264 CHINESE OPTICS LETTERS / Vol. 6, No. 4 / April 10, 2008
Research on identifying the order of fringe pattern traces
using angular scan and zone search method
Xiaojun Jiang (
¡¡¡
)
1,2
, Aijun Zeng (
QQQ
OOO
)
1
, Huijie Huang (
¨¨¨
###
)
1
, and Xiangzhao Wang (
)
1
1
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800
2
Graduate University of Chinese Academy of Sciences, Beijing 100049
Received September 21, 2007
A method for automatically identifying the order of fringe pattern traces is presented. It uses the simplified
Otsu algorithm for obtaining the threshold, the angular scan in the range of 45
◦
for searching the trace
positions, and the zone search technique for identifying different traces. Experimental results show that
the proposed method may reliably obtain the order of fringe pattern traces orientating from almost 45
◦
to
90
◦
.
OCIS codes: 100.2000, 100.2650, 120.1880.
Interferogram contains the profile information of the
measured object, which may help us to understand the
comprehensive profile of the object in some applications,
such as machine manufacture and inspection of optical
components
[1,2]
. To obtain the information, identifying
the interference fringes is necessary
[3]
. Manual graphi-
cal methods are utilized to meet the requirement of ap-
plications. However, the manual graphical methods are
tedious and sometimes introduce errors. Applying com-
puter to realize manual graphical methods is one of the
promising ways to obtain better profile information. In
the method, the image is firstly filtered and thresholded
to obtain a binary gray-level image, then scanned to ob-
tain the midpoints that consist of the traces. Finally, the
method of scan is utilized to determine the order of the
fringe pattern traces
[4−7]
. In practice, it is found that the
method of scan sometimes fails when different arrange-
ments and shapes of fringe pattern traces exist in the
interferogram or broken trace exists in the fringe pattern
traces.
In this paper, a new method is proposed which uti-
lizes the angular scan and zone search technique to over-
come these disadvantages. The method automatically
positions the trace location and marks the trace with
different number to obtain the order of fringe pattern
traces. By processing various interferograms, detailed
analysis is given.
In our experiment, a Fizeau interferometer equipped
with two different complementary metal-oxide semicon-
ductor (CMOS) cameras is utilized. Before the imaging
beam having the profile information of the test and refer-
ence surfaces reaches the eyepiece of the interferometer,
it is divided into two beams by a beam splitter. One
beam reaches the eyepiece for observation, and the other
beam passes through an imaging lens to form an appro-
priate image received by a CMOS camera. These two
cameras obtain two different sizes of interferograms. Af-
ter the interferogram is digitized and calculated, a two-
dimensional (2D) gray-level array G
1
(u, v) that has u
rows and v columns is acquired. Then noise filtering is
performed by using the spin filter that has a window of
5 × 5 pixels
[8]
. When the image is filtered, it is necessary
to binarize the image. Otsu algorithm is widely employed
to automatically obtain the threshold and acquire a bi-
nary image in interferogram processing applications, but
the amount of calculation is great
[9]
. In this experiment,
a simplified Otsu algorithm that can achieve less amount
of calculation is implemented. Let w
0
be the ratio of the
number of dots in the foreground to the size of the im-
age, u
0
be the average gray level of the foreground, w
1
be the ratio of the number of dots in the background to
the size of the image, and u
1
be the average gray level of
the background, then we can get
T = w
0
× w
1
× (u
0
− u
1
)
2
. (1)
The algorithm searches the maximum value of T by us-
ing Eq. (1). When the maximum is found, the value of
the expected threshold is obtained. The binary image in
the selected circular zone can be obtained by the value
of the expected threshold. Then the horizontal scan is
utilized to obtain the midpoints of dark fringes in the
binary image and the angular scan and zone search tech-
nique are implemented in the selected circular zone.
Let R be the radius of the angular scan, R
1
be the ra-
dius of the selected circular zone, and R
c
be the distance
between the origin of coordinates and the center of the
selected circular zone, then we can get
R = R
c
− R
1
. (2)
Let i and j be integers in the range [1, u] and [1, v]
respectively defining the pixel locations, TempR
1
and
TempR
2
be the functions of i and j, and k
1
and k
2
be
the parameters of TempR
1
and TempR
2
, respectively, we
can get
TempR
1
= k
1
×
p
i
2
+ j
2
, (3)
TempR
2
= k
2
×
p
i
2
+ j
2
. (4)
Considering the reliability of the angular scan, we can
select k
1
and k
2
be 0.9 and 1.1, respectively. We have
TempR
2
> R ≥ TempR
1
. (5)
When Eq. (5) is met and the midpoint on a trace is
found, we assign the midpoint a number and implement
the zone search technique to search its neighborhood
midpoints and identify different traces along the traces.
1671-7694/2008/040264-04
c
2008 Chinese Optics Letters
资源评论
