1354 OPTICS LETTERS / Vol. 33, No. 12 / June 15, 2008

Suppression of spectral interferences due towater-vapor rotational transitions in terahertz

time-domain spectroscopy

Yingxin Wang,1 Ziran Zhao,1,* Zhiqiang Chen,1 Yan Zhang,2 Li Zhang,1 and Kejun Kang1

1Department of Engineering Physics, Tsinghua University, Beijing 100084, China2Department of Physics, Capital Normal University, Beijing 100037, China

*Corresponding author: zhaozr@mail.tsinghua.edu.cn

Received March 21, 2008; revised April 29, 2008; accepted May 14, 2008;posted May 15, 2008 (Doc. ID 94120); published June 13, 2008

Absorption lines of atmospheric water vapor are commonly present in terahertz spectra measured in ambi-ent air. These spectral interferences are caused by the rotational transitions of water molecules. In thisstudy, we develop an effective method for suppression of the water-vapor effects by modeling the absorptionlines using Lorentzian line shape and spectroscopic parameters extracted from the HITRAN database andthen subtracting them iteratively in the frequency domain. The free-space terahertz pulse and the absor-bance spectrum of an explosive material are restored successfully in the experimental verification. © 2008Optical Society of America

OCIS codes: 120.3940, 300.6270, 010.1300.

Spectroscopic investigation in the terahertz rangehas received extensive attention. One of its attractiveproperties is that a large variety of molecules exhibitunique spectral responses in this band. The use ofthese responses for detection and identification ofchemical species of interest, such as polar gases [1]and biological molecules [2], has been demonstrated.Terahertz time-domain spectroscopy (TDS) is an ef-fective and promising technique for the characteriza-tion of the species, which allows us to measure thetemporal waveform of a terahertz pulse directly.

However, the atmospheric water vapor may limitthe application of terahertz TDS in a real-world en-vironment. Experimental studies [3] have shown thatthe pure rotational transitions of water moleculeswould be excited coherently during the propagationof terahertz pulses and reradiate a free-induction de-cay signal [4], causing additional fluctuations afterthe main pulse and sharp absorption lines in the cor-responding spectrum. Such effects will result in theattenuation of the terahertz radiation as well as com-plicate the spectroscopic characterization of the ma-terial. Conventionally, the terahertz setup is purgedwith dry nitrogen to remove water vapor. This treat-ment increases the system complexity and is not fea-sible for all situations. In a previous work [5], weused scaled absorbance subtraction to address thisproblem, but the reference spectrum of water vaporwas dependent on the atmospheric conditions. Re-cently, a relatively general approach based on theo-retical modeling of the water-vapor frequency re-sponse was reported [6]. Here, we follow this ideaand propose to eliminate the absorption lines by line-shape fitting in conjunction with the spectral sub-traction technique.

To interpret the spectral interferences induced bywater vapor, we first consider the interaction of theterahertz pulse with a gas sample containing polarmolecules. For the case of low power, this interactionprocess can be well described by the linear dispersiontheory [4]. The terahertz electric fields after propa-

0146-9592/08/121354-3/$15.00 ©

gating through vacuum, Er, and through the gassample, Es, have the following relation in the fre-quency domain:

Es��� = Er���V���, V��� = exp�−j�n��� − 1��L

c � ,

�1�

where n���=n���− j���� represents the complex re-fractive index of the sample, � is the angular fre-quency, L is the propagation length, and c is thespeed of light in vacuum. Since the collisional broad-ening dominates the rotational linewidths, the reso-nance profile of an individual transition can be ap-proximated by the Lorentzian line shape; thus theabsorption and dispersion profiles are expressed as in[7], respectively,

���� = Kc

2�� �

��0 − ��2 + �2 −�

��0 + ��2 + �2� , �2a�

n��� − 1 = Kc

2�� �0 − �

��0 − ��2 + �2 −�0 + �

��0 + ��2 + �2� , �2b�

where �0 denotes the transition frequency, � is thehalf-width at half-maximum of the absorption line,and K is the line intensity. Theoretically, knowingthese parameters, we are able to restore the refer-ence signal Er by deconvolving the complex responseof water vapor according to Eq. (1). But in practicesome factors, e.g., the limited time window and thedynamic range of the system will distort the observedsignal [8].

When the duration of the measured waveform issmaller than the dephasing time [3] of water mol-ecules, the experimentally obtained linewidth is de-termined by the observation period (or the windowwidth) and broadened owing to the loss of frequency

resolution. In fact, the measured sample spectrum

2008 Optical Society of America

June 15, 2008 / Vol. 33, No. 12 / OPTICS LETTERS 1355

results from the convolution of a Fourier-transformedsquare window function W��� with the actual spec-trum Es���, i.e.,

Es��� = Es��� * W��� � Er����V��� * W����. �3�

Here the asterisk denotes the convolution operation,and the approximation is valid when the linewidthsare much narrower than the spectral width of theterahertz pulse [9]. Taking the modulus and loga-rithm of both sides of Eq. (3) yields a spectral sub-traction [10] problem:

ln�Er���� � ln�Es���� − ln�V��� * W����. �4�

To take account of the limitation of the dynamicrange, we regard the line intensity K as an optimiza-tion variable and fit the water lines to the measuredspectrum Es���. The optimal subtraction of thewater-vapor spectrum is achieved by minimizingthe total variation (TV) [11] of the residual spectrumR�� ,K�=ln � Es��� �−ln �V���*W����, which corre-sponds to the following minimization problem:

minK

TV�R��,K�� = minK �R��,K�

��d�, K � 0. �5�

The different rotational transitions of water mol-ecules are excited simultaneously. Consequently, amultitude of absorption lines are present within theobserved frequency range. We assume the response ofwater vapor to be derived from a summation of allthese transitions and determine the absorptionstrengths line by line. The other spectroscopic pa-rameters, including line position and linewidth, areadopted from the HITRAN molecular spectroscopic da-tabase [12].

A typical terahertz TDS system [5] based on the op-tical rectification and electro-optic sampling tech-niques was used for collecting terahertz signals so asto validate our method. The measurement of a water-vapor-modulated pulse was carried out in ambientair with a relative humidity of 18.7%. In addition, thereference terahertz pulse was acquired under dry ni-trogen atmosphere (with a humidity of 4%), servingas the standard for comparison after the removal ofwater-vapor effects. Both signals are recorded in a20.68 ps time window (corresponding to an originalfrequency resolution of approximately 48 GHz), andthey provide a useful frequency range from 0.1 to2.6 THz �3.3–86.7 cm−1�. The temporal waveformswere zero padded to about four times prior to theFourier transform. All experiments were made at21°C and normal atmospheric pressure.

The time-domain waveforms and amplitude spec-tra of terahertz pulses are shown in Fig. 1. We canclearly see the temporal fluctuations and spectralresonances caused by water molecules. The small fea-tures for the reference signal are attributed to re-sidual water-vapor absorption. Performing deconvo-lution of the modulated signal with respect to thereference would give the absorption spectrum of wa-

ter vapor. Figure 2 shows an individual peak cen-

tered at 0.752 THz (the transition JKa,Kc=211←202 of

H2O) and three closely spaced peaks near 1 THz,where there actually exist six strong unresolved lines[12]. The two groups of profiles were fitted with theLorentzian model, accounting for the windowing ef-fect [see Eq. (3)]. There is good agreement betweenthe measured spectrum and the theoretical lineshape, which provides initial evidence for the feasi-bility of our proposed algorithm.

From the published values of HITRAN, more than300 transitions are present within the range3.3–86.7 cm−1. Nevertheless, only the 30 strongestones were considered in the analysis. This is suffi-cient, because most of these transitions have astrength lower than the noise level of the system.Furthermore, for simplicity, the adjacent water lineswith spacing less than the half-width were mergedinto a single one, ultimately yielding a total of 28lines involved in the interference elimination proce-dure. Note that a narrow time window will give rise

Fig. 1. (a) Time-domain waveforms of terahertz pulses ob-tained under nitrogen (solid curve) and air (dashed curve)atmospheres. (b) Corresponding amplitude spectra. Thedotted curves are the results with suppression of water-vapor effects. The curves are offset vertically for clarity.

Fig. 2. Measured (solid curves) and Lorentzian fitted (dot-

ted curves) rotational transitions of water vapor.

1356 OPTICS LETTERS / Vol. 33, No. 12 / June 15, 2008

to an additional broadening of the lines and makethem overlap, as seen in Fig. 2(b). The overlappingeffects may degrade the performance of the algorithmif implemented by dealing with each line separately.We thereby divided the concerned lines into 10groups in terms of their positions, and those in thesame group were removed at one time. All groupswere subtracted iteratively from low to high frequen-cies, which means that the amplitude spectrum wasupdated synchronously after removing one group.The optimization problem (5) was solved numericallyby a sequential quadratic programming method inthe MATLAB environment [13]. Finally, we plot the re-sulting spectrum with the compensation of water va-por bands in Fig. 1(b) (dotted curve). Comparing withthe reference spectrum, it is obvious that a majorityof interfering lines have been successfully elimi-nated, although a slight oscillation still remains,arising from incomplete compensation. In our algo-rithm, the phase information was also available to al-low the time-domain signal to be reconstructedstraightforwardly. As displayed in Fig. 1(a), the tem-poral fluctuations after the main pulse are signifi-cantly reduced, and one can find that the pulse am-plitude becomes nearly identical to that of thereference.

The experiment of material characterization withterahertz TDS was also conducted. A sample ofexplosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) was placed in the beam path, and thetransmitted terahertz pulses were measured underthe same conditions described above. Figure 3 illus-trates the absorbance spectra of HMX. For the case ofair atmosphere, many artifacts appear on the curve,especially around the strong signature at 1.8 THz. Byapplying the interference-elimination algorithm tothe signals taken in air (with and without HMXsample), the quality of the reproduced spectrum wasimproved, as shown in the middle of Fig. 3, except forthe peak region where the SNR is relatively low, ow-ing to saturated absorption. To perform a quantita-

Fig. 3. Absorbance spectra of HMX obtained under nitro-gen (solid curves) and air (dashed curves) atmospheres.The dotted curve in the middle is the result with suppres-

sion of water-vapor effects.

tive evaluation, we calculated the relative differencebetween the absorbance generated from the air–atmosphere measurement and that from the nitrogenatmosphere. The differences before and after the re-moval of water vapor absorption are 16.9% and10.9%, respectively.

In conclusion, suppression of water-vapor interfer-ing lines at terahertz frequencies has been performedusing line-shape fitting and spectral subtraction.Benefiting from the prior knowledge of the rotationaltransitions of water molecules, the proposed methodis not affected by the atmospheric conditions, andthus its generality is assured. This investigation ex-tends the applicability of terahertz TDS to the real-world environment. However, it should be pointedout that, for high-humidity environments or stand-offmeasurements, the applicability of the algorithmmay be limited to the lines without excessive absorp-tion. Also, the algorithm may not be suitable for thecharacterization of the sample that has a narrow ab-sorption feature at the same position as a water line.

This work is supported by Program for New Cen-tury Excellent Talents in University and the Funda-mental Research Foundation of Tsinghua University.

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