False detection of dangerous and neutral substances in commonly used materials by means of the standard THz Time Domain Spectroscopy

Essential limitations of the standard THz Time Domain Spectroscopy (TDS), which lead to false detection of dangerous and neutral substances in commonly used materials, are demonstrated using the physical experiment with chocolate under real conditions as well as with semiconductors under laboratory conditions. To overcome this disadvantage, we propose using the time-dependent spectrum of the THz pulse, transmitted through or reﬂected from a substance. For quality assessment of the standard substance absorption frequency presence in the signal under analysis, we use time-dependent integral correlation criteria. The inﬂuence of aperture placed in front of the sample on spectral properties of silicon wafers with different resistivity is demonstrated as well.


INTRODUCTION
As it is well known, the detection of explosives, drugs and other threats is one of the main security screening problems.To solve it, a THz radiation has been actively used during the past twenty years [1]- [18].The THz TDS also provides new opportunities in the field of non-destructive testing [19], pharmaceutical control [20], in studying technologically-related materials ranging from nanostructures to strongly correlated electron materials [21,22].
Currently, the standard THz TDS method of the substance detection is based on a comparison of absorption frequencies of a substance under consideration with standard absorption frequencies from the database.It should be stressed that under the standard method we mean not the ways of the THz signal measuring and corresponding experimental details, but only the fact that eventually the standard THz TDS deals with the spectral characteristics (Fourier spectra, absorbance or reflectance spectra) of the THz signal registered using those or other setups.Unfortunately, this method possesses obvious great disadvantages.For example, it was shown that many ordinary substances have the same absorption frequencies belonging to explosives.This leads to efficiency decreasing of the standard THz-TDS method using.Opaque packaging and complicated surface of the sample, and high humidity of an ambient medium also decrease this method efficiency [10]- [14].However, it should be stressed that the THz-TDS method may be applied with high efficiency for substance investigation and database development under laboratory conditions.
In the present paper, we continue to demonstrate essential limitations of the standard THz-TDS method using for the de-tection and identification of substances under real conditions -at long distance of about 3.5 m, in ambient air with relative humidity of about 50%.Our investigations demonstrate zerovalue efficiency of this method in real conditions.For this purpose, we use a neutral substance -a chocolate bar.Another example is a semiconductor identification under laboratory conditions -at short distance of about 15 cm, in dry air with relative humidity less than 2%.We show that the standard THz-TDS method detects the spectral features of hazardous substances in the commonly used neutral materials both under real and laboratory conditions.It is important, that this property is not inherent to any particular equipment, for example, to that used in the Lomonosov Moscow State University, because all data, which we used, were from various laboratories.
Measurement of the THz signal reflected from the chocolate bar at long distance was made at Lomonosov Moscow State University (Moscow, Russia).The THz signal transmitted through the RDX sample was registered in the Center for Terahertz Research, Rensselaer Polytechnic Institute (NY, USA); transmitted THz signals MA, MDMA, n-Si, p-Si -at Capital Normal University (Beijing, China).
At first glance, the example with the semiconductor may seem strange -why do we search for explosive or sugar in Si-wafer?However, currently almost every person has some electronic device (cell phone, or tablet PC) that contains semiconductor elements.If the false detection of explosives or some neutral substance instead of cell phone will take place many times, the remote screening efficiency will tend to zero.
We believe that the main disadvantage of the standard THz-TDS method consists in the following: it is impossible to make a conclusion about the actual absence of hazardous substances in the neutral sample under consideration.This fact leads to zero-value probability of the device developing, which can detect dangerous substances with high probability, because it will lead to a large number of false alarms.On the other hand, approach for the detection and identification of substances can be based on the spectral dynamics analysis (SDA) method [23]- [26], which may be one of the ways to overcome the THz-TDS method disadvantages.In this method the timedependent spectral intensities are analyzed at the chosen frequencies and this allows us to avoid false alarms appearing and to detect the explosive absence in the neutral substances; moreover, detecting them.To illustrate that the method does not depend on the particular installation, we use the results of experiments performed at different times and in different laboratories: in Poland (Military University of Technology, Warsaw) and Lithuania (Semiconductor Physics Institute, Vilnius).
Earlier, the SDA-method was successfully used for the identification of neutral substances, explosives and drugs in the transmission and reflection mode [23]- [26], [40].For quality assessment of a probability for dangerous substance presence in a substance under consideration, new integral criteria for the detection and identification were proposed for the first time in [27].In [28] these criteria were applied for the PWM C4 explosive detection with a complicated surface in the reflection mode using data from two Universities mentioned above.These facts illustrate a weak sensitivity of the SDA-method to specific measurements.In [29]- [34], [40] the identification of substance, placed at long distances also was made.Despite these investigations, there is a least one more problem that was not discussed at all: an influence of a diameter of the THz beam, which falls on a semiconductor wafer, on spectrum of the pulse transmitted through semiconductor.We show its essential influence on the spectrum in the frequency range ν > 1.65 THz.The beam diameter is changed using an aperture placed in front of a sample.

THE SETUP
In our physical experiments, we exploit a THz spectrometer EKSPLA developed by Teravil Inc., Lithuania [32].It uses a femtosecond fiber laser, which generates laser pulse with average power about 1 W, with 1030 nm centre wavelength, 75 MHz repetition rate, and its pulse duration is 80 fs.Lowtemperature grown GaBiAs is used as photoconductor.The spectral range of the spectrometer is 0.1-5.0THz, signal-tonoise is better than 10 3 : 1 (at 2 THz), 10 5 : 1 (at 1 THz) and 10 6 : 1 (at 0.4 THz), spectral resolution is better than 10 GHz (fast scan), 2.5 GHz (combined mode).The schematic of the system can be found in http://www.ekspla.com.We use a parabolic mirror for the THz beam focusing on the object.Because the femtosecond fiber laser has average power of about 1 W and the laser beam splits many times, we use additional flat mirror behind the object.Therefore, our setup operates in reflection-transmission mode simultaneously for each measurement.The measurements were carried out under real con-ditions with a temperature 18 • C and the relative humidity of about 50%.The distance between the parabolic mirror and the object was about 3.5 meters.
Measurement of explosive RDX was made in transmission mode using the Teraview TPS 3000 unit in the standard configuration.The main spectrometer parameters are: spectral range is equal to 0.06-3.6THz, signal-to-noise is better than 4000:1, dynamic range is higher than 3 OD in the range: from 2 cm −1 to 100 cm −1 , spectral resolution is equal to 0.06 THz and rapid scan mode can do 30 scans/second [14,26].The distance between a sample and the spectrometer receiver did not exceed 30 cm.Measurement procedure is described in detail in [9], but in our case, the RDX signal was measured in the ambient air.

Spectral properties of chocolate
In Figure 1(a), we present the sample investigated under real conditions, it is a chocolate bar with thickness 5-7 mm.Let us notice again that the THz pulse falls on the sample and reflects from the flat metallic mirror placed behind the sample.Then, this reflected pulse passes the same distance toward the parabolic mirror of the THz spectrometer.Of course, a part of the THz pulse is reflected from various parts of the chocolate including its inhomogeneity.
Figure 1(b) shows the measured Chocolate THz signal on the time interval t = [0, 110] ps.The strong noise, which is observed in the signal, can be a result of the ambient medium action.Nevertheless, maximal amplitude of the THz signal is 4 times more than noise amplitude.Note that the frequency resolution depends obviously on the time interval, during which the measurements are performed.As a rule, its duration in the experiment with chocolate was approximately 100 ps.Consequently, the minimum frequency difference ∆ν, which can be resolved by computer processing, is 10 GHz.Let us remind, that the standard THz-TDS method deals with the spectrum of a THz signal main pulse.In our case, its duration is about 25 ps.With this aim, the Fourier spectrum ( |P(ν)|, |P REF (ν)| are the spectral amplitude modulus of the reference and Chocolate signal main pulse.The curve construction is made with the frequency resolution ∆ν = 0.01 THz.In order to provide such resolution, we have cut the main pulse out from the long measured signal on the time interval t = [0, 25] ps, and then extended the main pulse by zeros over the time t = 100 ps.As we usually use a Fourier spectrum (or spectral line dynamics) for the detection and identification of substance while in the most of the articles absorbance is used for these purposes, we stress that the spectrum minima (Figures 2(a) and 2(b)) are in a good agreement with maxima in absorbance (Figures 2(c  and 2(d)).Therefore, using of these spectral characteristics of the pulse (Fourier spectrum and absorbance) is equivalent for the detection problem.The Chocolate signal spectrum corresponding to the time interval t = [0, 110] ps is depicted in [32].
It is obvious that in our case the chocolate does not contain dangerous substances.However, in the Fourier spectrum and absorbance (Figure 2) it is possible to see the spectral features of explosives and illicit drugs.Really, in accordance with [6,7,9], the absorption frequencies of explosives are: ν = 0.82,  [36] and they are used below in our investigations.
As usual, a substance is detected by using the set of known absorption frequencies from database.However, at measuring under real conditions, the part of such set of frequencies belonging to the measured pulse spectrum may be distorted by sample surface inhomogeneity or attenuated by water vapor (or other gases).So, one can find in the spectrum and absorbance the part (or only one) of these absorption frequencies.Therefore, we have to tell about belonging of the part (or only one frequency) to dangerous substance.That is why we show in Figure 2 (and also in Figures 3 and 4) not only  [12] and Chocolate ν = 1.75 THz [29].
Our aim is to distinguish these frequencies.In other words, we want to answer the question whether these minima (or peaks in absorbance) belong to dangerous substances or not.
For such cases, we develop and improve currently our criteria and show that they allow us to distinguish and separate the false absorption frequencies.
The false absorption frequencies can appear in the spectrum for several reasons: the presence of noise, the inhomogeneous structure of the sample and its surface, the presence of impurities with similar absorption frequencies, the influence of the environment -for example, water vapor in the air, the presence of layered covering, etc.Additional ingredients containing in chocolate (aromatic and food additives) or some agents used during manufacturing may also induce the appearance of certain frequencies.
Obviously, a spectral resolution of a THz spectrometer influences on the detection and identification of a substance.In ideal conditions (without presence of water vapor and other features mentioned above), the increase in spectral resolution leads to the increase in identification probability, because we can use the fine structure of the THz spectrum.However, the noise presence in the THz pulse can cardinally change this situation.The reason is obvious.Small-scale perturbations modulate a THz pulse and, therefore, many additional extremes appear in the spectrum.Nevertheless, in our opinion, there is a simple approach, which can partly avoid and distinguish these frequencies from the absorption frequencies of dangerous substances.Taking into account a spectral width of the absorption frequency of the standard substance from the database, one can decrease the spectral resolution of calculated spectrum in order to remove the small-scale perturbation influence.Figure 2 illustrates this statement by comparing the spectra calculated with various resolution. 1 -R D X ( 0 .8 3 , 0 .9 9 , 1 .chocolate, explosives and drugs for both spectral resolution ∆ν = 0.01 THz and 0.04 THz.

Spectral properties of Si-based semiconductors
Below we analyze spectral properties of n-Si, p-Si semiconductors and silicon wafers with resistivity 35 and 40 Ω•cm and measured with 12 mm aperture placed in front of the sample.We will call these signals as n-Si, p-Si, Si-35-12 and Si-40-12 for brevity.Our purpose is to show that even under laboratory conditions (at low humidity and at short distance from the receiver) the standard THz TDS method detects in the semiconductors the absorption frequencies, which belong to hazardous substances as well to neutral ones: L-tartaric acid (LTA) and sucrose.This means that we can detect any substance, which is really absent in the sample.
The n-Si, p-Si THz signal measurements were made at Capital Normal University (Beijing, China) by using a Ti:sapphire regenerative amplifier (Spectra-Physics Mai Tai) delivering optical pulses with a duration of 100 fs and a central wavelength of 800 nm at a repetition rate of 1 kHz, with noise less than 0.15% [36,43].The transmitted THz signal was detected by free-space electro-optic sampling in a 1-mm-thick <110> ZnTe crystal with the sampling pulse [37].The path with THz radiation was purged by nitrogen to prevent absorption by atmospheric water vapor.The p-Si and n-Si samples were 0.5 mm thickness.The Si-35-12 and Si-40-12 THz signals were measured at the South China Normal University (Guangzhou, China) in transmission mode, at short distance about 30 cm from the receiver at room temperature in the open air with non-zero humidity (about 30%).Measurements were made by using a Ti:Sapphire femtosecond oscillator (Mira 900, Coherent) pumped with a solid-state laser (Verdi-5, Coherent).The width and repetition rate of the laser pulse are 130 fs and 76 MHz.The wavelength of the femtosecond laser pulses was tunable from 760 to 840 nm [35].All Verdi are specified with the lowest noise commercially available (<0.02% RMS) [44].
In Figure 3  Comparing the spectra calculated with various spectral resolution (Figure 3), we see that the influence of spectral resolution on them is much less for THz signals measured in laboratory conditions than for noisy THz signals, measured in real conditions (see Figure 2).With decreasing the spectral resolution from ∆ν = 0.01 THz in Figures 3(a These examples demonstrate very important feature of the standard THz-TDS method: the method is not able to detect the hazardous and neutral substance absence in the sample under investigation if they are really missing.

SDA-METHOD AND INTEGRAL CORRELATION CRITERIA
4.1 Main features of the spectral dynamics analysis method (the SDA-method) The medium response to the action of a few-cycle THz pulse is strongly non-stationary.Hence, the analysis of the spectral intensity time evolution (spectral dynamics) at the chosen frequencies allows us to get much more information about the substance under investigation.Obviously, the standard THz TDS method gives only information about the spectrum averaged over the signal registration time, because it does not take into account the time-dependent changes of spectral intensities.Nevertheless, as we mentioned above, the standard THz TDS method is quite effective if the measurement of THz signal is carried out in laboratory conditions without the water vapor influence.However, in real conditions, the measured Fourier spectra (and therefore the absorption or reflection coefficients) are often noisy and distorted due to the water vapor influence, the packaging material, the inhomogeneous sample surface, etc.To overcome this effect on the detection and identification of a substance, we propose to use the integral correlation criteria (ICC).
ICC allow us to provide an effective estimation of spectral features presence of substances from database in the analyzed signal.The correlation coefficients themselves cannot be used to assess the presence of the standard substance spectral features in the signal under investigation due to their strong oscillations at different time moments because of the medium response modulation.Summing the correlation coefficient values corresponding to different time moments, one can decrease the noise influence, because at summing, the random fluctuations of this coefficient compensate partially each other and the noise influence is also partially suppressed.On the other hand, we accumulate positive information.This procedure is similar to the commonly used algorithm for noise influence decreasing in the measured signal.Therefore, integral correlation criteria are the very important part of the SDAmethod for detecting and identifying substances, especially under adverse conditions.
To check the efficiency of the ICC for the frequency detection, a computer modeling of a THz pulse interaction with medium possessing the known absorption frequency was carried out in [41].We placed the medium inside the disordered layered structure.As a result, many false absorption frequencies appear in the spectrum of both transmitted and reflected signals.
We use ICC for the detection of the substance with known absorption frequency in such conditions and demonstrate a feasibility and effectiveness of the method using this example.
In order to get information about the characteristic absorption frequencies and relaxation times of excited energy levels of molecules, we calculate the spectral intensity dynamics for the measured signal by using the Fourier-Gabor method.Then, we move the spectral intensity (spectral line) dynamics of the standard THz signal at chosen absorption frequency along the spectral intensity dynamics of the analyzed signal during the chosen time interval.As a standard signal, we use the THz signal, transmitted through explosives, drugs and so on, and measured under laboratory conditions, or a signal measured in room conditions in view of water vapor absorption frequencies.Analyzing the integral correlation between these spectral dynamics, we can conclude about the presence or absence of the standard substance absorption frequencies in the sample.Moreover, it is possible to separate the frequencies corresponding to water vapor absorption frequencies despite their presence in the standard spectrum.

Integral correlation criteria
To calculate the integral correlation between the spectral line dynamics for the reflected or transmitted signal S(t) and the standard transmitted signal s(t) at chosen frequencies, we introduce the following notations.We denote the discrete set of spectral amplitude modulus for the standard transmitted signal at chosen frequency ν as Let us note, that the calculation of the spectral line (or spectral intensity) dynamics P ν (t) at chosen frequency ν is described in a number of previous papers, for example, in [34].The corresponding set of spectral amplitude modulus of the analyzed THz signal S(t) at the frequency ν is denoted as and its part with M 1 components, which begins at time moment t n , as Then, summing these correlation coefficients over time interval [t 0 , t n ] , we get the following integral characteristic for the detection and identification problem [28]: In the present paper, we use the modified criterion (Eq.( 2)) taking into account the spectral brightness of each of frequencies ν 1 and ν 2 during the interval of correlation computing: where  Along with the criterion (3) we consider another criterion, in which the sets p 2 will be used instead of the sets p ν 1 and P ν 2 : In certain cases, it is necessary to use one more criterion, which was introduced in [28] and allows us to assess the similarity (or likeness) of two spectral line dynamics where The subscript N indicates that the corresponding variable in Eq. ( 6) is normalized, for example, in L 2 norm.

The RDX absence detection in the chocolate sample
In order to show the explosive RDX absence in the Chocolate sample, we will use the THz signal transmitted through the tablet containing 10% RDX and 90% PE in the ambient air as a standard one (we call it as RDX Air signal).The measurement was performed during the short time interval 0 < t < 10 ps at the room temperature 22 • C and relative humidity of about 50%.Since the measured THz pulse shape is shown in [28], then its Fourier spectrum (5(a)) and absorbance (5(b)) only are depicted in Figure 5 in the frequency range ν = [0.6,3.2] THz.In [28] we showed that the minima at frequencies ν = 1.15, 1.4, 1.68 THz in (a) are caused by the strong water vapor absorption of the THz radiation.However, the minima at ν = 0.82, 1.95, 2.2, 2.42, 3.0 THz (a) coincide with the absorbance maxima (b), and they can be used for the RDX identification, because they are in a good agreement with the RDX absorption frequencies given in other papers [6,7,9].
As we mentioned above in Section 3.1, the part of the set of known absorption frequencies can be distorted while measuring under real conditions.That is, the absence of the minima at these frequencies in the spectrum of the signal under investigation does not mean the absence of the substance itself and it is necessary to analyze also such frequencies.The Chocolate   C h o c o l a t e ( 1 .9 6 ) + R D X ( 1 .9 ( 1 .9 2 , 1 .9 ( 2 .0 , 1 .9 ( 1 .9 6 , 1 .9 FIG. 6 Time-dependent integral criterion CW p,P (t n ) at the frequencies ν=0.82 (a), 2.2 (b), 1.96 (c) THz for the Chocolate signal and RDX_Air signal as a standard one.
signal spectrum (Figures 2(e) and 2(f)) does not contain minima at frequencies, which are equal to the RDX Air absorption frequencies ν = 0.82, 2.2 THz.We will use the spectral line dynamics at these frequencies (presented in Figures 5(c) and 5(d)) for RDX detection in the Chocolate signal.
It should be stressed that the frequency ν 1 , belonging to a standard substance, is detected in the signal under investigation at the frequency ν if the integral criterion, calculated for the frequency pair (ν, ν 1 ), lies above all other characteristics in the frequency detection range (FDR).As a rule, the boundaries of the FDR are the spectrum extremes closest to the analyzed frequency.And vice versa, the frequency ν 1 is not detected if, at least, one of other lines lies above the integral criterion, calculated for the pair (ν, ν 1 ), in this frequency range.
In Figure 6 the integral criterion CW p,P (t n ) evolution is shown at the frequencies ν = 0.82 and 2.2 THz (Figures 6(a) and 6(b)), during the main pulse.In both cases, these RDX absorption frequencies are not detected in the Chocolate signal and, therefore, spectral features of RDX are absent in the signal under investigations.
It is very important for practice that the integral criteria in Eqs. ( 2) and ( 5) allow to show the explosive absence even if the spectrum of the THz signal under investigation contains the minimum, which is close or equal to the absorption frequency of the standard substance.To illustrate this, we consider the absortpion frequency ν = 1.96THz of the Chocolate signal (Figure 2(f)), which is close to the RDX absorption frequency ν = 1.95 THz. Figure 6(c) shows the integral criterion CW p,P (t n ) evolution, calculated for the frequency pair ν = (1.96,1.95) THz.We see that the criterion evolution line calculated for a pair ν = (2.0,1.95) THz lies above the line, corresponding to the pair ν = (1.96,1.95) THz.So, the frequency ν = 1.96THz is also not detected as the RDX absorption frequency in the Chocolate signal.Thus, using these three frequencuies, we show the RDX absence in the sample with chocolate.In the same way, it is possible to show the absence of illicit drugs MA, MDMA in this sample.
We stress that the integral criterion CW SQ p,P (t n ) gives the same result as CW p,P (t n ), but it increases the detection contrast.This criterion is reasonable for using if the criterion CW p,P (t n ) gives close or coinciding lines for different frequency pairs [29].

Sugar and chocolate detection in the sample
Below we detect absorption frequencies of sugar and chocolate in the Chocolate signal.For this purpose, we use the standard transmitted THz signals Sucr10 and Choc10.The Choc10 signal was measured in the Institute for Spectroscopy RAS (Troitsk, Russia) at short distance of about 15 cm from THz receiver, at room temperature and with humidity of about 50%.Measurements of transmitted Sucr10 THz signal was made in Semiconductor Physics Institute, Vilnius, Lithuania.The THz pulse shape and the corresponding Fourier spectra of the signals were depicted in [29,31].
The Chocolate main pulse spectrum (Figures 2(e) and 2(f)) contains minima at the frequencies ν = 1.7, 1.8 THz, which are close to the absorption frequencies ν = 1.75, 1.85 THz of the standard signals Choc10 and Sucr10, correspondingly.As we have seen above, the presence of a minimum at the standard substance absorption frequency in the spectrum of the signal under investigation does not mean the presence of this substance in the sample in reality.So, to find spectral properties of sugar and chocolate, we use the standard spectral line dynamics at frequencies ν = 1.75, 1.85 THz.
In Figure 7 the integral criterion CW p,P (t n ) evolution is depicted at frequencies ν = 1.7 THz (Figure 7(a)) and ν = 1.8 THz (Figure 7(b)) for the FDR ν = [1.6,1.72] THz and [1.72, 1.88] THz, correspondingly.In both cases, these frequencies are detected as the absorption frequencies of Chocolate signal.We see that sugar and chocolate are found in the chocolate bar.

Explosive and neutral substances absence in semiconductors
In [33] we showed the RDX, HMX and PETN absence in the n-Si and p-Si semiconductors with the help of integral correlation criteria in Eqs.(3)-( 5).In the same manner, it is possible to show the absence of LTA and Sucrose in these samples (in Figure 3 we see the minima at frequencies, which are close to absorption frequencies of LTA and Sucrose).For this purpose, along with the standard Sucr10 THz signal, we will use the transmitted LTA10 THz signal.It was also measured in Semiconductor Physics Institute, Vilnius, Lithuania.The THz pulse shape and the corresponding Fourier spectrum of the signal can be found in [29,31].

Aperture influence on the semiconductors spectral properties
Obviously, the detection and identification efficiency depends on a quality of the standard signal from the database.Among many factors influencing on the signal quality, the THz beam diameter can change the response of the medium under investigation.Consequently, a standard signal spectrum and its spectral line dynamics may also change, and the detection result can change as well.Therefore, understanding how the THz beam diameter influences on a measured signal, is a key question.To answer this question, below we compare the spectra of the THz signals passed through two types of semiconductors, with and without presence of aperture, placed in front of the sample.Our aim is to pay attention to this problem and to demonstrate its importance.We will call the THz signals measured without aperture as Si-35 and Si-40 signals, correspondingly.
In Figure 10

CONCLUSIONS
We have shown that the standard THz TDS method detects the spectral features of explosives RDX, HMX, PETN and illicit drugs MA, MDMA in the chocolate bar as well as explosives RDX, HMX, PETN and neutral substances L-tartaric acid and sucrose in silicon-based semiconductors despite their actual absence in the samples.This facts demonstrate the standard THz-TDS method non-efficiency not only under real conditions (at long distance, high relative humidity, influence of noise), but also under laboratory conditions (at short distance and low humidity).Therefore, this feature leads to a large number of false detections at security screening.
At the same time, the SDA-method together with the integral correlation criteria allow us to detect the dangerous and neutral substance absence in the samples.We demonstrate that these criteria allow to show the absence of RDX even if the spectrum of the analyzed THz signal contains the minimum that is close or equal to the absorption frequency of the standard signal.In order to enhance the detection reliability it is necessary to use the different types of integral criteria simultaneously.
We showed that the Chocolate signal demonstrates spectral features similar to those of sugar and chocolate, and the silicon-based semiconductor samples demonstrate similar spectral features of pure silicon.The influence of aperture on spectral properties of silicon wafers with different resistivity is also investigated.Thus, the aperture using leads to small decreasing of minimum at frequency ν = 1.1 THz and a slight shifting of other minima in the frequency range ν < 1.65 THz.At the same time, the spectra of the signals measured with and without aperture, essentially differ in the frequency range ν > 1.65 THz.
It is also shown that the increase in spectral resolution for very noisy THz signal leads to manifestating the small-scale perturbations caused by the influence of the external factors or the sample structure.At the same time, spectral resolution decreasing allows to exclude from consideration the false absorption frequencies caused by small-scale modulation.For THz signals measured in the laboratory conditions, the spectral resolution decreasing affects the spectrum much smaller.
Thus, the discussed method is promising and competitive tool for the effective detection and identification of various substances both in real and laboratory conditions in comparison with the THz TDS method, based on comparison of the substance spectra.The method can be used with success for security screening, non-destructive testing, as well as for quality control in the pharmaceutical industry.
Figure1(b) shows the measured Chocolate THz signal on the time interval t = [0, 110] ps.The strong noise, which is observed in the signal, can be a result of the ambient medium action.Nevertheless, maximal amplitude of the THz signal is 4 times more than noise amplitude.Note that the frequency resolution depends obviously on the time interval, during which the measurements are performed.As a rule, its duration in the experiment with chocolate was approximately 100 ps.Consequently, the minimum frequency difference ∆ν, which can be resolved by computer processing, is 10 GHz.Let us remind, that the standard THz-TDS method deals with the spectrum of a THz signal main pulse.In our case, its duration is about 25 ps.With this aim, the Fourier spectrum (Figures 2(a) and 2(b)) and absorbance (Figures 2(c) and 2(d)) of the Chocolate main pulse are depicted in Figure 2 in the frequency ranges ν = [0, 1.5] THz (Figure 2(a)), [1.5, 3.2] THz (Figure 2(b)), where A = − log 10 (|P(ν)|/|P REF (ν)|). )

Figures 2 (
Figures 2(e) and 2(f) shows the main pulse Fourier spectrum calculated with spectral resolution ∆ν = 0.04 THz.We see decreasing the number of minima in comparison with the spectrum, calculated with spectral resolution ∆ν = 0.01 THz (Figures 2(a) and 2(b)).In particular, we do not observe minima at frequencies close to RDX and MA absorption frequencies ν = 0.82 THz and ν = 1.25 THz, correspondingly.In our opinion, the appearance of these minima in the spectrum (Figures 2(a) and 2(b) was caused by small-scale signal modulation due to external factors, or the sample structure, or the noise.It should be noted that other minima, which are close to absorbance frequencies of RDX, MA, MDMA as well as Sucrose and Chocolate, retain in the spectrum.The same situation takes place in the absorbance, obtained with spectral resolution ∆ν = 0.04 THz (not shown in Figure2).Taking into account this fact, in Section 5, we will deal with spectrum obtained with resolution ∆ν = 0.04 THz.As we see, the sample with chocolate demonstrates the spectral features of sugar,

1 p 1 p
i a n d n -S i , ∆ν= 0 .0 i a n d n -S i , ∆ν= 0 .0
the main pulse spectra for the n-Si and p-Si signals in the frequency ranges ν = [0.0,3.0] THz (Figures3(a) and 3(c)) and [3.0, 4.0] THz (Figures 3(b) and 3(d)) are shown for two time intervals T = 100 ps (Figures 3(a) and 3(b)) and 20 ps (Figures 3(c) and 3(d)).So, the frequency resolution is equal to ∆ν = 0.01 THz in Figures 3(a) and 3(b) and 0.05 THz in Figures3(c) and 3(d), correspondingly.In accordance with our purpose, first we compare spectral features of n-Si and p-Si semiconductors and explosives.One can see clearly the spectrum minima in Figures3(a) and 3(c) corresponding to the explosive RDX, HMX, PETN absorption frequencies[6,7,9].The absorbance (Figure3(e)) also contains maxima at these frequencies (here spectral resolution is ∆ν = 0.01 THz).Moreover, the n-Si and p-Si signal spectra Figures3(a) and 3(c) and absorbance Figure 3(e) also contain extremes close to the absorption frequencies of LTA ν = 1.1 THz and pure Sucrose ν = 1.83 THz [12, 29].Therefore, one can do false detection of explosives or neutral substances in the semiconductors.Obviously, the semiconductor samples n-Si and p-Si demonstrate the spectral features of pure silicon.Let us note that a pure monocrystalline silicon possesses absorption frequencies ν = 2.24, 2.65 THz (Figure3(f)), which coincide with the corresponding minima in Figures3(a) and 3(c).Data in Figure 3(f) are taken from the THz database [42] (RIKEN, Sendai).The paper [39] reported about the frequency ν = 3.6 THz as the well-resolved absorption frequency of high-resistivity, floatzone silicon.The minima of n-Si signal at ν = 3.63 THz in Figure 3(b) and ν = 3.65 THz in Figure 3(d) are close to this frequency, the corresponding minimum of p-Si signal is shifted to ν = 3.73 THz (Figure 3(b)), ν = 3.7 THz (Figure 3(d)).
) and 3(b) to ∆ν = 0.05 THz in Figures3(c) and 3(d), the number of minima do not change and we can see the same minima.This fact confirms the conclusion made in Subsection 3.1.That is, for very noisy THz signal the spectral resolution increasing leads to manifestation of the small-scale perturbations caused by the influence of the external factors, or the sample structure, or the noise.At the same time, the spectral resolution decreasing allows to exclude from consideration the false absorption frequencies caused by small-scale modulation of the signal.For the THz signals measured in the laboratory conditions, the spectral resolution decreasing affects the spectrum much smaller because the influence of the environment medium is practically absent.In Section 5, we will use the spectra obtained with resolution ∆ν = 0.05 THz (Figure3(c)).Let us analyze another semiconductor samples.In Figure4the main pulse Fourier spectra of the Si-35-12 (Figures4(a) and 4(b)) and Si-40-12 (Figures 4(c) and 4(d)) signals are depicted in the frequency ranges ν = [0, 1.5] THz (Figures 4(a) and 4(c)); [1.5, 3.7] THz (Figures 4(b) and 4(d)).Fourier spectra were calculated on the time interval t =[4,24] ps (duration T = 20 ps) with spectral resolution ∆ν = 0.05 THz.The measurement of these signals was carried out with a non-zero humidity and we showed above that in this case, the spectral resolution increasing may lead to manifestation of the signal small-scale modulations.Then, below we do not present and do not use spectra obtained with the spectral resolution ∆ν = 0.01 THz.Note that in (Figures4(b) and 4(d)) one can see minima at frequencies, which are close to the absorption frequencies of pure Silicon ν = 2.24, 2.65, 3.61(3.6)THz[39, 42].As the maxima of Si-35-12 and Si-40-12 signal absorbance coincide with minima of the corresponding Fourier spectra, so we do not reproduce these figures in the paper.Absorbance for Si-35-12 and Si-40-12 signals can be found in[40].As above, the Si-35-12 and Si-40-12 samples also demonstrate spectral features of the explosives as well as neutral substances.

ν
(t n+m )|}.Here M 1 and M 2 are the numbers of time moments, in which the spectral amplitudes are calculated.Both sets p ν = {|p ν (t m )|} and P (n) ν = {|P(n) ν (t n+m )|} must be averaged at each step t n to avoid the influence of their constant component on correlation value.Moving the set p ν 1 along the set P ν 2 , we calculate in each time moment t n the correlation coefficient for two spectral dynamics c