Article

Atmospheric degradation correction of terahertz beams using multiscale signal restoration

Department of Electrical and Computer Engineering, Temple University, Philadelphia, Pennsylvania 19122, USA.
Applied Optics (Impact Factor: 1.78). 02/2010; 49(5):927-35. DOI: 10.1364/AO.49.000927
Source: PubMed
ABSTRACT
We present atmospheric degradation correction of terahertz (THz) beams based on multiscale signal decomposition and a combination of a Wiener deconvolution filter and artificial neural networks. THz beams suffer from strong attenuation by water molecules in the air. The proposed signal restoration approach finds the filter coefficients from a pair of reference signals previously measured from low-humidity conditions and current background air signals. Experimental results with two material samples of different chemical compositions demonstrate that the multiscale signal restoration technique is effective in correcting atmospheric degradation compared to individual and non-multiscale approaches.

Full-text

Available from: Seong G. Kong, May 13, 2016
Atmospheric degradation correction of terahertz
beams using multiscale signal restoration
Choonwoo Ryu* and Seong G. Kong
Department of Electrical and Computer Engineering, Temple University,
Philadelphia, Pennsylvania 19122, USA
*Corresponding author: choonwoo@temple.edu
Received 28 October 2009; revised 11 January 2010; accepted 15 January 2010;
posted 20 January 2010 (Doc. ID 119163); published 9 February 2010
We present atmospheric degradation correction of terahertz (THz) beams based on multiscale signal de-
composition and a combination of a Wiener deconvolution filter and artificial neural networks. THz
beams suffer from strong attenuation by water molecules in the air. The proposed signal restoration
approach finds the filter coefficients from a pair of reference signals previously measured from low-
humidity conditions and current background air signals. Experimental results with two material
samples of different chemical compositions demonstrate that the multiscale signal restoration technique
is effective in correcting atmospheric degradation compared to individual and non-multiscale
approaches. © 2010 Optical Society of America
OCIS codes: 300.6495, 110.7410, 200.4260.
1. Introduction
Rapid progress in the development of the sources and
detectors for generating and detecting the radiation
in the terahertz (THz) frequency range realizes a
wide variety of useful applications in spectroscopy
[13], imaging [4,5], and communications [6,7].
THz spectroscopy has demonstrated a great poten-
tial to detect various chemical or biological agents
through the identification of unique spectra l absorp-
tion patterns of the material. Since THz beams can
penetrate many nonmetallic materials, such as pa-
per, textiles, and wood panels, THz spectroscopy can
detect concealed threat materials from a distance. In
addition, THz radiation does not cause harmful ioni-
zation effects, as do x-rays or gamma rays, because of
its low photon energy, which presents an advantage
of body safety in THz measurement settings. The
THz range of the spectrum offers a broader com-
munication bandwidth than the microwave range
and enables secure, line-of-sight communication
capabilities.
THz beams are absorbed by molecules when they
propagate through the atmosphere. THz spectro-
scopy and imaging with the power and efficiency of
currently available radiation sources and detectors
undergo technical challenges, such as strong at-
tenuation in the atmosphere and spurious peaks in
the spectra produced mainly by water vapor. These
molecules create several absorption bands [8] or fre-
quency bands of high attenuation. Such false peaks
and dips make it difficult to identify material-specific
signatures in the THz spectroscopic measurements.
Atmospheric degradation of THz signals signifi-
cantly reduces the signal-to-noise ratio in THz signal
measurements and, therefore, limits the distance of
signal sensing and transmission. THz signal restora-
tion from atmospheric attenuation is importan t to in-
crease the range of THz spectroscopic measurements
and transmission, especially in humid atmospheric
conditions.
Signal restoration can be defined as a deconvolu-
tion process to restore an original signal from the
observed signal that is deformed by a degradation
process and the noise [9]. The objective of THz signal
restoration is to remove the effects of atmospheric at-
tenuation from the THz signal observed in the open
0003-6935/10/050927-09$15.00/0
© 2010 Optical Society of America
10 February 2010 / Vol. 49, No. 5 / APPLIED OPTICS 927
Page 1
air. Several approaches have been studied to restore
THz signals from atmospheric attenuation. An adap-
tive deconvolution technique using prior knowledge
of water absorption peaks is introduced by Withaya-
chumnankul et al. [10] for removing the water vapor
effects from observed THz signals. This approach uti-
lizes the frequency and strength information of
known water absorption peaks to find the best para-
meters for the modeled peaks that correspond to the
measured absorption peaks. This approach has the
advantage of adaptive removal of water absorption
peaks without training measurements. However,
only premodeled absorption peaks can be removed
from the observed signal, not other unmodeled de-
gradation effects. Furthermore, certain meaningful
signatures from the THz measurement may be lost
if the THz signal from a target sample has an over-
lapped frequency response with the modeled water
vapor response, because the parameter tuning algo-
rithm will be forced to match to the reference re-
sponse by changing the model parameters. Similar
approaches have been presented by Wang et al.
[11,12]. These model-based approaches have an
advantage of no training stage before the signal mea-
surements, but are effective only for the premodeled
frequency response of water vapor, not for unmodeled
responses that need to be removed from the degrada-
tion. Polynomial modeling of the THz absorbance
spectrum [13] approximately models the absorbance
by a low-order polynomial from the observed mea-
surements and finds matched absorbance from the
prestored absorbance of contraband. This modeling
may not be useful for general THz signal restoration.
Our previous approach [14] utilizes an artificial
neural network (ANN) to restore a THz signal from
atmospheric degradation with no prior knowledge of
degradation process models. The proposed multi-
scale signal restoration technique decomposes a THz
signal into approximation and detail components
using the discrete wavelet transform (DWT). A signal
restoration filter consi sting of a Wiener filter and an
ANN removes atmospheric degradation for each in-
dividual component.
Wavelet analysis decomposes a signal into approx-
imation and detail components in different scales
using the contracted and dilated versions of a wave-
let function [15]. The DWT has been widely used in
signal processing applications. A combined use of the
DWT and Wiener filtering was applied to signal de-
noising in multisensor signal estimation [16]. It has
also been demonstrated that the learning perfor-
mance of ANNs is improved by multiresolution sig-
nal decomposition [17,18]. Application examples of
multiresolution decomposition in THz signal proces-
sing include denoising [2,19], THz image compres-
sion and classification [20], and multiscale image
segmentation in THz computed tomographic ima-
ging systems [21]. In [19 ], THz measurements with
additive noise are used to compare denoising perfor-
mances of different wavelets. A THz classification
system utilizes wavelet denoising techniques for pre-
processing of the THz signals [22]. These techniques
focus on noise removal from THz signals by thresh-
olding small wavelet coefficients, rather than a th-
rough a systematic approach to restoration of THz
signals from atmospheric degradation.
This paper presents an atmospheric degradation
correction technique of THz beams based on multi-
scale signal decomposition, which does not require
the knowledge of the frequencies of absorption peaks
to be removed. An observed THz signal is decom-
posed into approximation and detail components
using the DWT. The restoration filter consists of a
Wiener deconvolution filter and an ANN. For each
component, a Wiener deconvolution filter is designed
using the inputoutput signal, where the input is a
degraded THz signal and the output is a desired sig-
nal obtained in low-humidity conditions. A Wiener
deconvolution filter is an optimal filter that mini-
mizes the error when the input signal contains noise.
An ANN is trained for restoring the residual signal
component that could not be restored in Wiener fil-
tering. A combined Wiener filter and ANN, trained
separately using the approximation and the detail
components, restores each signal component from
the fluctuations and the noise that cause absorption
bands in the spectrum observed in humid air condi-
tions. The experiments with two materials of differ-
ent chemical compositions in a humid condition
demonstrate that the proposed restoration technique
can remove atmospheric degradation due to humid
air conditions, while preserving the spectral signa-
tures of the material.
2. Terahertz Spectroscopy
Our time-domain THz spectrometer consists of a
femtosecond laser, a photoconductive THz wave
emitter, and an electro-optic (EO) detector [23,24].
Figure 1 shows an optical layout of the spectrometer
used in this experiment, adopted from the technique
presented by Wu et al. [23]. The laser source is a com-
pact mode-locked f iber laser (IMRA femtolite 780)
that emits approximately 100 fs laser pulses with a
center wavelength of 780 nm, a repetition rate of
48 MHz, and an average power of 30 mW. The THz
emitter is a photoconductive switch fabricated on a
low-temperature-grown GaAs chip, and modulated
by the amplified reference signal of a lock-in ampli-
fier. The modulation amplitude and frequency are ty-
pically 200 V and 9:5 kHz, respectively. The average
power of our THz beam is estimated to be about a few
microwatts. The THz pulses, generated by the emit-
ter, are focused onto a sample by a pair of off-axis
parabolic mirrors. The THz beams, transmitted
through or reflected by the sample, are then sent
to an EO detector by another pair of parabolic mir-
rors. The THz path length from the THz emitter to
the ZnTe EO crystal is about 1 m. The EO detector
consists of a ZnTe crystal, a quarter-wave plate, a
Wollaston prism, and a pair of photodiodes [23].
The probe beam, aligned by a pellicle beam splitter,
travels collinearly with the THz beam through the
928 APPLIED OPTICS / Vol. 49, No. 5 / 10 February 2010
Page 2
ZnTe EO crystal. Because of the EO effect of ZnTe
crystal, the THz field results in a polarization
change of the probe beam while it travels through
the ZnTe crystal. The Wollaston prism separates the
vertical-polarization and the horizontal-polarization
components of the probe beam. These vertical and
horizontal components are sent to the photodetector
pair, which produces the differential photocurrents.
Since the polarization of the probe beam is initially
set to be 45°, the vertical and horizontal components
are the same when the THz field is zero and, hence,
there is no differential photocurrent. The difference
between the electric currents and the photodiode
pair is measured by a DSP lock-in amplifier (Stan-
ford Research Systems SR-830) and a desktop
computer.
3. Modeling of Terahertz Signal Degradation Process
A. Atmospheric Attenuation in the Terahertz Range
Atmospheric attenuation is the rate at which a
beams energy is absorbed via interactions with
the atmosphere. Absorption is a main cause for the
attenuation of a beam traveling through a medium.
Absorption concerns the molecules gaining energy
from the beam through collision. THz beams are ab-
sorbed by molecules when they propagate through
the atmosphere. Nitrogen has no dipole moments
and no energy transitions in the THz region. Hence,
nitrogen will not be a major factor in the attenuation.
Water vapor in the air generates absorption lines in
the THz frequency range [1,2 ]. Water vapor is highly
variable in the atmosphere, ranging from 0% to 0.4%
of atmospheric content. Among the atmospheric con-
stituents, water vapor is the largest contributor to
atmospheric attenuation due to its variable content
coupled with the strong interaction of waters electric
dipole moment with electromagnetic radiation. With
the power an d efficiency of currently available THz
radiation sources, strong absorption by water vapor
in the atmosphere makes the range of THz sensing
and transmission substantially short.
To show the atmospheric degradation effects, time-
domain waveforms of THz signals are observed in
Fig. 1. (Color online) Schematic diagram of the time-domain terahertz spectrometer.
Fig. 2. (Color online) Atmospheric degradation of THz signals: (a) time waveforms, (b) Fourier spectra.
10 February 2010 / Vol. 49, No. 5 / APPLIED OPTICS 929
Page 3
two humidity conditions: a low-humidity condition of
less than 5% relative humidity (RH) and an open-
air condition of 60% RH. The low-humidity condition
is obtained by filling the measurement chamber of
the THz spectrometer with dry nitrogen gas. Figure 2
compares time waveforms and Fourier spectra of
THz signals measured at 18 °C in low humidity
and in open air. The THz waveforms observed in a
dry nitrogen gas condition show a smooth tail in ap-
proximately 5 ps and converge to zero current. How-
ever, the observed signals in open air show signal
attenuation in the main peaks, with a slight time de-
lay and strong fluctuations in the tail. In the Fourier
spectrum domain, the THz signals observed in low-
humidity conditions show a smooth spectrum over
the THz range, while the signal in open air reveals
several strong absorption bands.
B. Modeling of Atmospheric Degradation Process
A THz signal observed from a detector can be mod-
eled as the output of an atmospheric degradation
process with an additi ve external noise to an input
signal generated from a THz source. The atmo-
spheric degradation process is assumed as a system
with characteristic function H. Then the THz signal
degradation process can be expressed as
uðtÞ¼H½rðtÞ þ vðtÞ; ð1Þ
where uðtÞ represents the observed degraded THz
signal, rðtÞ is the original undistorted signal from
the THz source, and vðtÞ denotes the additive exter-
nal noise, which is assumed to be independent of rðtÞ.
Figure 3 shows a general restoration process of THz
signals from atmospheric degradation.
A signal restoration filter G takes the degraded
signal uðtÞ as an input and produces an output xðtÞ
that closely approximates the original signal rðtÞ:
xðtÞ¼G½uðtÞ: ð2Þ
If we assume that the inverse system of the degrada-
tion process H is known and well defined, the re-
stored original signal xðtÞ can be found by a direct
inverse filtering:
xðtÞ¼H
1
½uðtÞ: ð3Þ
The objective of THz signal restoration is to find a
restored signal xðtÞ that is a faithful reproduction
of the original signal rðtÞ measured in low-humidity
conditions. In this paper, the absorbance is utilized
as a metric to determine if the restored signal xðtÞ
is sufficiently close to the reference signal rðtÞ ob-
served from a low-humidity condition. The absor-
bance of a signal xðtÞ is with respect to a reference
signal can be defined as
Absorbance ¼ log
10
A
2
sample
A
2
ref
; ð4Þ
where A
sample
and A
ref
indicate the magnitude Four-
ier spectra of the sample and the reference signal,
respectively. Sectio n 5 presents time waveforms and
the absorption spectra, as well as relative improve-
ment (RI), to provide visual and objective compari-
sons of the THz restoration techniques.
4. Atmospheric Degradation Restoration
A. Wavelet Analysis of Terahertz Signal
DWT decomposes a signal xðtÞ into approximation
and detail components by applying low-pass and
high-pass filters to xðtÞ [25]. The decomposed signals
can be expressed as
AðtÞ¼
X
k¼−∞
xðtÞφðt kÞ; ð5Þ
DðtÞ¼
X
k¼−∞
xðtÞψ ðt kÞ; ð6Þ
where approximation AðtÞ and detail DðtÞ compo-
nents are generated by a low-pass filter φðtÞ and a
high-pass filter ψ ðtÞ. Figure 4 shows a level-2 wavelet
decomposition of signal xðtÞ using the DWT. The sig-
nals A
1
ðtÞ and D
1
ðtÞ represent level-1 approximation
and detail components of signal xðtÞ. Level-1 approx-
imation signal A
1
ðtÞ is further decomposed into level-
2 approximation and detail components.
Figure 5 shows the frequency response of level-2
decomposition results of a THz signal using the sym-
let wavelets, which are nearly symmetrical, modifie d
from the Daubechies wavelets. The frequency range
of interest is set to 03 THz because most frequency
components of our THz measurements are contained
in this range. The cutoff frequencies of neighboring
filters are approximately 2 and 4 THz. Level-1 detail
corresponds to a high-frequency range of over 4 THz,
where no significant signal compo nents exist and,
therefore, the level-1 detail is removed for signal de-
noising. In the multiscale restoration method, level-2
approximation A
2
and detail D
2
are restore d sepa-
rately because they contain the characteristics of
Fig. 3. Modeling of atmospheric degradation and restoration
process of THz signals.
Fig. 4. Level-2 discrete wavelet decomposition of a signal.
930 APPLIED OPTICS / Vol. 49, No. 5 / 10 February 2010
Page 4
the original signal in the ranges of 02 THz and
24 THz, respectively.
B. Atmospheric Degradation Restoration
The multiscale THz signal restoration tech nique
uses a combined Wiener filter and ANN for each sig-
nal component. Figure 6 shows the idea of the pro-
posed multiscale signal restoration technique. The
observed THz signal uðtÞ is decom posed in level 2
using the DWT for separate processing. The signals
g
A
ðtÞ and g
D
ðtÞ denote approximation A
2
ðtÞ and detail
D
2
ðtÞ components of level-2 wavelet decomposition.
Each signal component is filtered by a combined
Wiener deconvolution filter (W
A
and W
D
), and an
ANN (N
A
and N
D
). The filters for the approximation
component recover the signal in a frequency range of
02 THz and the filters for the detail component re-
move atmospheric degradation in a frequency range
of 24 THz.
A degradation process at each decomposition level
can be modeled by a linear system:
g
k
ðtÞ¼h
k
ðtÞr
k
ðtÞþv
k
ðtÞ; k ¼ A; D; ð7Þ
where g
k
ðtÞ denotes DWT components of the obser-
ved THz signal uðtÞ, h
k
ðtÞ is the impulse response of
the atmospheric degradation process, r
k
ðtÞ is the ref-
erence THz signal, and v
k
ðtÞ is the additive noise. Wi-
ener deconvolution filter WðωÞ is used for restoration
of the signal from overall atmospheric degradation:
WðωÞ¼
1
Hð ωÞ
jHðωÞj
2
jHðωÞj
2
þjVðωÞj
2
=jRðωÞj
2
; ð8Þ
where HðωÞ denotes the Fourier transform of the im-
pulse response of the atmospheric degradation pro-
cess hðtÞ,andjVðωÞj
2
and jRðωÞj
2
denote the power
spectra of the noise vðtÞ and the reference THz signal
rðtÞ. The restored signal with a Wiener filter is given
by
G
0
ðωÞ¼WðωÞGðωÞ; ð9Þ
where GðωÞ and G
0
ðωÞ denote Fourier transforms of
the degraded THz signal g
k
ðtÞ and its Wiener re-
stored signal g
0
k
ðtÞ. Wiener deconvolu tion filters
are determined using an inputoutput training data-
set of the background air, where the input and the
output are THz signals measured in low- and high-
humidity conditions, respectively.
A nonlinear filter based on ANNs is used for the
restoration of the residual signal that linear Wiener
filtering is unable to recover. ANNs offer a model-free
approach to the estimation of inputoutput charac-
teristics of underlying nonlinear systems. Without
a mathematical model of the restoration, a neural
network adjusts its internal parameters using a
representative set of training data. An ANN-based
restoration filter f ðÞ, trained using a set of input
output data pairs, finds a restored signal cðtÞ from
the output signal g
0
ðtÞ of the Wiener filter:
cðtÞ¼f ðg
0
ðtÞ; sÞ: ð10Þ
Here g
0
ðtÞ denotes an input vector of the signal gen-
erated by the Wiener filter and s indicates a param-
eter vector of its internal connection weights that
need to be determined in the training process. A mul-
tilayer feed-forward neural network model [26]is
used as an ANN-based restoration filter, with an in-
put layer of (2m þ 1) nodes and a single output node
in the output layer. An input vector g
0
ðtÞ consists of
(2m þ 1) delay-line elements of an input THz signal
in a noncausal fashion:
g
0
ðtÞ¼½g
0
ðt mIÞ; ; g
0
ðtÞ; ; g
0
ðt þ mIÞ
T
; ð11Þ
where an integer I denotes the interval between
adjacent data samples. The output of each layer is
computed by a nonlinear activation function of a
weighted sum of inputs from the previous layer.
The neural network is trained using the backpropa-
gation algorithm [27] to determine the internal pa-
rameter vector s from a set of training data pairs
ðg
0
j
; d
j
Þ, where d
j
denotes the desired output for a
given input g
0
j
, i.e., the THz signal obtained in low-
humidity conditions. In the multiscale restoration
Fig. 5. (Color online) Fourier magnitude spectra of approxima-
tion and detail components in level-2 DWT decomposition.
Fig. 6. Multiscale restoration filtering with Wiener filter and ANNs.
10 February 2010 / Vol. 49, No. 5 / APPLIED OPTICS 931
Page 5
approach, two individual neural networks N
A
and
N
D
are used for the restoration of residual signals
of approximation and detail components.
5. Experiment Results
A time-domain THz spectrometer measured THz sig-
nals from different material samples. In this experi-
ment, we used two solid substances with different
chemical compositions, dinitrotoluene (DNT) and di-
nitrobutane (DNB). The testing samples were pre-
pared in the form of a circular pellet of 25:4 mm
diameter and thickness of 2:98 mm for DNT and
1:52 mm for DNB. The THz beam focused on the sam-
ple was approxim ately 2 mm in diameter. THz spec-
troscopic measurements were made in two different
conditions: a low-humidity environment filled with
dry nitrogen gas at less than 5% RH and an open-
air environment at approximately 60% RH. From
these measurements we obtained 42 datasets, of
which we used 31 randomly selected datasets for
training the signal restoration filters. The remaining
11 datasets were utilized for testing signal restora-
tion performance.
In multiscale signal decomposition, the approxi-
mation component contains the overall shapes of
the original signals and t he detail includes high-
frequency signal components. Figure 7 shows the fre-
quency responses of the Wiener filters W
A
and W
D
for
approximation and detail components. The locations
of peaks of Wiener deconvolution filters W
A
and W
D
are observed to match with the major dips of the
Fourier spectrum of degraded signals to recover at-
mospheric degradation. The filter response of W
D
suppresses absorption in the 01:1 THz range, while
the absorption dips over 2:5 THz range are corrected
by filter W
D
.
Figure 8 shows typical Fourier spectra of the ma-
terials DNT and DNB measured in low-humidity and
open-air environments. The Fourier spectra show
many spectral dips due to the absorption of water
vapor in the THz range. Figure 9 demonstrates
time-domain waveforms approximation and detail
components generated by the multiscale restoration
filter for DNT. In Fig. 9(a), the multiscale restoration
filter restores the approximation component of the
THz signal for DNT with high accuracy. For the de-
tail component, strong fluctuations in the degraded
signal are greatly removed, as shown in Fig. 9(b).
The waveforms of the reference component and
the detail component restored using the multiscale
restoration technique overlap very closely. The re-
stored detail component shows small errors in low-
amplitude parts, where the estimation is difficult
because the signal in this high-frequency range
shows strong randomness. However, the error effect
is minimal because the magnitude of the detail com-
ponent is very small compared to approximation.
Figure 10 compares Fourier magnitude and ab-
sorption spectra of the multiscale restoration techni-
que with the reference DNT signal . The Fourier
magnitude spectrum of the restoration result is very
close to that of the reference signal in the 03 THz
range. All major dips in the frequency domain caused
by atmospheric degradation shown in Fig. 8(a) are
now successfully removed. The absorption spectrum
of the restored signal is similar to the reference ab-
sorbance for the most part (02:3 THz), except where
Fig. 7. (Color online) Frequency response of the Wiener deconvo-
lution filters for approximation and detail components.
Fig. 8. (Color online) Fourier magnitude spectra of the testing samples: (a) DNT, (b) DNB.
932 APPLIED OPTICS / Vol. 49, No. 5 / 10 February 2010
Page 6
Fig. 9. (Color online) Time waveforms of the approximation and detail components restored using the multiscale restoration filter for
DNT: (a) approximation (A
2
), (b) detail (D
2
).
Fig. 10. (Color online) Fourier magnitude and absorption spectra of the multiscale restoration filter for DNT: (a) Fourier spectra,
(b) absorbance.
Fig. 11. (Color online) Fourier magnitude and absorption spectra of the multiscale restoration filter for DNB: (a) Fourier spectra,
(b) absorbance.
Table 1. Comparison of Various Terahertz Signal Restoration Schemes in Relative Improvemen t
Materials Wiener Only ANN Only Wiener þ ANN Multiscale Wiener þ ANN
DNT 38.18 37.17 45.65 59.35
DNB 27.10 31.30 37.18 46.06
10 February 2010 / Vol. 49, No. 5 / APPLIED OPTICS 933
Page 7
Fourier magnitude is very small and, therefore, the
absorbance is sensitive to small changes even in low-
humidity conditions. In Fig. 11, the multiscale re-
storation obtains similar results for the DNB sample.
The restored Fourier spectrum is very close to that of
the reference signal measured in a low-humidity con-
dition. The reference spectrum of a DNB sample goes
as low as the noise level in the 11:8 THz range, as
shown in Fig. 11(a). Therefo re, the absorbance, which
is the ratio of spectral magnitudes of the restored and
the reference signals, becomes very sensitive in this
frequency range. Even though the restored spectral
magnitude is very close to the reference spectrum,
nonstationary absorbance peaks are observed in this
range. We could observe a similar pattern for a DNT
sample in the 2:53 THz range.
In order to compare different THz signal restora-
tion methods using a metric that shows relative im-
provement (RI), the ratio of the mean-square errors
of the restored signal and the refere nce signal is used
in Table 1:
RIðdBÞ¼10log
10
MSE
u
MSE
x
¼ 10log
10
1
n
P
ε
2
x
ðtÞ
1
n
P
ε
2
u
ðtÞ
;
ð12Þ
where ε
x
ðtÞ denotes the error between restored signal
xðtÞ and the reference signal rðtÞ, ε
x
ðtÞ¼xðtÞ rðtÞ,
and ε
u
ðtÞ denotes the error between degraded signal
uðtÞ and the reference signal rðtÞ, ε
u
ðtÞ¼uðtÞ rðtÞ.
Table 1 summarizes RI of various restoration
schemes for the two chemical samples, Wiener filter
only, ANN only, a combination of Wiener and ANN
filters, and the multiscale restoration. For both che-
micals, a combined Wiener and ANN filter shows
some improvement over single-restoration-filte r
cases (Wiener only and ANN only). The multiscale
Wiener and ANN restoration technique shows the
biggest improvement of all combinations in THz
signal restoration. The wavelet-based multiscale
restoration method represents a THz signal with ap-
proximation and detail components that reveal low-
and high-frequency characteristics of the signal.
Wavelet transforms have a pyramidal tree structure,
allowing successive decomposition of the lowest sub-
band at each level, which means finer resolutions
toward the lower frequency bands. In level-2 decom-
position, the approximation component contains a
low-frequency trend of a THz signal under 2:5 THz.
The detail component (D
2
) contains higher-frequency
signal details for the range of approximately 1.3 to
3 THz, as shown in Fig. 5. A combined restoration
filter designed for each individual component
reduces the degradation effect separately.
6. Conclusion
Although THz radiation has demonstrated potential
in detecting chemical substances from a distance, the
sensing range is significantly limited due to strong
attenuation by humid atmosphere. THz beams are
absorbed by water molecules in the air when they
propagate through the atmosphere. Therefore, it is
difficult to obtain high signal-to-noise ratio with
the power and efficiency of most currently available
THz radiation sources and detectors. Material-
specific THz signatures can be easily obscured by
strong attenuation and spurious peaks in the absorp-
tion spectrum. This paper addresses a THz signal
restoration technique to remove atmospheric degra-
dation of a THz signal measured in the open air. THz
signal restoration from atmospheric attenuation is
important to increase the sensing range of THz sig-
nals in humid environments. The proposed ap-
proach is based on multiscale signal decomposition
with combined signal restoration filters, a Wiener
deconvolution filter and an ANN, for each signal com-
ponent. A THz signal is decomposed into approxima-
tion and detail components using the DWT. A set of
Wiener deconvolution filter and an ANN restore each
signal component from the fluctuations and the noise
that cause strong absorption bands in the spectrum.
A restored THz signal is obtained by the inverse
DWT of the filtered signal components. Experimen-
tal results with two chemical substances demonstra-
te that the multiscale signal restoration technique is
effective in removing atmospheric degradation when
compared to individual approaches.
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  • Source
    • "A major hardship that can profoundly affect the performance of these methods is the difficulty in distinguishing THz signals from unwanted signals, such as emitter/detector noise, signal fluctuation from atmospheric attenuation, and multiple reflections of the THz wave caused by the etalon effect in samples and optical components in the THz-TDS setup [14]. Algorithms for signal restoration or removal of undesired effects have been mentioned previously [14,15], but are mainly focused on the procedure itself or the level of removal efficiency. Thus, widely applicable data processing schemes that directly decompose the raw THz signal which can lead to accurate material evaluation have received little or no attention in previous literature. "
    [Show abstract] [Hide abstract] ABSTRACT: Terahertz time-domain spectroscopy (THz-TDS) allows broadband noninvasive measurement of the optical parameters of various materials in the THz domain. The measurement accuracy of these parameters is highly influenced by the difficulty in distinguishing THz signals from unwanted signals such as noise, signal fluctuation, and multiple echoes,which directly affectsmaterial identification and characterization efficiency. We introduce a novel method that provides effective extraction and separation of THz signals from such undesired effects. The proposed algorithm was assessed through experiments that presented enhancement in material parameter evaluation, such as the decomposition of the sample-induced echoes (SIEs) from the complex THz sample signal with near-zero extraction error. Improved precision (±0.05μm) was achieved in the determination of the sample thickness compared to that of the mechanical method (±10μm). Furthermore, we could infer from the component concentration measurement results of a compound sample (44.2% decrease in the root mean square concentration error) that the material parameter calculation accuracy had improved, proposing a means to enhance the ultimate nondestructive material evaluation performance.
    Full-text · Article · Mar 2015 · Journal of Nondestructive Evaluation
  • [Show abstract] [Hide abstract] ABSTRACT: Terahertz (THz) radiation is extensively applied in diverse fields, such as space communication, Earth environment observation, atmosphere science, remote sensing and so on. And the research on propagation features of THz wave in the atmosphere becomes more and more important. This paper firstly illuminates the advantages and outlook of THz in space technology. Then it introduces the theoretical framework of THz atmospheric propagation, including some fundamental physical concepts and processes. The attenuation effect (especially the absorption of water vapor), the scattering of aerosol particles and the effect of turbulent flow mainly influence THz atmosphere propagation. Fundamental physical laws are illuminated as well, such as Lamber-beer law, Mie scattering theory and radiative transfer equation. The last part comprises the demonstration and comparison of THz atmosphere propagation models like Moliere(V5), SARTre and AMATERASU. The essential problems are the deep analysis of physical mechanism of this process, the construction of atmospheric propagation model and databases of every kind of material in the atmosphere, and the standardization of measurement procedures.
    No preview · Article · Mar 2011 · Journal of Physics Conference Series