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
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