Kushida et al., 1994a; Kushida et al., 1994b) and 
stereo photogrammetry in this paper. The simulated 
reflectance factor is compared with measured. Using 
this model, rice canopy bidirectional reflectance 
characteristics are analyzed. 
2. SIMULATION MODEL 
2.1 Field and light conditions 
Basically straight forward method, with which a 
photon is traced time sequentially is used. A photon 
comes out of a light, traveling in a canopy, and then 
absorbed in the canopy or gets out of the canopy. 
Radiative transfer in canopy and  bidirectional 
reflectance from canopy can be simulated by 
increasing the number of photon. The fate of a photon 
is decided by condition of both incident light and 
canopy physical state. The former is presented using 
light's incident direction - intensity characteristics as 
probability density function. The latter are mentioned in 
2.2 and 2.3 in detail. 
Simulation of wide spread canopy is restricted by 
capacity of computer memories. But, when a canopy 
can be presented by repeat of a basic unit, the 
simulation can be carried out with as much memories 
as necessary for basic unit simulation. Namely, a 
photon that gets out of a basic unit is equivalent to the 
one that entered from the opposite surface of the basic 
unit (Kimes et al., 1982). The conception of the model 
is shown in Fig. 1. 
2.2 Cell information 
When radiative transfer in canopy is tried to 
simulate more realistically, more canopy information is 
necessary. The framework of the simulation model is 
1cm x 1cm x 1cm sized rectangular solid cell. 
There supposed to be not more than two 
individual leaves in the space of each cell. Each cy 
has an attribute of air or leaf or soil. A cell that ha, 
attribute of leaf is given information on leaf area 
direction, and inclination. These information is obtaineg 
as follows. At first, leaf direction and inclination on each 
leaf edge lines are calculated using a 3-D measure. 
ment method, the leaf edge matching method ang 
stereo photogrammetry. The lines are divided int 
shorter unit lines. A cell that includes each point of 4 
unit line is given information on inclination and direction 
of the unit line. Vertical resolution of this method is 
about 1.7 mm, and the perpendicular resolution is 
about 6.8 mm. Then, the projected leaf area of each 
cell is calculated from the rectified disparily image 
obtained by the method. Cells that have only leaf area 
information are given information on leaf direction and 
inclination by supplementation. Attribute of soil is given 
to all the cell situated at 0 cm height. 
2.3 Cell-photon interactions 
1) Air cell: A photon is not forced by this cel. 
Namely, a photon goes straight forward in this 
cell. 
2) Leaf cell: Let p be leaf reflectance factor, 1 
leaf transmittance factor. S; and S, ar 
projected area of a cell and leaf in the cel 
respectively to a plane that is perpendicular to 
incident vector. When a photon enters the cell 
the probability of the photon distributing is 
(S,/S.)(O+T), and that of the absorbed is 
(S,/S;)(1- o- 1), and that of the transmitting is 
1-S,/S,. Distribution phase function of the cel 
obeys Lambertian. 
3) Soil cell: When a photon entered this cell, the 
photon is distributed at the incident point 
Distribution phase function obeys Lamberlian 
without the specular reflectance. The specular 
Sensor 
P 
  
Leaf Cell Light 
Inclination a Cd 
Direction 0 
Area L 
Reflectance po N 
A 
  
Transmittance 7 
  
  
  
r 
A 
Soil Cell 
Reflectance 0, 
t 
  
Fig. 1. The conception of the model 
390 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996 
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