(1)
sorption
(2)
rity, and
iion and
(3)
ature of
d, and
(4)
| the
(5)
(6)
ward at
th to
(7)
(8)
(9)
ion
(10)
the
; E
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.
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