332 
The second hypothesis, whereby k is independent on par 
ticle size, seems to be justified only in cases where 
the particle size is greater than the wavelength of 
incident radiation (Kortum, 1969). However, for most 
soils in natural condition, small particles tend to 
cluster in aggregates. Thus, in case of clayey samples 
particle size should be interpreted as the smallest 
existing aggregate size. The samples used by B&H were 
aggregates of clay particles and several times larger 
in diameter than the wavelength of incident radiation. 
Plots were made of Ln(r) versus wavelength for samples 
of different aggregate size and of Ln(r) versus aggre 
gate diameter at different wavelengths (Bouman, 1986). 
Interpretation of these plots led to the following 
formula, equating mean penetrated layer thickness d to 
wavelength X and aggregate diameter 0 : 
d = \T£*Ln(0/X) (in ) eq.3 
This equation was tested on the .(B&H) measured reflec 
tance values of the kaolinite and bentonite clay 
samples. To this end, the coefficients of absorption 
of the clay minerals were calculated as a function 
of wavelength, using two samples of different aggre 
gate size. With the aid of the values calculated for 
k, reflectance r was computed for the other aggregate 
sizes and compared with the measured values, see figu 
re 1. 
Figure 1. Calculated and measured reflectance values 
for kaolinite (o) and bentonite (x) clay samples, 
(measured values are from Bowers and Hanks, 1965) 
On the whole, there seems to be a great consistence 
between measured reflectance and reflectance computed 
using equation 3. Any decrease in reflectance with 
increasing particle size is fairly well predicted. The 
total mean deviation computed for the kaolinite and 
the bentonite samples is 3.5 % resp. 3.9 % (n = 70). 
Boundary conditions for the validity of equation 3 
could not be established for lack of data in literatu 
re. It should be clear however, that particles or 
aggregates infinitely small or very large are beyond 
the limits of this formula. In figure 1 it can be seen 
that for large values of 0, reflectance r tends to 
become overestimated. There appears to be a maximal 
particle/aggregate size beyond which reflectance is no 
longer significantly reduced (Belonogova, 1959; Stoner 
and Baumgardner, 1980). 
The influence of mineralogy 
It is assumed that the effect of different mineral 
composition on reflection can be described by means 
of a weighed average of the coefficients of absorption 
of the individual components. The coefficients of 
weight are based on the percentages of volume of each 
component. For a homogeneous mixture of minerals, the 
coefficient of absorption k^ is proposed to be : 
k = y*c. k. (m 2 ) eq.4 
s 1 1 
in which : k = coefficient of absorption of the mi 
neral mixture 
k. = coefficient of absorption of mineral i 
c^ = percentage of volume of mineral i 
In 1970, Hunt and Salisbury published the results of 
extensive reflectance measurements of samples of pure 
minerals of various particle sizes. With the aid of 
equation 3, the coefficients of absorption of three 
minerals quartz, gypsum and calcite, have been calcu 
lated as a function of wavelength of incident radia 
tion, see table 1. 
Table 1. Coefficient of absorption k as a function 
of wavelength of incident radiation for quartz, gypsum 
and calcite. 
Wavelength (^i) Coeff. of absorption (-1 ^ 2 ) 
Quartz Gypsum Calcite 
0.4 
i. 
086 
1, 
. 205 
1 . 
. 188 
0.6 
0 . 
983 
1, 
. 062 
1 . 
,062 
O 
CO 
0 . 
903 
o, 
. 974 
0 . 
,969 
1.0 
0 . 
851 
o, 
. 899 
0 . 
, 905 
1 . 2 
0 . 
808 
0 
.839 
0 . 
,855 
1 . 4 
0 . 
775 
o, 
.777 
0 . 
,82 1 
1.6 
0 . 
748 
o, 
.739 
0 . 
,793 
1.8 
0. 
72 1 
o, 
.7 19 
0 . 
.771 
o 
C\1 
0 . 
705 
0 
. 557 
0 . 
.741 
2 . 2 
0 . 
689 
0 
. 565 
0 . 
, 724 
2.4 
o . 
675 
0 
.451 
0 . 
, 688 
For any 
dry 
mixtu 
re of 
th 
ese m 
ine 
r a 1 s 
in a 
well so 
r ted 
parti 
ele s 
iz e 
c las 
S / 
r e f 1 e 
ctance 
r can n 
ow be 
calc 
ulate 
d w 
ith the 
aid o 
f equa- 
tion 3 
and 4 
. Table 2 
summariz 
es 
the m 
inera- 
logical 
prop 
er ti e 
s and 
me 
an pa 
rti 
cle s 
ize of 
two sam 
pies 
from ' 
Tunes 
ian 
soil 
su 
r f ace 
s (van 
den Ber 
gh, 1 
986) . 
The 
samples 
hav 
e bee 
n air- 
dried i 
n ord 
er to 
pres 
e rv 
e the 
ca 
leite 
and 
gypsum 
conte 
nt an 
d wer 
e placed 
in 
smal 
1 cups 
with a 
depth 
of about 
20 
mm . 
Table 2 
. Min 
¡éralo 
gical 
pr 
opert 
ies 
and 
mean 
partic1 
e s i z 
e of 
two T 
une 
■ s ian 
soi 
1 s am 
¡pies . 
Property 
S amp 1 
e A 
Sample 
B 
quartz 
(%) 
85 
70 
gypsum 
(%) 
5 
25 
calcite 
(%) 
10 
5 
organic 
matt 
er ( % 
) 0 . 
5 
0 . 
2 
mean pa 
rtic 1 
e siz 
e 75 
-12 
5 
1 2 
5-250 
(yim) 
Sample 
ref le 
ctanc 
es we 
re 
both 
cal 
culat 
ed and 
measure 
d with the 
NIWARS- 
spect 
rof 
otome 
ter ; 
results 
are 
given 
in f 
igu 
res 2 
a a 
nd 2b 
I 
100 .. 
'-'80 .. 
Figur« 
of sac 
60 
50 
iiR 
40 
§ 30 
1 20 
I I 
<D 
u 10 
Figur« 
of sari 
In gei 
the me 
reflec 
B is c 
dips c 
reflec 
pronoi 
ted r< 
tanc e 
bratic 
ces ii 
Hunt i 
and tc 
struct 
and S< 
sample 
The ii 
The ii 
from < 
many t 
dry sc 
sorpt; 
on it: 
which 
attemj 
water 
the ii 
ferenc 
1965)