COL 10(5), 052901(2012) CHINESE OPTICS LETTERS May 10, 2012
Experimental method for the extraction of intensity
profiles by imaging the scattered pattern with
a charge-coupled device
Haixia Li (ooo°°°___)
1,2
, Meina Zhang (ÜÜÜ{{{AAA)
2
, Xiaoyi Chen (²²²)
2
, Chunxiang Liu (444SSS)
2
,
and Chuanfu Cheng (§§§DDD444)
2∗
1
Department of Information Science and Technology, Shandong University of Politics Science and Law,
Jinan 250014, China
2
College of Physics and Electronics, Shandong Normal University, Jinan 250014, China
∗
Corresp onding author: chengchuanfu@sdnu.edu.cn
Received September 22, 2011; accepted December 12, 2011; posted online March 15, 2012
A practicable experimental method for measuring scattering on rough surfaces is reported. The scattered
patterns are captured on a screen comp osed of two pieces of ground glass and then imaged using a charge-
coupled device. The scattered intensity profiles are extracted by converting the patterns in real space
into the wave vector space. Isotropic and anisotropic samples of the rough backsides of silicon wafer
are investigated respectively, and their intensity profiles are measured. The profiles of the anisotropic
sample are obtained by reading the pixels on the specific orientation curves. The parameters of the
samples are extracted using angle-resolved light-scattering schemes and theories. The results well agree
with measurements obtained using an atomic force microscope.
OCIS codes: 290.5880, 120.5820, 120.6650.
doi: 10.3788/COL201210.052901.
Light scattering from random rough surfaces has been
a long-standing research subject. Since the 1990s,
significant advancements in the characterization of
rough fractal surfaces by light scattering have been
achieved
[1−4]
. Fundamentally, Sinha et al. proposed
a classical scattering model for rough self-affine fractal
surfaces
[5]
, and Yang et al. constructed mathemati-
cal relations of the half-width of the scattered intensity
profiles with the parameters of rough self-affine fractal
surfaces
[6]
. Eventually, more systematical theories and
angle-resolved experimental schemes were developed for
the extraction of the parameters of rough self-affine sur-
faces from the scattered intensity profiles
[7]
. Meanwhile,
in the area of light scattering, scattering models and ex-
perimental methods were continuously developed to deal
with the complexity of diverse practical problems
[8,9]
.
Nowadays, light scattering has become one of the most
important means of detecting surface characteristics and
nanostructures. In the experimental aspect, delicate
devices have been implemented for the measurement
of scattered intensity profiles. One of the most fre-
quently employed is the scatterometer designed by Shen
et al.
[10]
, which can be used to adjust scattering angles
conveniently. Most works use a single detector to cap-
ture scattered light
[7,10,11]
. Thus, the movement of the
detector makes the acquisition of an intensity profile
time consuming. Another alternative device is the linear
detector array
[7]
, in which a scattered intensity profile
is taken along a straight line on the measurement plane.
However, for some experimental methods, light inten-
sity has to be measured along a specific curve
[10,12]
. In
addition, the limited extending range of the linear detec-
tor array can receive only a small part of the intensity
profiles and thus induce errors in surface parameter ex-
traction.
In this letter, we propose an experimental method
for the extraction of intensity profiles by imaging the
scattered pattern with a charge-coupled device (CCD)
camera. The scattered pattern is first captured by a
screen composed of two pieces of ground glass and then
imaged by the CCD. The light intensity profiles are ob-
tained by reading the pixels of the scattered pattern
images along line segments or specific curves and are
converted into profiles in the wave vector space. The
parameters of the sample surface are extracted from the
light intensity profiles. Both the experimental operation
and data processing are time saving and convenient. The
method is demonstrated by practically investigating two
samples, one being isotropic and the other anisotropic.
The parameters of the two samples are obtained and
compared with measurements obtained by an atomic
force microscope (AFM).
The experimental setup is shown in Fig. 1(a). The
optical path lies in a horizontal plane. A light beam
from a He–Ne laser, which has a wavelength of 632.8
nm, is reflected by mirror M. Two polarizers, namely, P1
and P2, are used to adjust the intensity of the incident
light beam. The polarization of the incident beam is
kept vertical via P2. Pinhole H, which has a diameter
of approximately 4 mm, is used to filter out stray light.
Rough sample S is mounted on a rotational stage, with
which the orientation of the sample plane and the inci-
dent angle are changed. Lens L1, with a focal length of
18 cm, is placed in front of the sample to form the Fraun-
hofer diffraction geometry. A screen is used to receive the
scattered pattern on the focal plane of L1. The screen is
composed of two pieces of ground glass, G1 and G2, and
a piece of white paper clamped between them. Here, G1
and G2, having sufficient roughness (ground with 240#
Al
2
O
3
powder), and the paper piece are used so that the
1671-7694/2012/052901(5) 052901-1
c
° 2012 Chinese Optics Letters