Full text: Actes du Symposium International de la Commission VII de la Société Internationale de Photogrammétrie et Télédétection (Volume 1)

(1) 
sorption 
(2) 
rity, and 
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(3) 
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d, and 
(4) 
| the 
(5) 
(6) 
ward at 
th to 
(7) 
(8) 
(9) 
ion 
(10) 
the 
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LEES 
  
3. THREE BAND METHOD 
When three IR bands are simultaneously used, the radiative transfer 
equation (9) holds for each of them with common Ts and Ta. 
Thus 
Wii!) —9(03)-WQu Ts) t (1 TO) WOS, Ta) , (11a) 
W(A2,T2') = T(A2)-W(A2,Ts) + ( + 1 (42)): W(A2,Ta) 9 (11b) 
W(A3,T3') = T(A3)-W(A3,Ts) + ( 1 - T(A3))-W(3,Ta) , (le) 
where Ai is a wavelength representing spectral band i (i-1,2,3), and Ti' 
(i=1,2,3) is the apparent temperature for the band i. 
Wavelength Ai is selected to satisfy 
O TQu) «.105) « 10.) «1. (12) 
With the assumptions 
W(A2,T) = a2-W(A; ,T) + b2 : (13a) 
W(As,T) = ag:W(A1,T) + bs 9 (13b) 
where a2,a2,bs3,and ba are constants, equations (lla).(llc) are rewritten as 
W(A1,71') = T(A1) W(A1,T5) + C1 - T(A1))-W(A1,Ta) , (14a) 
W(A1,T2") = T(A2) Wii, Is) + (1 - T(A2)) W(A1,Ta) , (14b) 
W(A1,Ts') 7 1(33)-WOa, Ts) tC 1 - T(A3))-W(1ı,Ta) (14c) 
W(A1,T2') and W(\1,T3') are the equivalent radiances at the wavelength À;. 
From equations (14a)-(14c), it follows that 
T(A3) - T(A2) W(A1,T3') - WQ3,T2!) 
  
  
= . (15) 
T(A3) - TO) W(1,T3') - W(A1,T1") 
Let us define T as 
Te t(4,) 7 102))/ TO 3) = TA 1) (16) 
From inequalities (12) and definition (16), 
<<, (17) 
I is calculated from observed apparent temperatures T;', T;', and T;'. 
I represents the ratio of transmittance differences, and it varies according 
to the amount of path radiance if the spectral bands are selected properly. 
When Ts equals Ta ,the values of T;',T,',and T3' are the same, and denominator 
in the right side of eq.(15) is equal to zero. Then the value of I is not 
obtained. Therefore the case Ts - Ta should be excluded in applying this 
algorithm. 
4. SPECTRAL BAND SELECTION 
In order to get the pattern of path radiance by use of T the spectral 
bands should be selected so that I' is a monotone increasing or decreasing 
function of path radiance. 
371 
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