Abstract:
A highly advantageous terahertz spectrometer with phase modulation and associated method are disclosed which utilize a second harmonic for generating an error signal to control a phase modulator to at least reduce nulls of an interference pattern.

Description:
REFERENCE TO RELATED APPLICATIONS 
     The present invention is related to co-pending U.S. patent application Ser. No. 12/465,219 filed May 13, 2009, Ser. No. 12/861,651 filed Aug. 23, 2010, Ser. No. 13/565,021 filed Aug. 2, 2012, Ser. No. 14/212,542 filed Mar. 14, 2014, and Ser. No. 14/262,291 filed Apr. 25, 2014. 
     BACKGROUND 
     The present invention is related to terahertz spectroscopy and, more particularly, to an advanced apparatus, system and methods for employing terahertz frequency radiation for characterizing and/or detecting materials. 
     Electromagnetic radiation in the sub-millimeter and terahertz (THz) frequency ranges has been employed for characterizing molecular gases, including materials of atmospheric importance. Recently terahertz radiation has been utilized for the characterization and/or detection of solids as well as gases. Many different materials have distinct and measurable characteristic signatures in the terahertz frequency range. For example, these materials can absorb electromagnetic radiation at certain terahertz frequencies that are unique for a given material or materials and which can be used to identify the given material. Materials that exhibit these characteristics signatures include: illicit drugs, biologically important compounds such as sugars and hormones, and explosives. Terahertz radiation can also be used in the field of art conservation, for example, to determine the proper materials for restoring paintings. 
     Many dielectric, nonmetallic materials are transparent at terahertz frequencies which makes it is possible to measure or detect other materials that are hidden behind such terahertz transparent materials. Some examples of terahertz transparent materials include: fabrics, packaging materials, and paper. Also, in the case of art characterization, layers of paint are also transparent to terahertz frequency radiation. Nonpolar liquids are also transparent to terahertz radiation. 
     In addition, terahertz radiation is non-ionizing and is completely eye safe. Because of this, terahertz radiation can be used in public areas without the risk of harm to humans, flora, or fauna. This can be especially beneficial because people using the terahertz frequency radiation are not encumbered by unwieldy radiation protection such as is common, for example, when using x-rays. 
     The foregoing examples of the related art and limitations related therewith are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those of skill in the art upon reading of the specification and a study of the drawings. 
     SUMMARY 
     The following embodiments and aspects thereof are described and illustrated in conjunction with systems, tools and methods which are meant to be exemplary and illustrative, not limiting in scope. In various embodiments, one or more of the above-described problems have been reduced or eliminated, while other embodiments are directed to other improvements. 
     In general, a method and associated apparatus are described for identifying a terahertz frequency spectral characteristic of a material in a sampling region. In an embodiment, the first terahertz signal and a second terahertz signals are generated. The phase of at least one of the first terahertz signal and second terahertz signal are modulated relative to a phase offset in a periodic manner at a modulating frequency. A terahertz electromagnetic radiation beam, based on the first terahertz signal, is transmitted to the sampling region such that a characterized terahertz radiation is produced by an interaction of the terahertz electromagnetic radiation beam with the material in the sampling region. The characterized terahertz radiation includes the terahertz frequency spectral characteristic that is related to the material. The characterized terahertz electromagnetic radiation is received from the sampling region and a characterized terahertz signal is produced responsive to the received radiation. The characterized terahertz signal and second terahertz signal are mixed to produce a detector signal that includes a characterized signal component related to the characteristic of the material. The detector signal also includes a first harmonic signal component at a first harmonic of the modulating frequency resulting from the phase modulation; and a second harmonic signal component at a second harmonic of the modulating frequency resulting, at least in part, from the phase offset which is a difference between the phases of the characterized terahertz signal and the second terahertz signal. The characterized signal component is extracted from the detector signal to identify the terahertz frequency spectral characteristics of the material in the sampling region. The extracted characterized signal component defines a characterized power curve that includes nulls which are reduced power levels at certain frequencies related to the second harmonic signal component of the detector signal. The phase offset is controlled using the second harmonic signal component such that the nulls are, at least in part, removed from the characterized power curve. 
     In another embodiment, a method is disclosed for identifying a characteristic of the material in a sampling region. In this embodiment, a first terahertz signal and a second terahertz signals are generated. A modulating waveform having a modulating waveform frequency is generated. The phase of the first terahertz signal is modulated using the modulating waveform to produce a modulated terahertz signal. The terahertz electromagnetic beam, based on a selected one of the modulated terahertz signal and the second terahertz signal is transmitted to the sampling region such that a characterized terahertz radiation is produced by an interaction of the terahertz electromagnetic beam with the material in the sampling region. The characterized terahertz radiation includes a component that is related to a characteristic of the material. A detector signal based at least in part on a difference between the characterized terahertz signal and the other one of the modulated terahertz signal and the second terahertz signal is produced. The detector signal includes a characterized signal component that is related to the characteristic of the material. The phase is modulated such that the detector signal includes a first harmonic component that is dependent, at least in part, on the modulating waveform frequency and a second harmonic component that is dependent, at least in part, on a phase offset between the characterized terahertz signal and the other one of the modulated terahertz signal and the second terahertz signal. The second harmonic component is indicative of nulls in the detector signal. The second harmonic component of the detector signal is detected. The phase offset is controlled during the modulation based on the detected second harmonic component such that the second harmonic component is essentially eliminated from the detector signal to thereby essentially eliminate nulls from the detectors. The phase of the first terahertz signal is modulated relative to the phase offset. The characterized signal component is extracted from the first harmonic of the detector signal and the characteristic of the material in the sampling region is identified based on the characterized signal component. 
     In another embodiment, a method is disclosed for identifying a terahertz frequency spectral characteristic of the material in a sampling region. In this embodiment a terahertz beam is generated that passes through the sampling region thereby producing a characterized terahertz radiation that is influenced by the material. A terahertz local oscillator signal is generated at the same frequency as the terahertz beam. Phase modulation is applied in a way that modulates the phase of at least one of the terahertz beam and the terahertz local oscillator signal based on the modulation input. An output signal is produced based on the characterized terahertz radiation and the terahertz local oscillator signal that can exhibit a pattern of nulls resulting from the phase modulation and which includes a first harmonic that characterizes the terahertz spectral characteristic of the sample. A second harmonic of the output signal is detected to produce an error signal. The modulation input is driven based on the error signal to at least reduce the nulls. 
     In addition to the example aspects and embodiments described above, further aspects and embodiments will become apparent by reference to the drawings and by study of the following descriptions. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating an embodiment of a simplified terahertz spectrometer without phase modulation and phase offset control. 
         FIG. 2  is a graph of a power curve which can result from using the spectrometer shown in  FIG. 1 . 
         FIG. 3  is a diagrammatic illustration of an embodiment of a terahertz spectrometer with a phase modulator and phase offset control in accordance with the present disclosure. 
         FIG. 4   a  is an illustration of a phase modulation waveform at a zero degree phase offset that can be used in the spectrometer of  FIG. 3 . 
         FIG. 4   b  is an illustration of components of a detector signal which can result from the waveform of  FIG. 4   a.    
         FIG. 5   a  is an illustration of a phase modulation waveform at a non-zero degree phase offset. 
         FIG. 5   b  is an illustration of components of a detector signal which can result from the waveform of  FIG. 5   a.    
         FIG. 6  is an illustration of a power curve that can be produced when the phase offset is not controlled. 
         FIG. 7  is an illustration of a characterized power curve which can be produced using the terahertz system shown in  FIG. 3 . 
         FIG. 8  is a method for identifying a terahertz frequency spectral characteristic of a material in a sampling region. 
     
    
    
     DETAILED DESCRIPTION 
     The following description is presented to enable one of ordinary skill in the art to make and use the invention and is provided in the context of a patent application and its requirements. Various modifications to the described embodiments will be readily apparent to those skilled in the art and the generic principles taught herein may be applied to other embodiments. Thus, the present invention is not intended to be limited to the embodiments shown, but is to be accorded the widest scope consistent with the principles and features described herein including modifications and equivalents, as defined within the scope of the appended claims. It is noted that the drawings are not to scale and are diagrammatic in nature in a way that is thought to best illustrate features of interest. Descriptive terminology may be adopted for purposes of enhancing the reader&#39;s understanding, with respect to the various views provided in the Figures, and is in no way intended as being limiting. 
     Attention is now directed to the Figures wherein like items may refer to like components throughout the various views.  FIG. 1  is a diagrammatic representation of a simplified terahertz system  10  which can be employed for terahertz radiation production and detection. Terahertz system  10  has been presented for purposes of providing a framework for the discussion of Applicant&#39;s recognitions in the context of problems which can arise in prior art terahertz frequency spectrometers. Terahertz system  10  includes a first laser  12  and a second laser  14  which are optically coupled to a 2×2 optical coupler  16  through optical fibers  18  and  20 , respectively. The 2×2 coupler is optically coupled to a source photoconductive switch (PCS)  22  through an optical fiber  24  and to a detector PCS  26  through an optical fiber  28 . The source and detector PCSs are positioned relative to a sampling region  30  in which a material  32  is positioned. The detector PCS is electrically connected to a detection circuit  34  through an electrical cable  36 . 
     The first and second lasers can be semiconductor diode lasers, such as distributed feedback (DFB) lasers, that each produce laser light at a different single frequency from one another at any given time. The first laser can generate a first laser light  38  and a second laser can generate a second laser light  40 . The frequency of the light from either one or both of the lasers can be controlled by changing the temperature of one or both of the lasers; and the difference between the laser light frequencies is in the terahertz frequency range. A range of terahertz frequencies can be produced over a time period by changing the difference between the laser light frequencies over the time period. 
     The 2×2 optical coupler receives laser light  38  and  40  from the lasers and optically outputs a combined light  42  that is made up laser light  38  and  40 . Of course, the frequency of the light from the respective lasers is not modified. The source and detector PCSs can be low-temperature grown GaAs photoconductive switches. The source and detector PCSs receive combined light  42  and optically photo mixes the two laser light frequencies to produce and detect terahertz radiation, respectively. The source PCS includes a biased antenna (not shown), and the mixing of the two frequencies of light on the biased antenna of the source PCS generates a free space terahertz frequency radiation beam  44 . The mixing of the two frequencies of light on the detector PCS, which is unbiased, provides a local oscillator required for homodyne detection. The terahertz radiation generated by the source PCS can be swept through a range of frequencies over a time period by changing the frequency difference between the laser light frequencies over the time period. The radiation beam is directed from the source PCS through a sampling region  30  in which the beam interacts with material  32  to produce a characterized radiation beam  46  which is received by the detector PCS. Characterized radiation beam  46  contains a terahertz frequency spectral characteristic which is related to characteristic frequencies that are at least partially absorbed when the terahertz radiation is swept through the range of frequencies. 
     The detector PCS detects the characterized radiation beam and produces a characterized terahertz signal which is mixed with the local oscillator internally in the detector PCS to produce a detector signal  48 . Detector signal  48  is supplied to the detection circuit  34  over electrical cable  36 . The detection circuit receives the detector signal and produces a response that can be characterized by a graph  60  ( FIG. 2 ) of power data  62  for the terahertz frequencies applied to the material. As shown in graph  60 , the terahertz frequencies applied to the material in the present embodiment are in a range from about 200 GHz to just over 1.5 THz. Graph  60  also shows noise  64  in the system. Power data  62  contains terahertz frequency spectral characteristic information of the material. However, Applicants recognize that the characteristics of the material as shown in power data  62  are largely indistinguishable because the detector signal contains a null signal component  66 . 
     Referring again to  FIG. 1 , terahertz system  10  is fully coherent, meaning that the local oscillator in the detector PCS used in the homodyne detection is generated by the same frequency source as the radiation beam from the source PCS. However, the path length of the light and terahertz radiation through the sampling region is different than the path length of the light to the detector PCS where the local oscillator is generated. Also, the terahertz radiation can be subjected to dispersion between the source and detector PCSs, including dispersion caused by the free space atmosphere as well as the material in the sampling region. The dispersion and path length difference can create a phase difference between the characterized terahertz signal, resulting from the characterized terahertz radiation beam and the local oscillator that is frequency dependent. As a result, when the terahertz frequency is generated and swept through the frequency range of about 200 GHz to just over 1.5 THz, as shown in  FIG. 2 , the characterized terahertz signal and the local oscillator periodically move between being completely in phase with one another to completely out of phase with one another. When these signals are completely in phase, the phase offset between the signals is zero degrees and when these signals are completely out of phase the phase offset between the signals is 180 degrees. When the offset is zero degrees, the signals constructively interfere, which results in a strong signal, and when the offset is 180 degrees, the signals destructively interfere, which results in the nulls, which are weak signals at those points. The series of nulls can be referred to as an interference pattern and the distance between the nulls is indicative of the frequency of the interference pattern. In the embodiment shown in  FIG. 2 , the interference pattern has a frequency of roughly 4 GHz. 
     The existence of the interference pattern can negatively impact system performance. In order to avoid aliasing, the frequency resolution employed by the system should fully resolve the interference pattern regardless of the width of the characteristic of the material in the sampling region. For example, the explosive composition RDX has a characteristic with a width of over 100 GHz. However, if a system with the fringe spacing shown in  FIG. 2  were employed to characterize a sample of RDX, a resolution of 0.5 GHz is required to properly record the interference pattern. Otherwise, aliasing occurs and the characteristic RDX absorption feature cannot be discerned. Also, a technique in which a background scan is recorded prior to introducing the sample into the sampling region and then is subtracted from the scan of the material cannot be used because the introduction of the material into the sampling region changes the effective path length and introduces dispersion which can cause the nulls of the interference pattern to shift. 
     Referring now to  FIG. 3 , an embodiment of a terahertz system  100  is shown which can be utilized for identifying a terahertz frequency spectral characteristic of a material  102  in a sampling region  104 . Unlike system  10 , terahertz system  100  can reduce and/or eliminate the interference pattern nulls so that the terahertz frequency characteristic of the material can be determined without the negative impact on the system performance introduced by the interference pattern nulls. 
     Terahertz system  100  includes a first laser  106  that produces a first laser light  108  and a second laser  110  that produces a second laser light  112 . The first and second lasers can be single frequency semiconductor diode lasers, such as for example, distributed feedback (DFB) lasers, that each produce laser light at a different, single frequency (at least from a practical standpoint) from one another at any given time. The frequency of the light from either one or both of the lasers can be controlled, such as for example, by changing the temperature of the laser, using a controller  114  which can be connected to one or both of the lasers through a control line  116 . The difference between the frequencies of first laser light  108  and second laser light  112  can be controlled within a range from gigahertz to terahertz, which can be referred to herein generally as a terahertz frequency range. The terahertz frequency range can include those terahertz frequencies that can be used to identify the material in the sampling region. One or both of the lasers can be controlled such that the difference between the frequencies of the laser lights can be swept over all or part of the terahertz frequency range over a time period. 
     Terahertz system  100  also includes 1×2 optical splitters  118 ,  120  and  122  and a phase modulator  124 . Splitter  118  receives first laser light  108  from the first laser through an optical fiber  126  and splits the first laser light at least approximately equally to supply the first laser light to phase modulator  124  and splitter  122  through optical fibers  128  and  130 , respectively. Splitter  120  receives second laser light  112  from the second laser through an optical fiber  132  and splits the second laser light at least approximately equally to supply the second laser light to phase modulator  124  and splitter  122  through optical fibers  134  and  136 , respectively. 
     Optical splitter  122  receives first laser light  108  from optical fiber  130  and second laser light  112  from fiber  136  and combines the light to supply a combined laser light  140  without frequency modification. Splitter  122  is optically connected to a detector PCS  142  through an optical fiber  144  over which combined laser light  140  is carried from splitter  122  to detector PCS  142 . 
     Phase modulator  124  receives first laser light  108  from optical fiber  128  and second laser light  112  from fiber  134  and combines the light into a combined laser light  146  having the same frequencies as combined laser light  140 . Phase modulator  124  is optically connected to a source PCS  148  through an optical fiber  150  which carries combined laser light  146  from the phase modulator to the source PCS. Although phase modulator  124  is shown optically connected to the source PCS and splitter  122  is shown optically connected to the detector PCS, in other embodiments the phase modulator can be optically connected to the detector PCS and splitter  122  can be optically connected to the source PCS. Phase modulator  124  receives a phase modulator control signal  154 , for controlling the phase modulator, over a control signal line  152 . 
     Phase modulator control signal  154  includes both a capacitively coupled AC signal component  156  and a resistively coupled DC signal component  158 . The AC signal component controls the phase modulator to periodically modulate the phase difference between the first and second laser lights at a modulating frequency. The DC signal component is utilized by the phase modulator to control a phase offset between the first and second laser lights relative to which the phase is periodically modulated, as will be discussed in further detail. 
     AC signal component  156  is supplied through an AC signal component conductor  162  by an AC driver  164  to control signal line  152 . DC signal component  158  is supplied through a DC signal component conductor  166  by a DC driver  168  to control signal line  152 . A reference oscillator  170  generates a low frequency reference waveform  172  and supplies the reference waveform to the AC driver through a reference waveform conductor  174 . The low frequency reference waveform can have a frequency of a few kilohertz to a few megahertz. The reference oscillator can originate the waveform as a square wave and the reference oscillator can include a waveform shaping circuit that converts the square wave into either a triangle wave or a sign wave that has slower transitions between maximum and minimum values than the square wave. Any suitable waveform can be used. The AC driver circuit receives the reference waveform and produces the AC signal component; the AC driver circuit can adjust an output voltage swing of the AC signal component, as will be discussed in further detail. 
     Source PCS  148  is connected to a DC bias source  180  through a DC bias line  182  which supplies a fixed DC bias to the source PCS. Combined laser light  146 , received by the source PCS, creates a beat pattern which produces a combined optical amplitude that varies at a rate given by the difference between the two optical frequencies in the combined laser light. This varying optical amplitude causes a resistance of the source PCS to vary at the difference frequency rate and the DC bias causes a corresponding current signal through the varying resistance. Since the difference frequency is in the terahertz range, the current signal is also in the terahertz range and the terahertz current signal from the source PCS flows through a connected spiral antenna (not shown) and generates a free space terahertz electromagnetic radiation beam  184 . The phase of electromagnetic radiation beam  184  depends upon the relative phase of the two laser lights at a point where the photoconductive switch is illuminated. Therefore, phase modulating and controlling the phase offset optically using phase modulator  124  also phase modulates and controls the phase offset of electromagnetic radiation beam  184 . The terahertz electromagnetic radiation beam is collimated by terahertz optics  186  which directs the terahertz radiation beam toward the detector PCS, through sampling region  104 . The terahertz radiation beam interacts with material that is positioned in the sampling region, such as material  102 , and a characterized terahertz radiation  188  is produced which includes terahertz frequency spectral characteristics that are related to the material. For example, as terahertz radiation beam  184  is swept through the range of terahertz frequencies, certain characteristic terahertz frequencies, which depend on the type of material, can be absorbed by the material to some extent. Other terahertz frequencies of terahertz radiation beam  184 , which are not absorbed by the material, can pass through the material from the source PCS to the detector PCS without any substantial loss of power. These characteristic terahertz frequencies are spectral characteristics which can be used for identifying a compound material and/or materials in the compound material. 
     Detector PCS  142  receives combined laser light  140  from splitter  122  to create a beat pattern in the detector PCS. The beat pattern produces a resistance in the detector PCS that serves as a homodyne local oscillator that varies at the same terahertz rate as the resistance in the source PCS. The resistance in the detector PCS varies at the same terahertz rate as the varying resistance in the source PCS because the combined laser light  140  contains the same two light frequencies as combined laser light  146 . 
     Detector PCS  142  includes terahertz optics  190  which focus characterized terahertz radiation  188  onto a spiral antenna (not shown) of the detector PCS. For example, a spiral antenna can receive the characterized terahertz radiation and produce a characterized terahertz voltage signal across the varying resistance in the detector PCS. The characterized terahertz voltage signal across the varying resistance produces a detector signal current  192  that is the product of the characterized terahertz voltage signal and the terahertz varying resistance. Because the resistance is modulated by the optical field of the two laser lights illuminating the detector switch which are also used for generating the terahertz radiation beam, the result is a homodyne mixing of the locally-generated terahertz signal (the terahertz varying resistance which serves as the local oscillator) and the incoming characterized terahertz signal in the antenna from the characterized radiation. The homodyne mixing of the locally generated terahertz signal in the detector and the characterized terahertz signal eliminates the terahertz frequency content. 
     Detector signal  192  includes low frequency content based on the reference waveform frequency that is produced by the phase modulation. The low frequency content includes a first harmonic signal component and can include a second harmonic signal component depending on the phase offset, as will be discussed in further detail. Detector signal  192  also includes a characterized signal component that is related to the terahertz frequency spectral characteristic of the material. The detector signal is supplied by the detector PCS to an amplifier  194  via a detector signal conductor  196 . Amplifier  194  can be a low noise amplifier that amplifies detector signal  192  and produces an amplified detector signal  198  which is supplied to a signal conductor  200 . Detector signal  198  is supplied to a 1 F lock-in amplifier  202  and a 2 F lock-in amplifier  204 . The lock-in amplifiers are connected to reference waveform conductor  174  to receive reference waveform  172  from reference oscillator  170 . 
     The 1 F lock-in amplifier receives detector signal  198  and uses reference waveform  172  as an input to extract the characterized signal component from the detector signal. The 1 F lock-in amplifier provides an amplitude measurement of the first harmonic of the detector signal. This lock-in amplifier is referred to as a 1 F lock-in amplifier because the reference input to the lock-in amplifier is at the same frequency as the signal that it is detecting. The output of the 1 F lock-in amplifier is a characterized signal  210  that is supplied on a signal line  212  which can be processed and/or displayed on a display device  216 , for example, as a characterized power curve  214 . 
     The 2 F lock-in amplifier also receives detector signal  198  and reference waveform  172  as a reference input. Lock-in amplifier  204  is referred to as a 2 F lock-in amplifier because this amplifier provides an amplitude measurement of the second harmonic of the detector signal. The 2 F lock-in amplifier produces an error signal  220  on an error signal conductor  222  that is a magnitude of a second harmonic of the reference waveform frequency in detector signal  198 . Error signal conductor  222  is connected to an integrator  226  that applies a bias and a biased error signal  228  is supplied by the integrator over an error signal conductor  230  to DC driver  168  which provides the DC signal component of the phase modulator control signal to the phase modulator. 
     Referring now to  FIG. 4   a  and  FIG. 4   b  in conjunction with  FIG. 3 , in an embodiment, phase modulator control signal  154  can include an AC signal component in the form of a triangle wave  240 . AC driver  164  can adjust the output voltage swing of the triangle wave to produce a peak-to-peak optical phase shift of 180 degrees which produces the terahertz electromagnetic radiation with a periodic phase shift of 180 degrees peak-to-peak. A one cycle sinusoidal waveform  242  is shown that represents the phase relationship between the reference terahertz signal (the local terahertz oscillator in the detector PCS) and the characterized terahertz signal resulting from the detection of the characterized terahertz electromagnetic radiation received by the detector PCS as the two signals are mixed in the detector PCS. When the fringes ( FIG. 2 ) are at a maximum the terahertz signals are in phase and when the fringes at a minimum the terahertz signals are 180 degrees out of phase. The optical phase modulator is biased using DC signal component  158  of phase modulator control signal  154 . When the phase modulator is biased at zero degrees offset  246 , which can also be referred to as quadrature, the triangle wave drives the phase shift to be equally balanced between the maximum or minimum of a fringe. When the phase modulator is biased at zero degrees offset, detector signal  192  includes a first harmonic sine wave  244  ( FIG. 4   b ) that is at the same frequency as reference waveform  172  and does not include a second harmonic. 
     Referring now to  FIG. 5   a  and  FIG. 5   b  in conjunction with  FIGS. 3 ,  4   a  and  4   b , when phase offset  246  is not set at zero degrees, detector signal  192  from the detector PCS includes a waveform  248  ( FIG. 5   b ) that can have a first harmonic component and a second harmonic component. In the embodiment shown in  FIGS. 5   a  and  5   b , the optical phase modulation is centered on a fringe maximum which is a negative 90 degree phase offset and waveform  248  exhibits a period of twice the modulation frequency such that the signal is positive going. In an embodiment in which the optical phase modulation is centered on a fringe minimum, which is a positive 90 degree phase offset, the waveform exhibits a period of twice the modulation frequency and the signal is negative going instead of positive going. That is, the signal is a mirror image of the signal shown in  FIG. 5   b . Although shown in  FIGS. 5   a  and  5   b  in the context of a 90 degree phase offset, whenever there is a non-zero phase offset between the characterized terahertz signal and the local terahertz oscillator, the detector signal will contain nulls in characterized signal  210  from the 1 F lock-in amplifier caused by the second harmonic component in the detector signal. Because of this, when the 2 F lock-in amplifier detects the second harmonic, the 2 F lock-in amplifier produces the error signal. The latter is used to create the DC signal component of control signal  154  which shifts the offset to reduce or eliminate the second harmonic and thereby reduce or eliminate the nulls. By continuously adjusting the phase modulator bias voltage so that the characterized terahertz signal and the local oscillator in the detector PCS continually maintain an optimal, in-phase, alignment regardless of the material in the sampling region, the nulls can be eliminated (at least from a practical standpoint) so that the characterized power curve can be clearly produced. 
     Referring now to  FIG. 6 , an example of an embodiment of a graph  260  (for illustrative purposes) shows an example of a power curve  262  that can be produced when the phase offset between the characterized terahertz signal and the local oscillator is not controlled. As the characterized terahertz signal and local oscillator are swept through the range of terahertz frequencies causing the phase offset to change. Applicants recognize that nulls  264  are produced which obscure the spectral characteristics of the material. 
     Referring now to  FIG. 7 , a graph  270  illustrates an embodiment of a characterized power curve  272  which can be produced using terahertz system  100 . Power curve  272  can include a terahertz frequency spectral characteristic 274 of the material in the sampling region which can be used for identifying the material. In this embodiment, the terahertz electromagnetic radiation and local oscillator are swept through a frequency range from about 200 GHz to about 1200 GHz; and the terahertz characteristic of interest occurs at approximately 820 GHz. In this embodiment, the phase offset is controlled using the error signal produced by the detection of the second harmonic while the frequency of the terahertz radiation and local oscillator are swept through the terahertz the frequency range, thereby eliminating the second harmonic and allowing the extraction of the characterized signal component from the first harmonic using the 1 F lock-in amplifier. 
     Referring now to  FIG. 8 , a method  290  is shown for identifying a terahertz frequency spectral characteristic of a material in a sampling region. Method  290  begins at  292  and proceeds to  294  where a first terahertz signal and a second terahertz signal are generated. The method then proceeds to  296  where the phase of at least one of the first and second terahertz signals is modulated relative to a phase offset in a periodic manner at a modulating frequency. The method then proceeds to  298  where a terahertz electromagnetic radiation beam is transmitted that is based on the first terahertz signal. The radiation beam is transmitted to the sampling region such that a characterized terahertz radiation is produced by the interaction of the terahertz radiation beam with the material in the sampling region. The characterized terahertz radiation includes a terahertz frequency spectral characteristic that is related to the material. Method  290  then proceeds to  300  where the characterized terahertz radiation is received from the sampling region and a characterized terahertz signal is produced responsive to the received radiation. The method then proceeds to  302  where the characterized terahertz signal and the second terahertz signal are mixed to produce a detector signal that includes a characterized signal component related to the characteristic of the material. The detector signal also includes a first harmonic signal component at a first harmonic of the modulating frequency resulting from the phase modulation; and a second harmonic signal component at a second harmonic of the modulating frequency. The second harmonic component is a result, at least in part, of the phase offset between the phases of the characterized terahertz signal and the second terahertz signal. Method  290  then proceeds to  304  where the characterized signal component is extracted from the detector signal to identify the terahertz frequency spectral characteristic of the material in the sampling region. The extracted characterized signal component defines a characterized power curve that includes nulls which are reduced power levels at certain frequencies related to the second harmonic signal component of the detector signal. The method then proceeds to  306  where the phase offset is controlled using the second harmonic signal component such that the nulls are, at least in part, removed from the characterized power curve. Method  290  then proceeds to  308  where the method ends. 
     Various embodiments of systems and techniques are disclosed herein in which terahertz frequency spectral characteristics of a material can be identified using second harmonics to produce an error signal for eliminating interference pattern nulls. These techniques can be used for identifying materials that have terahertz frequency characteristic signatures through materials that are transparent at terahertz frequencies, and for other purposes. The systems and techniques described herein are non-destructive to the material being tested so a material can be tested multiple times and the material can be used for its intended purpose even after testing. Applicants submit that apparatus, systems and methods according to the present disclosure provide sweeping and heretofore unseen benefits that are not recognized by prior art. 
     While a number of exemplary aspects and embodiments have been discussed above, those of skill in the art will recognize certain modifications, permutations, additions and sub-combinations thereof. It is therefore intended that the following appended claims and claims hereafter introduced are interpreted to include all such modifications, permutations, additions and sub-combinations as are within their true spirit and scope.