2-2-2 MOVEMENT CHANGES AROUND 
THE PITCH AXIS 
This appear as a change in the direction of 
the y-axis that is perpendicular to the scan 
direction of CCD. Thus, the equation 1s: 
kw, = Ho. (5) 
2-2-3 MOVEMENT CHANGES AROUND 
THE YAW AXIS 
Movement changes around the yaw axis 
rotates the imaging position; as shown in 
Fig.2(c). Since this is very small angle change it 
can be represented by the following equation if 
L isset as an observation width on earth: 
kw: =(L/2-x)x(1-cosd) 
=(L/2-x)& /2, (6) 
EM; = (1 /2- x)ó.- CT 
In the high resolution earth observation 
system, the normal H number is 800 km (832 
km for SPOT satellite ); L is smaller than 
200 km (60 km for SPOT satellite): the effective 
changes around the yaw axis is relatively small 
compared to the movement changes of the roll 
and pitch axis.[3] 
2-3. EFFECT OF FLUCTUATION FOR TDI 
The image pick-up position of the CCD is not 
completely same because of satellite's attitude 
fluctuation. 
Considering the interference from contiguous 
picture elements, 2-D repeating high-frequency 
input signals are most sensitive to the attitude 
fluctuation. Therefore, we use 2-D sinusoidal 
wave pattern defined by 
|l * cos(2zf,x)cos(2z/,y) 
3 
  
fx,y)Yys (8) 
where f, and f, are the repeating signal 
frequency in the x direction and in the 
y direction. Fig.3 shows the simulation pattern 
generated by Eq.(8). 
In this case, the amplitude component of a sin 
signal at 2xf:= 2mz and 22f: = (2m+1)æ 
( m; integer ) is represented by 
Sue rS Hy umor E cos(2ik.) 
Msn zn Poesia p: ©) 
Tc:Ww,'3p, 
where 
ki fkuw xt fekywW y. (10) 
k = fxkxw x Fr fykyw JA. (11) 
Ciz fujps- Kw (12) 
és: = Jfp,tkiií. (13) 
  
  
  
  
  
  
  
| —$— without fluctuation | 
| —3— with fluctuation | 
| MO 
O7 Dr 
= — 
» 6 FE 
+ 
S 5 
1 
| 3 3 
| = 
E 2 
> 1 
N 
(008 
| 0 10 20 30 40 
| times 
  
  
Fig.4 The result of performing TDI with Eq.(8). 
The simulation result of performing TDI with 
Eq.(8). From Fig.4, we can't acquire the S/N 
improvement ratio more than 3 without 
detection and correction of the satellite attitude 
fluctuation. 
18 Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 
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