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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.

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

[1–3], 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 spectral 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.

Introduction

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 important 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

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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 watervapor, 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 wavelettransform (DWT). A signal

restoration filter consisting 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 input–output 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.

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 fiber laser (IMRA femtolite 780)

that emits approximately 100fs laser pulses with a

center wavelength of 780nm, a repetition rate of

48MHz, and an average power of 30mW. 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 200V and 9:5kHz, 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 1m. 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

Terahertz Spectroscopy

928 APPLIED OPTICS / Vol. 49, No. 5 / 10 February 2010

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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 is the rate at which a

beam’s energy is absorbed via interactions with

Atmospheric Attenuation in the Terahertz Range

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 water’s electric

dipole moment with electromagnetic radiation. With

the power and 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 OPTICS929

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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 5ps 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.

A THz signal observed from a detector can be mod-

eled as the output of an atmospheric degradation

process with an additive 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

Modeling of Atmospheric Degradation Process

uðtÞ ¼ H½rðtÞ? 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:

xðtÞ ¼ G½uðtÞ?:

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:

ð2Þ

xðtÞ ¼ H−1½uðtÞ?:

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 −log10

?A2

sample

A2

ref

?

;

ð4Þ

where Asampleand Arefindicate the magnitude Four-

ier spectra of the sample and the reference signal,

respectively. Section 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.

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

Wavelet Analysis of Terahertz Signal

AðtÞ ¼

X

∞

k¼−∞

xðtÞφðt − kÞ;

ð5Þ

DðtÞ ¼

X

∞

k¼−∞

xðtÞψðt − kÞ;

ð6Þ

where approximation AðtÞ and detail DðtÞ compo-

nents are generated by a low-pass filter φðtÞ and a

high-pass filter ψðtÞ. Figure 4 shows a level-2 wavelet

decomposition of signal xðtÞ using the DWT. The sig-

nals A1ðtÞ and D1ðtÞ represent level-1 approximation

and detail components of signal xðtÞ. Level-1 approx-

imation signal A1ðtÞ 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, modified

from the Daubechies wavelets. The frequency range

of interest is set to 0–3THz because most frequency

components of our THz measurements are contained

in this range. The cutoff frequencies of neighboring

filters are approximately 2 and 4THz. Level-1 detail

corresponds to a high-frequency range of over 4THz,

where no significant signal components exist and,

therefore, the level-1 detail is removed for signal de-

noising. In the multiscale restoration method, level-2

approximation A2and detail D2are restored sepa-

rately because they contain the characteristics of

Fig. 3.

process of THz signals.

Modeling of atmospheric degradation and restoration

Fig. 4.Level-2 discrete wavelet decomposition of a signal.

930 APPLIED OPTICS / Vol. 49, No. 5 / 10 February 2010

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the original signal in the ranges of 0–2THz and

2–4THz, respectively.

B.

The multiscale THz signal restoration technique

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 decomposed in level 2

using the DWT for separate processing. The signals

gAðtÞ and gDðtÞ denote approximation A2ðtÞ and detail

D2ðtÞ components of level-2 wavelet decomposition.

Each signal component is filtered by a combined

Wiener deconvolution filter (WAand WD), and an

ANN (NAand ND). The filters for the approximation

component recover the signal in a frequency range of

0–2THz and the filters for the detail component re-

move atmospheric degradation in a frequency range

of 2–4THz.

A degradation process at each decomposition level

can be modeled by a linear system:

Atmospheric Degradation Restoration

gkðtÞ ¼ hkðtÞ ? rkðtÞ þ vkðtÞ;

where gkðtÞ denotes DWT components of the obser-

ved THz signal uðtÞ, hkðtÞ is the impulse response of

the atmospheric degradation process, rkðtÞ is the ref-

erence THz signal, and vkðtÞ is the additive noise. Wi-

ener deconvolution filter WðωÞ is used for restoration

of the signal from overall atmospheric degradation:

k ¼ A;D;

ð7Þ

WðωÞ ¼

1

HðωÞ

jHðωÞj2

jHðωÞj2þ jVðωÞj2=jRðωÞj2;

ð8Þ

where HðωÞ denotes the Fourier transform of the im-

pulse response of the atmospheric degradation pro-

cess hðtÞ, and jVðωÞj2and jRðωÞj2denote the power

spectra of the noise vðtÞ and the reference THz signal

rðtÞ. The restored signal with a Wiener filter is given

by

G0ðωÞ ¼ WðωÞGðωÞ;

ð9Þ

where GðωÞ and G0ðωÞ denote Fourier transforms of

the degraded THz signal gkðtÞ and its Wiener re-

stored signal g0kðtÞ. Wiener deconvolution filters

are determined using an input–output 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 input–output 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 fðÞ, trained using a set of input–

output data pairs, finds a restored signal cðtÞ from

the output signal g0ðtÞ of the Wiener filter:

cðtÞ ¼ fðg0ðtÞ;sÞ:

Here g0ðtÞ 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 g0ðtÞ consists of

(2m þ 1) delay-line elements of an input THz signal

in a noncausal fashion:

ð10Þ

g0ðtÞ ¼ ½g0ðt − mIÞ;…;g0ðtÞ;…;g0ðt þ mIÞ?T;

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

ðg0j;djÞ, where djdenotes the desired output for a

given input g0j, i.e., the THz signal obtained in low-

humidity conditions. In the multiscale restoration

ð11Þ

Fig. 5.

tion and detail components in level-2 DWT decomposition.

(Color online) Fourier magnitude spectra of approxima-

Fig. 6.Multiscale restoration filtering with Wiener filter and ANNs.

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