Efficient background removal based on two-dimensional
notch filtering for polarization interference imaging
spectrometers
Tingyu Yan (颜廷昱), Chunmin Zhang (张淳民)*, Qiwei Li (李祺伟),
Yutong Wei (魏宇童), and Jirui Zhang (张吉瑞)
Institute of Space Optics, School of Science, Xi’an Jiaotong University, Xi’an 710049, China
*Corresponding author: zcm@xjtu.edu.cn
Received May 27, 2016; accepted November 8, 2016; posted online November 30, 2016
A background removal method based on two-dimensional notch filtering in the frequency domain for polariza-
tion interference imaging spectrometers (PIISs) is implemented. According to the relationship between the spa-
tial domain and the frequency domain, the notch filter is designed with several parameters of PIISs, and the
interferogram without a background is obtained. Both the simulated and the experimental results demonstrate
that the background removal method is feasible and robust with a high processing speed. In addition, this
method can reduce the noise level of the reconstructed spectrum, and it is insusceptible to a complicated back-
ground, compared with the polynomial fitting and empirical mode decomposition (EMD) methods.
OCIS codes: 300.0300, 070.0070, 110.4234.
doi: 10.3788/COL201614.123002.
Image and spectrum offer us important information on the
characteristics of the object. Fourier transform imaging
spectrometers (FTISs) are powerful instruments used in
the fields of imaging spectroscopy
[1,2]
. They can acquire
the image and spectrum of the object at the same time
and have wide applications in remote environmental mon-
itoring
[2–5]
, atmospheric measurements
[6]
, observations of
distant objects
[7,8]
, and biomedical fields
[9,10]
. Polarization
interference imaging spectrometers (PIISs) are one kind
of typical FTIS
[11]
. However, as is shown in Fig. 1, the
raw data acquired by PIISs are a series of physical
superpositions of the interferogram and background
[12,13]
.
Therefore, background removal becomes an essential
step in the spectral retrieval procedure for PIISs. Other
processing steps such as apodization and phase correction
are implemented after background removal because
the background can introduce false information into the
spectrum retrieved by Fourier transform
[14]
. That false in-
formation mixed in the spectrum is difficult to recognize
and separate.
There are several existing background removal methods
for PIISs. One-dimensional (1D) digital signal processing
methods such as differential calculation, polynomial fit-
ting
[13,14]
, and empirical mode decomposition (EMD)
[15]
are used in most background removal procedures. The dif-
ferential calculation method is simple with a high speed of
computation, but some information will be lost because
only N − 1 points are reserved after processing. In addi-
tion, differential calculation is susceptible to noise and
a complicated background. The polynomial fitting method
is widely used in background removal, but it is not suitable
to a complicated background because higher order fitting
is needed. The EMD method is a self-adaptive method
that can get the background without prior knowledge
[15]
.
However, the interpolation algorithm used in EMD needs
heavy computation, which affects the speed of the algo-
rithm
[15]
.Muet al.
[16]
proposed an optical assistant method
to overcome the drawbacks of digital signal processing
methods, but the limitation of their system is that all
polarizers must be placed at ideal positions. In
practical applications, digital image processing methods
have better adaptability and can be applied to different
PIISs more easily.
Notch filtering in the frequency domain is a powerful
tool for feature extraction in two-dimensional (2D) image
processing that can extract the frequency of the useful
features in the frequency domain by a special notch
filter. It has been successfully employed in various appli-
cations
[17–19]
. However, background removal based on 2D
notch filter ing for PIISs has not been reported. In this
Letter, we present a background removal method based
on notch filtering in the frequency domain for PIISs. This
method has some obvious advantages compared with
existing background removal methods. First, it is easy
Fig. 1. Data acquisition process of PIIS. The modulated scene
is the superposition of the interferogram and the background (fu-
sion generated by computer). The scanning system is not shown.
COL 14(12), 123002(2016) CHINESE OPTICS LETTERS December 10, 2016
1671-7694/2016/123002(5) 123002-1 © 2016 Chinese Optics Letters