a sin 
dz 
. (9) 
(10) 
(11) 
(12) 
(13) 
  
40 
  
q.(8). 
with 
o. S/N 
thout 
titude 
3.DETECTION AND CORRECTION OF 
ATIITUDE FLUCTUATION 
3-1.DETECTION 
As shown in Fig.5 when satellite has the 
movement changes around roll axis, the 
anterior CCD takes the image of the difference 
point from posterior CCD with distance. /x. To 
detect this /x, we calculate the mean square 
error / , between posterior CCD output 
f(x,y) and anterior CCD output g(x,y). Here 
we calculate / by following equation. 
1(k) = | Foros») PS E. ids 
From the /x when [is the smallest. the 
attitude fluctuation /x can be acquired. 
Posterio 
CCD 
LIST 
i i 
: : 0 
Anterio : 
CCD 4 
à 
€ 
Fig.5 Detection of attitude fluctuation. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
3-2.CORRECTION 
When the satellite's attitude fluctuation value 
around the roll axis is detected to /x, we divide 
this distance to tow components as follows 
Ix=np+ Ae, (15) 
where p is the pixel with, 7 is the integer 
number and Ae is the residual distance 
smaller than pixel width. 
To correct the attitude fluctuation for TDI, 
first we shift the pixels n times. Then, as 
shown in Fig.6, we corrects anterior CCD 
output g(x,y) by following equation. 
g(x, =~ AY x g(x =p, ¥) 
+Aex g(x—(n+1)p,y). (16) 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Posterio 
CCD 
Anteriog 
CCD 
F4 
ide 
met 
1 —- A E 
Fig.6 After shifting on pixel. 
In the same way, we can correct movement 
change around pitch. The attitude fluctuation 
around pitch is detected to ly . we divide this 
distance to two component as follow 
ly =np+ Ag (17) 
We corrects anterior CCD output g(x,y) by 
following equation. 
g(x,y) zl FE Ag) X g(x,y FE np) 
+Aexg(x,y-(n+1)p). (18) 
Here we dont simulate the attitude 
fluctuation around yaw axis, because 6, 18 
smaller than § and g,, so. from Eq.(7), kw, 
is much smaller than Ho . 
4. SIMULATION RESULTS 
In the following simulations, we use 2-D 
sinusoidal pattern defined by 
  
fix ui (1 + cos(16 -theta(x,y)) : (19) 
2 
where 
256 256 B 
theta(x,y) = > 3 aan ded A) (20) 
x=0 y=0 x— 128 
The simulation is image generated by Eq.(19) is 
shown in Fig.7. 
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 19