The atmosphere has some lens effect and has 
own MTF characteristic. The image of object 
on the ground is degraded by this atmosphe- 
ric effect and the spatial resolution will 
be decreased in higher frequency domain, 
and the contrast of image decreases. 
Another important problem is a decrease of 
spatial resolution by a cross talk between 
the sensor elements. This cross talk is 
large in long wave length, and spatial re- 
solution power is lower in longer wave 
length. 
To do analyze these problems and to evalu- 
ate the performance of imaging spectrometer 
, it is necessary to simulate the imaging 
operation of the spectrometer in detail. 
2.0PERATION MODEL OF IMAGING SPECTROMETER 
To analyze the operational behaviors of 
imaging spectrometer in detail, the opera- 
tion model was originated at first. In 
followings, both of the pushbroom scan and 
the whiskbroom scan are considered. 
Here, following symbols are defined. IS is 
abbreviation of imaging spectrometer. 
h(x,y) : point spread function(PSF) of IS 
r(x,y) : radiance distribution of ground 
s(x,y) : sampling function of the IS 
g(X,y) : sampling output of the IS 
go(X,y): hold output of pushbroom IS 
gu (x,y): hold output of whiskbroom IS 
d : Spatial coordinate 
p,q : pitch of sensor element 
Box(p,1): hold function of width p and 
height 1. 
] : along track flight distance for integ- 
ration time 
lo: initial point of the integration 
H(u,v) : Fourier transform of h(x,y) 
R(u,v) : Fourier transform of r(x,y) 
S(u,v) : Fourier transform of s(x,y) 
G(u,v) : Fourier transform of g(x,y) 
Go(u,v): Fourier transform of g»(x,y) 
G,(u,v): Fourier transform of g.(x,y) 
u,v : spatial frequency 
Ws, : =1/p, Sampling picth 
Vs, * : =1/d, sampling picth 
p:sinzup/ztup : Fourier transform of 
108 
hold function Box(p,1) 
l:sinzvl/zvl :Fourier transform of 
hold function Box(l,1) 
2.1 Operation model in cross track 
In the case of pushbroom scan, the output 
of linear array is a pulse train and ex- 
pressed as follows. 
Co 
gG)s fr(x) *h(x)] : Xó6(x- np) (1) 
TL -co 
And the hold output of pushbroom IS is, 
Geli ht) «66 -my« 
N=-0 
Box (p, 1) (2) 
In the frequency domain, these expressions 
are as follows. 
G(u)= {R(u) - | H(u) | } # 
Us S6(u - flus) (3) 
N=-09 
And the Fourier transform of hold output is 
ber NS eire on ml: 
n=-0 
sin7cup/ up (4) 
In the case of whiskbroom scan, one sensor 
element scans continuously. Then the output 
is. 
oo 
g(x)= {r(x} * hix)}.- $ 8(x.- p)dp 
= r(x) * h(x) (5) 
In the frequency domain, 
Gu(u) = R(u) - | H(u) | (6) 
2.2 Operation model in along track 
In the case of pushbroom scan, the signal 
is integrated for a while and the spatial 
resolution is degraded. The output g(y) is 
given by, 
go(y)= [r(y) * h(y)] * Box(1,l.,1) (7) 
In frequency domain, g(y) is transformed to 
Gp (Vv): 
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