6A-5-3 
■HI 
When the image after adjustment is as Fig.6, we regard 
that the rough assembly error on x, y direction is 
controlled in 1/2 pixel. 
3.2 Accurate Assembly and Judging 
Since the assembly error is less than 1/2 pixel after 
rough assembly, it is hard to further improve the 
assembly accuracy with traditional precise measure 
instrument. In order to improve the assembly accuracy 
to a high level, we introduce the CCD moiré effect into 
the process of judging assembly error and take a new 
method-digital correlation filtering to locate the 
position of moiré fringe of CCD. 
According to [Zhong, 1997], we know that expression 
of the light intensity of moiré fringe and displacement of 
CCD is: 
I(xx 0 ,y)= 0 0I O + 2I 0 ZX n B kn cos{23in{(xu x +y u )x 0 ucos 9j]} 
n=l 
The expression indicates that it represents the 
fundamental component when equal to 1, it represents 
the harmonic component when n equal to other value. In 
this expression a, (3 is the space factor of main and slave 
grating respectively, A,B is Fourie factor, ul is the 
spatial frequency of photosensitive cell, ox, oy is 
component of the spatial frequency of CCD light 
responsive function (x represents horizontal direction, y 
represents vertical direction), 0j is the angle between the 
vertical grating of CCD and y axis, 0 2 is the angle 
between the Ronchi grating and y axis. 
The moiré effect of CCD generate vertical fringe 
whenO,=0 2 =O; o,=co 2 (c is positive fraction). 
The moiré effect of CCD generate horizontal fringe 
when0, = -0 2 =( 1 /2) 0; o,=co 2 2 (c=l,2,3...) 
The moiré effect of CCD generate slope fringe when©, 
^0 2 ; ul=cu2 (c is a positive fraction) 
In the accurate assembly process, the target is a Ronchi 
grating. We can obtain moiré fringe of different 
behavior by adjusting the position and object distance of 
Ronchi grating. Then we can determine the assembly 
error by making a correlating operation between the 
moiré fringe light intensity at each side of assembly 
boundary. We adopt the following expression: 
...(2) 
To make correlating operation, x(n), y(n- t ) is light 
intensity discrete signal at each side of assembly 
boundary. The step is as followed: 
1. Make the digitalization of moiré signal at the 
assembly boundary of CCD at areal and conduct self- 
correlating; record the position(no) of the center of main 
peak. 
2. Make the digitalization of moiré signal at the 
assembly boundary of CCD at area2,conduct cross 
correlating of x(n) and x(n- t ) and obtain the position 
...(1) 
(n^, )of the maximum value of cross correlating 
1. By expression: 
Ay = «0 - n„ 
...(3) 
We can determine the assembly error on y direction. In 
the way we can determine the assembly error on x 
direction. 
As for general condition, when both direction have 
assembly error, we determine the assembly error by 
following steps: 
1. Determine the assembly error( A y ) on y direction 
with vertical moiré fringe according to method just 
mentioned. 
2. Determine the displacement ( A z )of slope moiré 
fringe at the position of assembly boundary with the 
same method. The displacement of slope moiré fringe is 
caused by the assembly error on both directions. Then 
we can use formula: 
•Ax = tJaz 2 -Ay' 
...(4) 
To calculate the assembly error on x direction. Finally, 
we record the data of assembly position after accurate 
adjustment with displacement sensor. 
4 EXPERIMENT 
According to the steps of whole assembly, we present 
the assembly images in the process of assembly and the 
images after assembly completion. (Omit the rough 
assembly result), In figure 7, figure 8, figure 9. The 
table 2 shows the result of assembly. 
Table. 2 Errors of assembly 
Unit: nm 
X direction 
Y direction 
1—2 
0 
0 
2—3 
0 
0 
3—4 
-0.88 
0.57 
1—4 
0.02 
0