 
(Nicodemus et al., 1977) (Schaepman-Strub et al., 2006). The 
basic quantity of this theory is the bidirectional reflectance 
distribution function/(BRDF) [sr 1 ] defined by 
where the brackets () indicate the average over the finite solid 
angle intervals Q, and Q s . 
2.2 Cross Section 
(l) 
E i\QiA) 
where L s is the scattered (reflected) radiance, E, is the irradiance, 
and 0 and (f> are the zenith and azimuth angles. The subscripts i 
In radar remote sensing one deals with coherent radiation which 
requires that scattering phenomena are described using the laws 
of electrodynamics. In electrodynamics the basic quantity to 
describe the scattering of a wave by an object is the cross 
section <r[m 2 ] customarily defined by (Jackson, 1983) 
and s refer to the incident and scattered radiation respectively. 
The radiance L [Wm' 2 sr'‘] is defined as 
1 = — (2) 
cosOdA dd. 
(e,-e;\ 
cr = lim 4kR 1 ' / (7) 
R -> 00 |e,| 2 
where d2P is the radiant flux [W] through an area dA in the 
direction (0, ((>) within the cone dil The irradiance E [Wm-2] is 
£ = — (3) 
dA 
where R is the distance to the target, E, and E, v are the incident 
and scattered electric field vectors respectively, the brackets () 
denote the ensemble average (for the case of rough targets), * is 
the symbol for the complex conjugate, and 11 is the absolute 
value. The incoming wave E, is usually assumed to be a plane 
wave travelling along the direction (B h <fi,). The scattered field 
E 5 is found by considering the boundary conditions imposed by 
the target (geometry and dielectric properties). 
Thus, the BRDF can be expressed in terms of the incident and 
scattered power: 
f&AA.tsh - f , P : „ (4) 
cos 6(5 dPj dQ s 
In radar remote sensing of the earth’s surface the target is larger 
than the resolution cell of the radar system. In such a situation it 
is advantageous to introduce the cross-section per unit- 
illuminated area [m 2 m' 2 ] (Ulaby et al., 1982): 
a°=^- 
A: 
(8)