Patent Publication Number: US-2010108888-A1

Title: Reducing scattering related features in terhertz time domain spectroscopy bz averaging the impulse waveform over a plurality of sample points

Description:
The present invention relates generally to the field of apparatus and methods for imaging and/or investigating samples in the far-infrared (far-IR)/Terahertz (THz) frequency range from 100 GHz to 100 THz. Preferably the radiation utilised is in the frequency range of 500 GHz to 100 THz and more preferably from 1 THz to 100 THz and most preferably from 700 GHz to 10 THz. 
     It is well established that many chemicals and pharmaceutical agents have spectral signatures in the THz region. The reason for the spectral signals in this frequency range is considered to be associated with inter-molecular or intra-molecular crystalline vibrations or collective phonon oscillations. It is known that in THz spectroscopy the spectral information of transmitted and/or scattered radiation can be used to identify materials. Most materials interact with terahertz waves to some degree, and each material has its own frequency pattern, which can be considered as a kind of ‘fingerprint’. 
     Of late security concerns have increased the need for a system that is able to identify hidden explosives, such as under a person&#39;s clothing, in a person&#39;s suitcase or in a postal package. 
     US Patent Application Number 2001/0033636 discloses a method of detecting explosives in luggage which uses X-rays to determine an average atomic number of a material. The average atomic number is then compared with known average atomic numbers of explosive materials to determine if the material being examined is an explosive. This technique, however is unsuitable for routine-security screening of people as its radiation is ionising. 
     In a paper entitled “Spectroscopy with electronic terahertz techniques” by D. W. van der Weide et al published in Proc Spie 3828 (99), electronic pulses in the microwave range, up to 450 GHz, are used to investigate explosives. These pulses are generated electronically using non-linear transmission lines, coupled with varactor diodes that are patterned on a semiconductor. A sine wave is applied to the transmission line and the result at the other end is a rapid (1-2 ps) voltage step, which is used to produce the microwave pulse from the semiconductor device. This paper demonstrates spectral features of explosives, but only in the sub-terahertz or microwave frequency range. 
     THz radiation is suitable for screening people and their possessions as it is non-ionising and can pass through clothing, paper, cardboard, wood, masonry, plastic and ceramics. Therefore, it is safer than x-ray techniques. 
     It has been speculated that THz radiation could be used to obtain spectral information of explosive materials, as the organic molecular nature of explosives, and their crystalline structure are of the appropriate form. To date, however, this has not been effectively achieved. 
     Many practical embodiments of THz systems utilise the transmission of THz radiation through the sample under investigation to a detector. In laboratory conditions samples can be prepared to avoid attenuation effects. However, in practice, samples are often granulated which leads to scattering of the irradiating radiation. Terahertz pulse spectroscopy is a coherent detection system which means that it has a large dynamic range. However, the effects of scattering or attenuation means that a THz signal may be too weak to detect in certain samples. 
     THz systems which utilise the reflection of THz radiation from a sample will not be limited by attenuation effects in the same way that transmission-based systems are. However, reflection-based systems experience different problems which in practice has meant that effective THz reflection spectroscopy is not possible. 
     In any THz system emitted Thz radiation will impinge upon the surface of the object under investigation. The surface of the object represents an interface between a medium with a first refractive index (usually air) and the object itself (which has a second refractive index which is different to the first refractive index). 
     The difference in the refractive indices means that a proportion of the radiation will be transmitted into the object (for an air/polythene interface this amounts to around 96% of the incident radiation) and a proportion will be reflected (for the air/PE example this therefore equates to around 4% of the incident radiation). 
     It can therefore be seen that the reflected beam will always have a weaker intensity than the transmitted beam. This means that the reflected beam is more susceptible to noise such as scattered radiation. 
     A further problem arises when the sample under investigation comprises scattering centres capable of scattering any radiation that penetrates the object. For both transmission based and reflection based systems the arrival times of radiation arriving at the detector from the surface of the object and scattering centres will be different. For reflection the time of arrival will depend on the depth of the scattering centre from the surface of the object. For transmission based systems the time of arrival depends on the extra path length the scattered radiation has traveled relative to radiation that has directly passed through the object. This spread of arrival times causes artificial spectral features which can either mask actual features or create false features. 
     One technique for mitigating the effects of scattering is to window the radiation detected at the detecting means. By gating the arrival time within which the system will detect photons any late arriving photons (from scattering events) will not be detected. Such a technique however reduces the efficiency of any spectroscopic analysis of the sample in question as it inevitably loses spectral information. 
     It is therefore an aim of the present invention to overcome or alleviate at least some of the problems associated with both transmission based and reflection based the prior art systems. 
     According to first aspect the present invention provides a method of investigating an object, comprising the steps of
         (a) irradiating the object with an optically-generated pulse of electromagnetic radiation, said pulse having a plurality of frequencies in the range from 100 GHz to 100 THz;   (b) detecting radiation transmitted and/or reflected from the object to obtain a time domain waveform;   (c) repeating steps (a) and (b) for a plurality of points on the object and   (d) combining data from step (c) to produce a time domain waveform for the object which has been averaged over the plurality of points.       

     The invention which is the subject of the present invention is suitable for use in both transmission based systems and also reflection based systems. The method comprises irradiating the object under investigation and detecting the radiation reflected/transmitted from a point on the object. The irradiation/detection steps are then repeated for a plurality of points such that an averaged time domain waveform can be calculated for the object. 
     The method of the present invention acknowledges that signals due to scattering depend strongly on the geometry of the scattering centres within the object whereas directly reflected or transmitted signals do not. By taking repeated measurements the random signal elements introduced by scattering effects are removed and the true reflection/transmission signals, which have no phase dependence on the geometry of the object, remain. 
     In conventional optical spectroscopy methods, the intensity of the incident (I o (ν) and the transmitted (I t (ν)) radiation is measured. The optical absorption coefficient, α(ν), can then be calculated from the following equation: 
         T   int (ν)≡ I   t (ν)/ I   o (ν)= e   −2α(ν)d    
     where ν is the frequency. 
     In terahertz pulsed spectroscopy (TPS) measurement however, the electric field, instead of the intensity, of the (THz) radiation is measured. The electric field of the transmitted THz radiation can be described as: 
         T (ν)≡ E   t (ν)/ E   o (ν)= e   −α(ν)d   e   jk(ν)d    
         k (ν)= n (ν)2πν/ c    
     The fact that the electric field is measured as opposed to the intensity of the radiation, as in other spectroscopic systems, allows the detected radiation to be “averaged” as claimed in this aspect of the invention. This is because the electric field, E, can be both positive and negative and so the scattering events will tend to cancel each other out over a large enough sampling of points whereas intensities will always add. 
     It is clear that both absorption coefficient (α(ν)) and refractive index (n(ν)) can be calculated from a single measurement because the electric field measurements provide both amplitude and phase information. 
     At absorption peaks, the transmittance drops significantly from 100% to a few percent. Therefore the transmission measurement is very sensitive to absorption. The reflection loss at the air/sample interfaces, which is mainly determined by the refractive index difference, only causes a baseline shift in the transmission spectrum. 
     In reflection measurement, things are different. The reflectance can be calculated from the measured electric field of THz radiation as: 
         R (ν)≡ E   r (ν)/ E   o (ν)=(√{square root over (ε(ν))}−1)/(√{square root over (ε(ν))}+1) 
       √{square root over (ε(ν))}= n (ν)+ jα (ν) c/ 2πν≈ n (ν) 
     Preferably steps are taken to remove features in the detected radiation that relate to the system components. Therefore, preferably a reference measurement is taken in the absence of a sample. The signal detected in the absence of a sample can then be subtracted from the signal detected in the presence of a sample. 
     Alternatively the reference measurement can be taken in the presence of a reference sample with well known THz properties. Such a reference sample could be air, water or polyethylene. 
     Preferably, an absorption profile of the object can be determined by transforming the averaged time domain waveform into the frequency domain by means of a Fourier transform. The composition of the sample can be derived from this absorption profile. 
     Any absorption features will produce maxima and minima in the absorption profile. Conveniently, the derivative of the absorption profile with respect to frequency can be determined. 
     It is clear that the greater the area over which the sample is averaged the better the removal of the scattering features will be. However, averaging over the maximum area possible may not be necessary in order to resolve the true absorption features of a sample. Therefore, preferably, the method according to the first aspect of the present invention further comprises the step of progressively increasing the number of points that are irradiated until the scattering related effects are sufficiently reduced in order to determine the features of the object under investigation. 
     When an object is irradiated with an impulse of radiation then detected radiation will comprise an initial impulse feature and subsequently received signal. The signal that follows the initial impulse function is known as the “late time response”. It has been suggested that this “late time response” provides useful information about the sample and therefore preferably the method according to the first aspect of the invention comprises the step of removing that portion of the averaged time domain waveform that corresponds to directly reflected/transmitted radiation and performing a Fourier transform on the remainder of the detected radiation in order to derive compositional information relating to the object. 
     In a second aspect of the present invention the “late time response” is analysed and there is therefore provided a method of investigating an object, comprising the steps of
         (a) irradiating the object with an optically-generated pulse of electromagnetic radiation, said pulse having a plurality of frequencies in the range from 100 GHz to 100 THz;   (b) detecting radiation transmitted and/or reflected from the object to obtain a time domain waveform;   (c) separating that portion of the detected radiation that corresponds to directly reflected or transmitted radiation and applying a Fourier transform to the remaining portion of the detected radiation.       

     In a third aspect of the present invention there is provided an apparatus for investigating an object comprising
         (a) a source of electromagnetic radiation for irradiating a point on the object with an optically-generated pulse of electromagnetic radiation, said pulse having a plurality of frequencies in the range from 100 GHz to 100 THz;   (b) a detector for detecting radiation transmitted and/or reflected from the object to obtain a time domain waveform;   (c) scanning means for sequentially irradiating a plurality of points on the object and   (d) means for combining time domain waveforms from each of the plurality of points to produce a time domain waveform for the object which has been averaged over the plurality of points.       

     Compositional information relating to a sample can be determined by investigating the sample according to the method of the first aspect of the present invention. A compositional image of the sample can then be derived by imaging the sample through a spectral filter that is arranged only to let radiation relating to one (or more) of the components of the sample through to the detector. Therefore, in a fourth aspect of the present invention there is provided of imaging a sample comprising the steps of
         a) investigating the sample according to a method according to the first aspect of the invention;   b) deriving a spectral waveform from the time domain waveform obtained in step (a)   c) identifying the components of the sample from the spectral waveform in step (b)   d) re-irradiating the sample with an optically-generated pulse of electromagnetic radiation, said pulse having a plurality of frequencies in the range from 100 GHz to 100 THz   e) detecting radiation transmitted and/or reflected from the object to obtain a time domain waveform, the detected radiation having first passed through at least one bandpass filter corresponding to at least one component of the sample   f) generating an image from the radiation detected in step (e)       

     An alternative method of reducing the effects of scatter is to use a diffuse irradiating beam of radiation. Accordingly, in a fifth aspect of the present invention there is provided a method of investigating an object, comprising the steps of:
         (a) irradiating the object with an optically-generated pulse of electromagnetic radiation, said pulse having a plurality of frequencies in the range from 100 GHz to 100 THz;   (b) detecting radiation transmitted and/or reflected from a first point on or within the object to obtain a time domain waveform;   wherein the irradiating pulse of radiation is focussed at a second point on or within the object.       

    
    
     
       The present invention will now be described with reference to the accompanying drawings in which: 
         FIG. 1  illustrates a schematic of a pulsed terahertz reflection investigative technique utilised in a first embodiment of the present invention; 
         FIG. 2  illustrates a schematic of a pulsed terahertz transmission investigative technique utilised in a second embodiment of the present invention; 
         FIG. 3  shows a schematic representation of an air/polythene interface showing the various reflection, transmission and scattering components 
         FIGS. 4   a  and  4   b  show time domain waveforms for samples composed of sucrose and PE powder. 
         FIG. 5  shows a series of waveform traces measured from a mixture of fine lactose particles and large sucrose particles (500-800 μm size/diameter). 
         FIGS. 6   a  and  6   b  show absorption plots at a single point ( FIG. 6   a ) and an averaged dataset ( FIG. 6   b ). 
         FIGS. 7   a  and  7   b  show the first derivative of the absorption plots of  FIGS. 6   a  and  6   b.    
         FIGS. 8   a  and  8   b  show refractive index plots of the sample imaged in  FIGS. 6   a  and  6   b.    
         FIG. 9  shows various THz reflection spectra of the same sample for various sample areas. 
         FIG. 10  shows a schematic of a layered PE/lactose/PE sample. 
         FIG. 11  shows various temporal waveform traces obtained from the sample shown in  FIG. 10   
         FIG. 12  shows various spectral plots obtained from the sample shown in  FIG. 10 . 
         FIG. 13  shows a chemical mapping image of a sucrose/lactose/polyethylene sample  FIG. 14   a  shows a further chemical distribution image of the surface of a sample. 
         FIG. 14   b  shows temporal waveforms associated with the image shown in  FIG. 14   a.    
         FIG. 15  shows an imaging configuration for a THz system 
     
    
    
     Referring to  FIG. 1 , a terahertz pulsed investigating arrangement is illustrated, which comprises an ultra-short pulse laser  10  which may be, for example, Ti:sapphire, Yb:Er doped fibre, Cr:LiSAF, Yb:silica, Nd:YLF, Nd:Glass, Nd:YAG, Alexandrite Yb:Phosphate Glass QX, Yb:GdCOB, Yb:YAG, Yb:KG d(WO 4 ) or Yb:BOYS laser. This laser  10  emits pulses of radiation  11 , such as a collimated beam of pulses, each of which comprise a plurality of frequencies. The pulses generated by the laser preferably having a pulse duration of less than 200 fs. 
     The beam of generated pulses is directed into beam splitter  12 . The beam splitter splits the beam into a pump beam  13 , which is used to irradiate the sample, and a probe beam  14 , which is used during detection. 
     The probe beam  14  is directed, via plain mirror  15 , into scanning delay line  16 . Scanning delay line  16  is a variable optical delay, which in its simplest form comprises two mirrors that serve to reflect the beam through a 180° angle. Using a computer as a controller, these mirrors can be quickly swept backwards and forwards in order to vary the path length of the probe beam  14 . In this way the scanning delay line  16  assists in matching the relative path lengths of the pump and probe beams. The probe beam is then focussed onto receiver  26  for combining with the Terahertz beam. 
     The pump beam  13  is directed onto a source  17 . For pulsed approaches this source  17  preferably comprises a GaAs based photoconductive switch. GasAs based devices use the principle of photoconductive mixing to generate their THz output. 
     The THz radiation  18  emitted by the emitter  17  is directed via a hyper-hemispherical lens (not shown) towards a first parabolic mirror  19 , which is preferably an off axis parabolic (OAP) mirror, as are all the parabolic mirrors referred to herein. The beam is then reflected off the first parabolic mirror  19  and onto second parabolic mirror  20 , which directs the radiation onto sample  21 . 
     To analyse a particular sample in situ, the sample  21  may be moved relative to the beam of radiation through the focal plane of the THz beam or the beam may be moved relative to the sample or both. As shown in  FIG. 1 , the sample may be placed on a translation stage to appropriately move the sample. This translation stage could move the sample one dimensionally along one axis of movement or through two or three axes of movement. 
     The THz radiation that is reflected from sample  21  is collected by third parabolic mirror  22  and onto a fourth parabolic mirror  24  via plain mirror  23 . The fourth parabolic mirror  24  directs the reflected radiation  25  onto a second hyper-hemispherical lens (not shown) and onto a detector  26 , such as an electro-optic detector or a photoconductive detector. 
     Photoconductive detectors comprise a detection member which may be, for example, GaAs, InGaAs, Si on Sapphire etc. The detection member  26  is used to detect both the amplitude and phase of the radiation emitted from the sample  20 . In these detectors, the THz radiation  25  from the sample is incident on the back surface of the detection member  26 . The radiation is collected by a lens (not shown), which may be hemispherical or have another shape. The Terahertz radiation  25  incident on the detection member  26  induces a photocurrent through the region between electrodes  26   a  and  26   b , located on the opposing side of the detection member  26 , which is being illuminated by the laser radiation. As the detector needs to know information about the phase of the radiation emitted from the generator  17 , the radiation illuminating the region between electrodes  26   a  and  26   b  is preferably the probe beam  14 , which carries this information. The current that can then be detected by the electrodes is proportional to the strength of the THz field  25 . 
     The electrodes  26   a ,  26   b  may be of a simple diode formation embedded in a transmission line. Alternatively, they may be triangular and arranged in the shape of a bow-tie to form a so-called bow-tie antenna. They may also be interdigitated electrodes at the centre of a bow-tie or spiral antenna. 
       FIG. 2  illustrates an alternative pulsed arrangement, whereby the sample is investigated using transmitted radiation rather than reflected radiation and the detector is an EOS detector rather than a photoconductive detector. To avoid unnecessary repetition with respect to  FIG. 1 , like reference numerals will be used to denote like features. 
     In  FIG. 2 , it is apparent that a variable delay is introduced to the probe beam  14  and that the pump beam  13  is projected onto the sample in the same manner as was illustrated in  FIG. 1 . The sample in  FIG. 2 , however is now generally perpendicular to the incident pump beam, in order to maximise radiation transmission. 
     Transmitted radiation  25  is combined with the probe beam  14 . One particularly popular way to do this is to use electro-optic sampling (EOS). In this technique, the transmitted THz beam  25  and the probe beam  14  co-linearly propagate through an EOS detector  28 . The transmitted radiation  25  passes through the detector  28 , which modulates the probe beam  14 . 
     The EOS detector  28  may be comprised of any material which possesses good non-linear characteristics, such as GaAs or Si based semiconductors and NH 4 H 2 PO 4 , ADP, KH 2 PO 4 , KH 2 ASO 4 , Quartz, AlPO 4 , ZnO, CdS, GaP, BaTiO 3 , LiTaO 3 , LiNbO 3 , Te, Se, ZnTe, ZnSe, Ba 2 NaNb 5 O 15 , AgAsS 3 , proustite, CdSe, CdGeAs 2 , AgGaSe 2 , AgSbS 3 , ZnS, organic crystals such as DAST (4-N-methylstilbazolium). 
     The modulated beam is then passed into quarter wave plate  30 . This serves to circularly polarise the emitted radiation. The circularly polarised light is then fed through a Wollaston prism  32 , which divides the polarization of the light onto two orthogonal components. These two orthogonal components are then directed onto balanced photodiode assembly  34 . The balanced photodiode assembly comprises two photo diodes to respectively detect each of the orthogonal components from the Wollaston prism  32 . The output of the photodiodes are then linked together such that the balanced photodiode assembly  34  only outputs an electrical signal if there is a difference between the readings of the two photodiodes. This output signal corresponds to the strength of the transmitted THz beam  25 . 
     This is because, where there is no THz beam present, there is no difference between the two photodiode signals. However, where there is a THz beam  25 , the THz beam  25  serves to make the radiation exiting the detector  28  slightly elliptically polarised. This change in the polarization still remains after the radiation is passed through quarter waveplate  30 . Extracting the orthogonal components of this radiation using prism  32  causes a different signal to be measured at the two photodiodes, and hence balanced photodiode assembly  34  outputs a signal corresponding to the strength of the THz field. 
     Therefore EOS detection enables the phase and amplitude of the transmitted radiation to be detected. It is to be appreciated that it will be apparent to those skilled in the art that this type of analysis could be performed for any type of detector. 
     It is also to be appreciated that it is also possible to combine the arrangements of  FIGS. 1 and 2 , whereby both reflected and transmitted radiation from the sample is measured. 
     Further, rather than combining the beam which has been reflected from or transmitted by the sample with the probe beam  14 , it is also possible to combine the THz beam with another beam of radiation which has substantially the same wavelength or which differs in frequency by at most 10 GHz. Such combined radiation can be detected using a bolometer, Schottky diode etc. 
       FIG. 3  shows a schematic representation of an air/polythene interface  40  showing the various reflection, transmission and scattering components. It can be seen that the transmitted signal  42  is much stronger than the reflected signal  44 —96% to 4%. 
     Scattering centres  46  introduce additional scattered signals  48 . The reflected beam is much more susceptible to these scattered pulses as it has a weaker intensity. In both transmission and reflection however scattering events can give rise to false spectral features. 
       FIG. 4   a  shows four time domain waveforms for samples composed of 60 mg of sucrose and 260 mg of PE powder. Each sample was measured within a powder cell. Curve  1  shows the recorded waveform when shows a reference trace of an empty powder cell. Curve  2  shows a sucrose sample with particle sizes of 53-75 μm. Curve  3  shows a sucrose sample with particle sizes greater than 250 μm. Curve  4  is also for particles greater than 250 μm but at a different location in the powder cell. 
     In order to show the waveforms due to the sample only, the recorded waveforms from  FIG. 4   a  were then de-convolved with the reference trace (curve  1 ). The de-convolved THz waveforms are shown in  FIG. 4   b . It should be noted that in both  FIGS. 4   a  and  4   b  the curves have been offset for clarity. Also, the signal intensity of curve  1  has been reduced by a factor of 4. 
     The presence of features due to scattering can clearly be seen in  FIG. 4   b  (arrows  50 ,  52  and  54 ) and are more common with increasing size of the sucrose particles. These scattering features would give rise to false spectral features if the data of  FIG. 4   b  were analysed in the frequency domain (by Fourier transforming the data). 
       FIG. 5  shows a series of waveform traces measured from a mixture of fine lactose particles and large sucrose particles (800 μm size/diameter). Curves  2 ,  3  and  4  show readings taken from three different points on the sample. It can be seen that after the main initial pulse there is a series of ripples caused by the absorption/reflection characteristics of the sample. Three additional features (highlighted by arrow  56  in curve  2 , arrow  58  in curve  3  and arrow  60  in curve  4 ) are however visible in these curves. These additional features come from scattering events and will result in false spectral features following a Fourier transform of the data. 
     Curve  1  shows an averaged waveform (including the three curves  2 ,  3  and  4 ) taken over an area of 5 mm 2 . It can be seen that the scattering related features are now absent from the waveform. 
       FIGS. 6   a  and  6   b  show a comparison in the frequency domain between a spectroscopic measurement at a single point ( FIG. 6   a ) and an averaged dataset ( FIG. 6   b ). In  FIG. 6   a  a Fourier transform of a waveform trace (similar to those in Curves  2 - 4  of  FIG. 5 ) has been plotted. This therefore corresponds to an absorption profile. 
     In  FIG. 6   b  the waveform data has been averaged first and the Fourier transform of the averaged data has been plotted. It can been seen that, in comparison to  FIG. 6   b , the trace in  FIG. 6   a  comprises a number of false spectral features. 
     The trace in  FIG. 6   b  shows a rising level of absorption with increasing wavenumber. This is due to absorption by the sample and/or the scattering of polyethylene (PE). The phase difference between reference and sample measurement will also cause a similar shift of the absorption spectrum. In order to remove this aspect and aid interpretation of the spectral features the so-called “First derivative” (d(absorption)/a(Frequency) has been plotted in  FIGS. 7   a  and  7   b . It should be noted that  FIG. 7   a  corresponds to  FIG. 6   a  and  FIGS. 7   b  to  6   b.    
     It is clear from  FIGS. 7   a  and  7   b  that the presence of spectral features in  FIG. 7   a  makes spectral analysis virtually impossible. 
       FIGS. 8   a  and  8   b  show plots of refractive index versus wavenumber. The refractive index is calculated from time domain and phase information. Again,  FIG. 8   a  corresponds to  FIGS. 6   a  and  7   a .  FIG. 8   b  corresponds to  FIGS. 6   b  and  7   b . It can be seen that compared to  FIG. 8   b  the presence of scattering events in  FIG. 8   a  introduces many errors into the derivation of the refractive index. 
       FIG. 9  shows various THz reflection spectra of the same sample obtained by averaging over a sample area of different size. The sample comprised a mixture of sucrose and lactose particles. 
     The number of points (pixels) used in averaging is shown next to each spectrum and the images have been off-set for clarity. It is clear that averaging over a larger sample area improves the results. However, in this example it can be seen that a sample area of 13×13 pixels is sufficient to resolve the absorption features of lactose and sucrose. 
     A sample that is investigated using reflection spectroscopy will return a temporal waveform that comprises an initial impulse feature corresponding to the reflection from the surface of the sample and subsequent waveform data. By analysing the waveform trace following the initial impulse feature further information can be derived about a sample. This type of analysis is often referred to as the “late time response” of a sample. 
       FIG. 10  shows a layered sample  62 . A central layer  64  of a lactose and sucrose mixture is sandwiched between two layers of polythene  66 ,  68 . Terahertz radiation  70  is incident on one of the polythene layers and the reflected radiation  72  detected. The sample comprises an air/PE interface  74  and two PE/LT interfaces  76 ,  78 . 
       FIG. 11  shows temporal waveform traces obtained from the sample shown in  FIG. 10 . Curve  1  is a polythene reference trace obtained by focussing the incident radiation on a separate reference sample. Curve  2  shows the trace obtained by focussing incident radiation on the air/PE interface. Curves  3  and  4  show the trace obtained by focussing the incident radiation at the first PE/LT interface (Curve  4  is obtained at a single pixel whilst curve  3  is averaged over the whole area). The THz signal reflected from the first PE/LT interface is much weaker than that from air/PE, ‘×5 ’ means that the corresponding signal is multiplied by a factor of 5. 
       FIG. 12  shows a comparison of the whole response from the sample of  FIG. 10  with the late time response measured from the sample following a Fast Fourier Transforms. In each case the incident radiation was focussed on the LT/PE interface. 
     Curves  1  and  2  relate to the whole response. Curve  1  represents the averaged response from the sample and curve  2  shows a typical response from one imaging point. Curves  3  and  4  show the late time response from the sample. It is clear that the spectral feature of lactose at 18 cm −1  can now be clearly resolved. Curve  3  represents a combination of late time response and averaging. 
     By using a method relating to the present invention it is possible to identify the true spectral components of a sample. Once these features have been identified it is possible to image the sample at the wavelengths relating to the components of the sample. In this way a spectral image can be compiled of the sample.  FIG. 13  shows a chemical mapping image of a sucrose/lactose/polyethylene sample using the spectral features of (a) sucrose and (b) lactose. 
       FIG. 14   a  shows a further chemical distribution image of the surface of a sample. The spectral features of sucrose, lactose and polyethylene have been used to identify the location of the components on the surface of the sample. Sucrose is denoted by  80 , lactose by  82 , and polyethylene by  84 . The area labelled  86  comprises both lactose and sucrose. The corresponding THz reflection spectra are shown in  FIG. 14   b.    
     An alternative method of reducing the effects of scatter is to use a diffuse irradiating beam of radiation. Such an arrangement is shown in  FIG. 15 . In a typical system configuration the emitter optics  88  are arranged to focus the irradiating THz radiation  90  on a single point  92  on the sample  94 . However, as an alternative the focus  95  could deliberately be moved such that a “diffuse” THz irradiating beam  96  probes the sample. This will have a similar effect to the “averaging” method of the first aspect of the invention and consequently scattering effects will tend to cancel each other out across the width of the beam.