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
