WO2003042670A1

WO2003042670A1 - Method and system for performing three-dimensional teraherz imaging on an object

Info

Publication number: WO2003042670A1
Application number: PCT/US2002/036279
Authority: WO
Inventors: Bradley Ferguson; Shaohong Wang; Xi-Cheng Zhang
Original assignee: Rensselaer Polytechnic Institute
Priority date: 2001-11-13
Filing date: 2002-11-13
Publication date: 2003-05-22
Also published as: WO2003042670B1

Abstract

A method and a system for obtaining a series of images of a three dimensional object by transmitting pulsed terahertz (Thz) radiation (37) through the entire object (38) from a plurality of angles, optically detecting changes in the transmitted THz radiation using pulsed laser radiation, and constructing a plurality of imaged slices of the three dimensional object (38) using the detected changes in the transmitted THz radiation. The THz radiation may be transmitted through the object (38) as a scanning spot, a scanning line or a two dimensional array of parallel rays. The optical detection may similarly be a single detector or an array of detectors such as a CCD sensor (70).

Description

METHOD AND SYSTEM FOR PERFORMING THREE-DIMENSIONAL TERAHERZ IMAGING ON AN OBJECT

FIELD OF THE INVENTION The invention relates to T-ray imaging, and more particularly, to techniques for obtaining and imaging three dimensional spectroscopic information of objects using radiation in the THz spectrum. BACKGROUND OF THE INVENTION

Terahertz imaging is a relatively recently developed technology that operates in the submillimeter-wave region of the electro-magnetic spectrum (about from 100 GHz to 10 THz, hereinafter collectively referred to as terahertz radiation or simply THz ). Recent advances in highspeed optoelectronic and femtosecond laser technology facilitate generation and detection of short bursts of terahertz radiation, which has been proven to be extremely useful for spectroscopic measurements in the submillimeter-wave range. Terahertz imaging combines these coherent spectroscopic measurements with real-time imaging and advanced signal processing and recognition, so that each pixel element of the image contains spectroscopic information about the object. Terahertz radiation is described in greater detail in an article by M. Nuss entitled "Chemistry is Right for T-Ray Imaging," Circuits & Devices, IEEE (March, 1996.)

Typical apparatus and associated imaging methods for free-space electro-optic characterization of propagating terahertz beams are described in United States patent 5,952,818 issued Sep. 14, 1999 to Zhang et al. and assigned to the assignee of the present invention, Rensselaer Polytechnic Institute. The sensing technique is based on a non-linear coupling between a low- frequency electric field (terahertz pulse) and a laser beam (optical pulse) in an electro-optic crystal, such as a zinc telluride (ZnTe) crystal. Modulating the crystal's birefringence by applying the polarized electric field thereto modulates the polarization states of an optical probe beam passing through the crystal. This ellipticity modulation of the optical beam is then polarization-analyzed to provide information on both the amplitude and phase of the applied electric field. A further improvement in Terahertz imaging is disclosed in United States patent 6,414,473 issued July 2, 2002 to Zhang et al and is also assigned to Rensselaer Polytechnic Institute. The described imaging system in this reference employs a chirped optical beam and dynamic subtraction to rapidly reconstruct an image thereby providing a system that is suitable for real time imaging applications. According to this patent the imaging system includes means for generating a free-space electromagnetic radiation pulse positionable to pass through the object to be imaged, and one of an electro-optic crystal or a magneto-optic crystal positioned so that the electromagnetic radiation pulse passes through the crystal after passing through the object. The system further includes means for generating a chirped optical probe signal to impinge the crystal simultaneous with the electromagnetic radiation pulse passing therethrough so that a temporal waveform of the radiation is encoded onto a wavelength spectrum of the chirped optical probe signal. The chirped optical probe signal modulated by the free-space radiation is then passed to decoding means for decoding a characteristic of the free- space electromagnetic radiation using the chirped optical probe signal with the temporal waveform of the radiation encoded thereon. The system further includes means for determining a characteristic of the object using the characterization of the free-space electromagnetic radiation pulse after passing through the object.

Both of the above patents are incorporated in the entirety herein by reference. United States patent number 6,078,047 issued to Mittleman et al. June 20, 2000 discloses a method for providing a compositional image of an object in real time by reflecting pulses of electromagnetic radiation in the terahertz frequency range of an object and thereby obtaining the positions of dielectric interfaces in the object.

Systems such as described in the aforementioned patents have been used for diverse applications, including imaging semiconductors, leaf moisture content, flames, skin burn severity, tooth cavities and skin cancer. However, these systems and associated imaging techniques have not made available the three dimensional structure and far-infrared refractive index of the imaged object. Such knowledge can provide significant information in the examination, inter alia, objects that may not provide sufficient contrast when subjected to X-ray examination or sonograms. SUMMARY OF THE INVENTION

Thus, one aspect of the invention comprises a method of obtaining a series of images of a three dimensional object by transmitting pulsed terahertz (THz) radiation through the entire object from a plurality of angles, optically detecting changes in the transmitted THz radiation using pulsed laser radiation, and constructing a plurality of imaged slices of the three dimensional object using the detected changes in the transmitted THz radiation. The THz radiation may be transmitted through the object as a scanning spot, a scanning line or a two dimensional array of parallel rays. The optical detection may similarly be a single detector or an array of detectors such as a CCD sensor.

Still according to this invention, there is provided a THz imaging method comprising emitting a THz pulse and an optical probe pulse, transmitting the THz pulse in a first path through the object and transmitting the optical probe pulse through a second path not through the object. The optical probe pulse is modulated by the transmitted THz pulse in an electro-optic crystal to create a modulated optical pulse, which is detected with a two-dimensional CCD imaging system. Information corresponding to the detected optical pulse is stored. Stored information is gathered for a plurality of delay times between the THz pulse and the optical pulse sufficient to characterize a full waveform of the THz pulse, and for a plurality of projection angles relative to the object collectively representing a full or partial revolution of the object. Two dimensional slices, and optionally, a three-dimensional image of the object, are then constructed using the stored information.

Another aspect of the invention comprises a system for performing T-ray imaging generally comprising means for simultaneously providing a THz pulse and an optical pulse; means for directing the THz pulse in a first path through an object; and means for directing the optical pulse through a second path not through the object. An electro-optic crystal at a point of conversion of die first path and second path, provides modulation of the optical pulse with the THz pulse to create a modulated optical pulse. The system also comprises means for detecting the modulated optical pulse and means for storing information relating to the detected modulated optical pulse. The system comprises means for obtaining the stored information for the temporal profile of the THz pulse for a plurality of pixels along an x-axis of the object and a y-axis of the object for a plurality of projection angles. Accordingly, in one embodiment, the system may include means for rotating the object relative to the THz pulse about a z-axis of the object to obtain the plurality of projection angles. In such an embodiment, the object may be physically rotated or the means for providing the THz pulse may be physically rotated. In another embodiment, the THz pulse may be transmitted from a plurality of projection angles simultaneously, with a corresponding detector provided for each of the projection angles. Finally, the system comprises means for constructing a three-dimensional image of the object using the information obtained for the plurality of pixels for the plurality of projection angles. In one embodiment, the means for obtaining the stored information for the THz pulse comprises means for providing a chirped optical pulse, and the means for detecting the modulated optical pulse comprises a spectrometer and a CCD camera. In another embodiment, the means for obtaining the stored information for the THz pulse comprises a delay stage for providing a plurality of delays between the THz pulse and the optical probe pulse, and the means for detecting the modulated optical pulse comprises a two-dimensional CCD imaging system.

In another embodiment, the means for obtaining the stored information for the THz pulse comprises a delay stage for providing a plurality of delays between the THz pulse and the optical probe pulse, and the means for detecting the THz pulse is a photoconductive antenna or an array of such antennas. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a schematic representation of the relative positions of a sample and the THz radiation and associated detector for examining the sample in accordance with this invention. Figure 2 is a schematic representation of a system useful in implementing THz-CT in accordance with this invention.

Figure 3 is a schematic representation of an alternate system for implementing THz-DT in accordance with this invention.

Figure 4 is a schematic representation of an alternate system for implementing THz-CT in accordance with this invention. Figure 5 shows an image of an "S" shaped piece of polyethylene film obtained in accordance with the present invention.

Figure 6 shows an image of a table tennis ball obtained according to this invention. Figure 7 shows a plurality of tomographic slices taken across the table tennis ball shown in figure 6 reconstructed with one of the methods according to the present invention. Figure 8 shows an alternate plurality of tomographic slices taken across the table tennis ball shown in figure 6 reconstructed with another of the methods according to the present invention.

DETAILED DESCRIPTION OF THE INVENTION. The invention will next be described with reference to the figures where same numbers are used to indicate same elements in all. Such figures are used herein to illustrate the invention and are neither to scale nor do they include elements not needed in explaining the invention, so as not to unduly clutter and complicate the illustrations.

The techniques disclosed herein involve imaging technology for obtaining structural and spectroscopic dielectric information of three dimensional objects and are also described in B. Ferguson, S. Wang, D. Gray, D. Abbott, and X.-C. Zhang, "Towards functional 3D THz imaging," Physics in Medicine and Biology, 47, pp. 4735-4742, 2002. This article is incorporated by reference herein in its entirety. This information is obtained by first obtaining through multiple exposures information about the product structure in the form of a plurality of exposure data comprising information obtained by exposing the three dimensional object from different angles and at different cross sections. This data is then used to create a sequence of images representing a plurality of slices through the body of the object much as is done in conventional X-ray computed tomography. Figure 1 helps explain the fundamental concept. A sample 100 is scanned with THz radiation in the x,y plane in the direction of line L while the sample is rotated in the direction shown by the arrow θ. In the alternative, the radiation source and detector may be rotated while the target remains stationary. The sample is scanned in x and y dimensions to produce an image for a given projection angle. The sample is then rotated and scanned again. This process is repeated to generate 2D images (including the temporal THz profile) for a number of projection angles.

The mathematical field of inverse problems for 3D image reconstruction is very well established and a large number of potential algorithms exist in reconstructing the THz data. For example, the filtered backprojection algorithm may be used to perform the inverse Radon equation to reconstruct the sample. See for example, A.C. Kak and M. Slanley, "Principles of Computerized Tomographic Imaging", Society of Industrial and Applied Mathematics, 2001.

The Radon transform assumes a shadow model and does not consider diffraction effects, nor does it account for the direction dependent Fresnel loss encountered in T-ray tomographic imaging. It is given by: P(θ, t) = . fa, y)dl; where θ is the projection angle, t is the horizontal offset of the projection from the axis of rotation, P is the Radon transform anάfa,y) is the projected slice of the sample which we wish to reconstruct. The measured data is assumed to be a simple line integral. To formulate the reconstruction algorithm for T-ray computed tomographic imaging the detected THz signal is assumed approximately related to the transmitted pulse by a line integral of the form

where Pd is the Fourier transform of the detected THz signal at a frequency ω, a projection angle θ and a horizontal offset from the axis of rotation /. Pt is the Fourier component of the incident THz signal at the same frequency, L is the straight line between tl e source and detector, c is tlie speed of light, and n(τ) = n(r) + ιk(r) is the unknown complex refractive index of the sample.

T-ray CT allows the reconstruction of both the absorption coefficient k and the real refractive index n of the sample at all available frequencies by extracting different information from the measured data as input to the filtered backprojection algorithm. For example, to perform the reconstruction for the real refractive index n(ω) at a given frequency, we use ^'P_d (ω,θ,l)) s(ΘJ) = arg (2)

Pi .ω,θ,l) )

The filtered backprojection algorithm involves computing the Fourier transform of the projection data, s(θ,l), to yield S(θ,w), where w is the spatial frequency in the / dimension. The filtered backprojection algorithm can be described by the following equation:

^s(x_> y) - , (3)

where / =x cosθ + y sinθ. The refractive index is then recovered by n(x,y,ω) = 1 + (s(x,y) c) I (ω dr), where dr is the reconstruction grid size.

Alternatively, dispersion may be neglected and phase and amplitude parameters may be estimated directly from the time domain data. In particular the timing of the peak of the THz pulse can be used as the input to the filtered backprojection algorithm. The timing of the peak may be estimated with subpixel accuracy by interpolating the measured THz pulses and crosss-correlating them with a reference THz pulse. The timing of the peak of the cross-correlation gives the phase information with high accuracy. Numerous other techniques for estimating the phase of the pulses in the time domain may be used. This reconstruction algorithm is performed to reconstruct a number of features from the measured data depending on the desired application. The amplitude of the THz pulse and the timing of the peak of the pulse are prime examples. The reconstructed amplitude image gives a 3D image dependent on the bulk absorption of the sample in the far-infrared (including Fresnel losses) while the reconstructed timing image provides a refractive index map of the sample in 3D. Full reconstruction algorithms use the Fourier transform of the obtained data to reconstruct the frequency dependent refractive index and absorption coefficient for every voxel in the 3 dimensional sample space. This spectral information may then be used to identify different materials within the target.

One embodiment of the method for terahertz tomographic imaging according to this invention comprises simultaneously emitting a THz pulse and a chirped optical probe pulse, transmitting the THz pulse through the object in a first path and the chirped optical probe pulse in a second path not though the object. The chirped optical probe pulse is then modulated by the transmitted THz pulse in an electro-optic crystal to create a modulated optical pulse. The modulated optical pulse is detected, such as with a spectrometer and a CCD camera, and information is stored corresponding to the detected signal.

The steps of obtaining the stored information are then repeated for a plurality of x and y locations relative to the object and for a plurality of projection angles relative to the object. Such projection angles may collectively represent a full or partial revolution of the object, for example a 180 degree or 360 degree revolution, but lesser revolutions may also be used. Then, a plurality of two-dimensional tomographic slices of the object may be constructed from the collected and stored information using any algorithm known in the art, such as but not limited to a filtered backprojection algorithm as discussed earlier. A three-dimensional image of the object may then further be constructed from the two- dimensional slices. Numerous techniques of data processing can next be borrowed from X-ray technology to create three dimensional virtual images of the object, sections, flight through internal portions as is well known in the art.

Figure 2 illustrates a system 10 for performing T-ray tomography as hereinabove described using a chirped laser probing beam. A femtosecond laser 12 beam 14 is split using a pellicle 16 into pump and probe beams 20 & 18, respectively. The pump beam 20, is directed through a fixed delay path formed by reflectors 22, 24 and 26 onto a THz generator radiation emitter 28. The fixed delay path is only used for the positioning of the THz pulse, within the duration of the synchronized probe pulse, (acquisition window) and for temporal calibration. The terahertz beam 37 is directed through a reflector system (31,34) to pass through a sample 38. Sample 38 is positioned in the THz bean path through a holder 41 which is preferably adapted to provide rotation and translation of the sample as needed to accomplish scanning of the sample with the THz beam. Following transmission through the sample, beam 37 is directed onto a sensor 48 comprising an electro-optic crystal, through a system of reflectors 42 and 44 and a pellicle 46. The system also includes a grating pair 52 & 54 for chirping and stretching the optical probe beam 18. The probe beam is frequency chirped and temporally stretched by grating pair 52 & 54 by passing beam 18 through a pellicle 50 to the grating pair for reflection off mirror 56. The linearly chirped pulse is equivalent to a series of sub-pulses that have different wavelengths and are temporally delayed. Due to the negative chirp of the grating (pulse with decreasing frequency versus time), the blue component of the pulse leads the red component. The use of chirping the probe beam permits substantially real time information acquisition. The chirped probe signal is returned from grating pair 52, 54 to the reflective surface of the pellicle 50 and passed through a first polarizer 62 to generate a purely linearly polarized probe beam 64. The probe beam is modulated inside the electro-optic crystal 48, and becomes slightly elliptical due to phase modulation. A second polarizer 68 is used to convert the phase modulation into an intensity modulation. This second polarizer has a polarization axis that is perpendicular to the polarization axis of the first polarizer.

When the chirped probe beam and a THz pulse co-propagate in the electro-optic crystal, different portions of the THz pulse, through Pockels effect, modulate the different wavelength components of the chirped pulse. Therefore, the THz waveform is encoded onto the wavelength spectrum of the probe beam. A spectrometer, e.g., comprising a grating and lens combination, and a detector array (LDA or CCD) generally shown as block 70 are used to measure the spectral distribution. The spectrometer spatially separates the different wavelength components and thus reveals the temporal THz pulse. The spatial signal output from the spectrometer is then measured using a CCD. A computer 72 is used to process and store the retrieved data. The temporal THz signal can be extracted by measuring the difference between the spectral distributions of the probe pulse with and without THz pulse modulation applied via the electro-optic crystal 48, as is known in the art and described in detail in the aforementioned United States patent 6,414,473.

Dynamic signal subtraction may be employed if desired. If dynamic signal subtraction is used, a synchronization signal is provided between the THz emitter 28 and the pulse detector 70 using a frequency divider and an EO modulator 78 such that the pulse rate of the pump beam incident on the THz emitter is one half the scanning frequency of the CCD detector. Dynamic subtraction techniques and their use in improving terahertz imaging is fully described in an article entitled "Improvement of terahertz imaging with a dynamic subtraction technique" by Zhiping Jiang, X. G. Xu and X. C. Zhang published in Applied Optics, Vol. 39, No 17, 10 June 2000, pp. 2982-2987. This article is incorporated herein by reference in its entirety.

Dynamic subtraction is optional, and is simply one way of improving SNR. Other method of increasing SNR include increasing the THz power by using a different source or a higher THz antenna bias, for example, or increasing the CCD acquisition/averaging time. Increasing the CCD acquisition/averaging time, however, has the disadvantage of slowing the imaging speed. In an alternate embodiment of the present invention image data is captured using the arrangement shown in figure 3. Laser source 12 emits a laser pulse 14 that is split by splitter 16 into a pump pulse 20 and a probe pulse 18' . Pump pulse 20' travels through a delay stage comprising mirrors 24' and 26' that move in tandem back and forth in the direction of arrow A to enable scanning of the temporal length of the THz pulse, as is known in the art. The pump pulse then illuminates THz emitter 28' , which is typically an EO crystal. Alternatevely, the emitter may be a biased photoconductive antenna as is known in the art. See Mourou, G.A., Stancapiano, CN. Antonetti, A. & Orszag, A. "Picosecond microwave pulses generated with a subpicosecond laser driven semiconductor switch. " Appl. Phys. Lett. 39, 295-296 (1981).

Emitter 28' emits a divergent THz beam 35 that is collimated by parabolic mirror 32 to create a parallel or "expanded" THz pulse 36. The expanded pulse is transmitted through target sample 38, which is preferably mounted on a rotational stage 41' . Transmitted THz pulse 39 arrives at the THz detector 48 and modifies expanded optical probe pulse 61, creating a modulated optical pulse 63. The modulated optical pulse is then analyzed by polarizer 68 and a two-dimensional profile of the analyzed optical pulse is detected by a CCD camera 80. The rotational stage 41 ' permits rotating the sample 38 to obtain imaging data from a plurality of viewing angles.

The expanded optical probe pulse 61 is created by sending the collimated probe pulse 18' (typically a short pulse of 800 nm light) through negative lens 58 to create a divergent optical beam, which is then sent through positive lens 60 to form recollimated beam 61 having a broader beam waist so that the optical probe pulse has a diameter larger than the expanded THz beam. The lens focal lengths and separation distances are chosen to provide the desired beam diameter, as is known in the art. The recollimated beam 63 is then passed through polarizer 68. While not illustrated, dynamic subtraction may also be provided for this system, by the introduction of an electrooptical modulator in the pump beam path and the synchronization circuit as shown in figure 2.

Structurally, the system shown in figure 3 differs from that shown in figure 2 in that an expanded THz pump pulse and an expanded optical probe pulse are used for performing the imaging. As is well-known in the art, when a THz pulse is generated by an EO crystal or other means, it is a diverging beam. For a THz CT system, two parabolic mirrors are typically used to focus the beam. A first parabolic mirror collimates the THz beam into a parallel beam with a beam size of approximately 2 to 2.5 cm, however larger beams are possible and may be required for some applications. This parallel beam can be referred to as an "expanded beam." The second parabolic mirror is then used to focus the collimated THz beam to a small spot on the target. For such system, the second parabolic mirror is removed or replaced by a flat mirror, so that the parallel or expanded beam can be used for transmission through the target. Accordingly, the target is typically smaller than the diameter of the expanded beam.

The system illustrated in figure 3 captures the presence of a diffraction pattern in the information collected by the CCD camera. Because of this difference in the obtained data, we distinguish the system shown in figure 2 from that of figure 3 by referring to the system of figure 2 as

T-ray CT and the system shown in figure 3 as T-ray DT. The sensor crystal 48 is typically positioned as close as possible to the target 38 to maximize the angular range over which the diffracted radiation is collected. Alternatively, several measurements may be made by sequentially placing the detector at different angles relative to the target. Because of this difference in the data collected by the T-ray DT system, the algorithms used for reconstruction of 3D images from the collected data are also different from those used for T-ray

CT. A great deal of information about algorithms for reconstruction of 3D objects from projection data is already known, much of which was derived from work in the ultrasound domain and in the X- ray domain, including techniques used in positron-emission tomography (PET) and single photon emission computed tomography (SPECT). Additional knowledge in the field of reconstruction algorithms has been developed through work for electro-magnetic (RF) tomography, optical tomography, and seismic tomography.

At least some algorithms developed for RF tomography are suitable for T-ray DT tomography for very small targets (< about 1 mm). Exemplary such algorithms involve making linear approximations to the wave equation. The two most common approximations known in the art are the Born and Rytov approximations, but the invention is not limited to any particular approximation.

The Fourier Slice Theorem is then used together with interpolation or back propagation techniques to solve for the object function/, as is known in the art. These techniques are described in more detail by Kak and Slaney in "Principles of Computerized Tomographic Imaging," Society of

Industrial and Applied Mathematics, 2001, incorporated herein by reference.

For larger objects, algorithms developed for ultrasound tomography specifically, algorithms that invert the non-linear wave equation using iterative finite difference techniques may be applied.

One state of the art method is an adjoint method developed by Natterer, referred to as the Propagation-back propagation (PBP) algorithm. This and other algorithms are described in more detail by Natterer and Wubbeling in "Mathematical Methods in Image Reconstruction," Society of

Industrial and Applied Mathematics, Philadelphia, U.S.A., 2001, incorporated herein by reference. The T-ray DT system described herein allows measurement of the diffraction pattern caused by a target. In addition to allowing 3D reconstruction of the target using a plurality of projection angles, a 2D profile may be reconstructed using the data from a single projection angle. A time- reversal of the Huygen-Fresnel diffraction integral may be used: The use of this algorithm with the T-ray DT system is advantageous because it allows such a profile to be created using only a single pulse measurement, whereas previous uses of this algorithm for object reconstruction as detailed in Ruffin et al. in "Time reversal and object reconstruction with single-cycle pulses," Optics Letters, 26(1), 681-683 (2001), required multiple pulses. Furthermore, this method permits to reconstruct a 2D profile despite having only a fairly limited view angle to collect the diffracted pattern. This method may also be used as the basis for a 3D reconstruction technique.

In more general terms, Terahertz computed tomography according to this invention may be practiced using any system able to simultaneously provide a THz pulse and an optical pulse whereby the THz pulse is directed in a first path through an object, and the optical pulse is directed through a second path not through the object. While the figures show an electro-optic crystal as sensor 48, which provides modulation of the optical pulse with the THz pulse to create a modulated optical pulse, a photoconductive antenna can also be used as sensor 48 at a point of conversion of the first path and second path.

The system also comprises a detector for detecting the modulated optical pulse, such as a ccd array or measuring the photocurrent created by the probe pulse biased by the THz pulse etc. , and memory means for storing information relating to the detected modulated optical pulse. The system is capable of obtaining the stored information for the THz pulse for a plurality of pixels along an x- axis of the object and a y-axis of the object for a plurality of projection angles. Accordingly, in one embodiment, the system may include means for rotating the object relative to the THz pulse about a z-axis of the object to obtain the plurality of projection angles. In such an embodiment, the object may be physically rotated or the source of THz pulse and detector may be physically rotated relative to the sample. In another embodiment, tlie THz pulse may be transmitted from a plurality of projection angles simultaneously, with a corresponding detector provided for each of the projection angles. Finally, the system comprises a computer for constructing a three-dimensional image of the object using the information obtained for the plurality of pixels for the plurality of projection angles. Figure 4 illustrates a modified version of the system shown in figure 3 which may be used for performing T-ray CT. The arrangement is substantially the same as the arrangement shown in figure 3. As before a laser 12 is used to provide a beam 14 which is split by pellicle 16 into a pump beam 20 and a probe beam 18. The probe beam 18 is expanded through a first optical arrangement 86 comprising a combination of lenses to provide a collimated expanded probe beam 17' which is transmitted through first polarizer 62 and a system of reflectors 50 and pellicle 46 onto sensor 48. The pump beam 20 is also expanded and collimated through a lens system 84, and transmitted through a pulse delay mirror system 22, 24 and 26 onto a THz generator 28. The THz is again transmitted through the target object 38 which is mounted on a supporting platform 41 which permits rotating the target object to obtain different views. The THz beam is then transmitted through an optical system 82 comprising a focusing lens 81 and a limiting aperture 83 placed at the focal point of the lens. This serves to attenuate the scattered radiation and only allow the parallel beam transmitted THz radiation to pass (similar in nature to confocal microscopy). Another lens 85 is then used re- collimate the THz beam 90.

Beam 90 is also directed onto sensor 48 along the same path as the probe beam in a manner similar to the manner described above relative to figure 3. The probe beam, is again modulated as it is transmitted through detector 48 as a result of the THz which has itself been modulated as it was transmitted through the target object and carries information about the target object. The modulated probe beam is next transmitted through an analyzer 68 and detected using a 2D CCD detector 70.

Figures 2 and 3 and 4 show systems with a plurality of optical elements whose selection is a matter of directing beams along paths determined by the particular geometric requirements of the space and equipment available. Therefore, although the systems are shown schematically with a number of flat mirrors and beam splitters to create a logical schematic diagram, it should be understood that an actual system may have more or fewer mirrors and splitters, if any, as needed to fit the geometry of a particular workspace.

In general terms, this invention comprises a method for performing T-ray diffraction tomography on an object. The method comprises the steps of emitting an expanded THz pulse and an expanded optical probe pulse and transmitting the expanded THz pulse in a first path through the object and transmitting the expanded optical probe pulse in a second path not through the object. The method further comprises modulating the expanded optical probe pulse with the transmitted expanded THz pulse in an electro-optic crystal to create a modulated expanded optical pulse. The modulated expanded optical pulse is detected with a charge coupled device (CCD) camera and information corresponding to the detected pulse is stored, including diffraction information. The generation, transmission, modulation, and detection of the pulses is repeated for a plurality of projection angles relative to the object collectively representing a 360 degree revolution of the object. Then, a three- dimensional image of the object is reconstructed using the information collected by the CCD camera. The reconstruction step may comprise using a mathematical algorithm based on a linearization of the wave equation, such as a Born or Rytov approximation; an algorithm that inverts the non-linear wave equation using iterative finite difference techniques, such as a PBP algorithm; an iterative technique such as the Contrast Source Inversion method (P. M. van den Berg, R. E. Kleinman, "A contrast source inversion method," Inverse Problems, 13, pp. 1607-1620, 1997, which is incorporated herein by reference, or an algorithm based upon reconstruction of two-dimensional profiles of tlie object using Fresnel Diffraction. The method may comprise using a dynamic subtraction technique to improve the signal to noise ratio.

The system also comprises computer means for constructing a three-dimensional image of the object using the information obtained for the plurality of projection angles. The means for constructing the three-dimensional image comprise any suitable mathematical algorithm known in the art, including but not limited to those discussed above, included as part of computer software tangibly embodied in a computer memory device and operable by a computer processor to manipulate the stored information detected by the CCD camera.

Still in accordance with the present invention there is provided a method for providing a two- dimensional profile image of an object. The method comprises the steps of emitting an expanded THz pulse and an expanded optical probe pulse; transmitting the expanded THz pulse in a first path through the object and transmitting the expanded optical probe pulse in a second path not through the object; modulating the expanded optical probe pulse with the transmitted expanded THz pulse in an electro-optic crystal to create a modulated expanded optical pulse; and detecting the modulated expanded optical pulse with a charge coupled device (CCD) camera and storing information corresponding to the detected pulse. A two-dimensional profile image of the object is then constructed using a mathematical algorithm based upon the time-reversal of the Huygen- Fresnel Diffraction integral.

Figure 5 shows a piece of polyethylene film bent into an "S" shaped curve placed on stage 41 of tlie system illustrated in figure 2. and four reconstructed cross sections are also shown. These sections were created by applying to the captured data the Fourier transform and applying the filtered backprojection algorithm to the imaginary part of the Fourier domain coefficients at four different frequencies. The frequencies corresponding to each of the cross sections are: (i) 0.2 THz, (ii) 0.4 THz, (iii) 0.6 THz, and (iv) 0.8 THz. Figure 6 shows the reconstructed image of a table tennis ball imaged by scanning the ball with THz radiation in accordance with the present invention using the system illustrated in Figure 2. Part of the data has been cut away to allow the interior of the ball to be viewed. Figure 7 shows a series of tomographic type slices representing a reconstruction of the tennis ball using the peak of the THz pulses as the input to the filtered backprojection algorithm. Figure 8 is a similar reconstruction of the tennis ball using the timing of the peak of the pulse estimated with subpixel accuracy.

The terahertz radiation exposure and detection method described above may be used to identify specific materials by detecting the change in the radiation as a function of the frequency of the radiation, because such change is dependent on the dielectric constant of the irradiated material . Such information is obtained using spectroscopic detection of the THz pulse in detecting the changes in the electromagnetic radiation for each of the plurality of exposure angles.

Biomedical diagnosis is another area where the submillimeter spectroscopic measurements obtained through THz radiation exposure systems in accordance with the present invention have applications as they provide a wealth of information about the sample under test. Such technology is described in detail in an article entitled "Terahertz imaging of biological tissue using a chirped probe pulse" in Electronics and Structures for MEMS II, N.W. Bergmann, Editor, Proceedings of SPIE Vol. 4591, pp. 172-184, 2001 the contents of which are fully incorporated by reference herein.

Although described with respect to T-ray pulses, the CT methods of this invention may also be extended outside the THz range, such as, for example to wavelengths from the visible band to the THz range. Additionally, although described herein with respect to exemplary embodiments, tlie invention is not limited to the embodiments discussed herein. For example, methods using optical pulses other than chirped optical pulses may be used, as are known in the art. Furthermore, the method is not limited to use only with EO crystals. For example, photoconductive dipole antenna (PDA) detection may also be used.

Claims

We claim: 1. A method for obtaining a compositional image of an object comprising obtaining a series of images of said object by transmitting pulsed electromagnetic radiation in a frequency range between about 100 GHz to 10 THz through the entire object from a plurality of angles, detecting changes in the electromagnetic radiation following transmission through said object for each of said plurality of angles and constructing a plurality of imaged slices of the three dimensional object using the detected changes in the transmitted THz radiation.

2. The method according to claim 1 wherein the step of detecting comprises optically detecting said changes in said electromagnetic radiation.

3. The method according to claim 2 wherein the step of optically detecting said changes in said electromagnetic radiation further comprises using pulsed laser radiation.

4. The method according to claim 3 wherein said pulsed laser radiation is a chirped probe pulse and said changes are detected in substantially real time.

5. The method according to claim 1 wherein said detecting changes in the electromagnetic radiation comprises receiving both transmitted and scattered electromagnetic radiation pulses following transmitting said electromagnetic pulse through said object for each of said plurality of angles.

6. The method according to claim 1 wherein said detecting changes in the electromagnetic radiation following transmission through said object for each of said plurality of angles comprises detecting spectroscopic dielectric information.

7. The method according to claim 4 further comprising using said spectroscopic dielectric information to identify specific materials in said objects.

8. The method according to claim 4 wherein said object is a biological tissue.

9. A method for performing T-ray computed tomography on an object, the method comprising the steps of: (a) emitting a THz pulse and an optical probe pulse;. (b) transmitting the THz pulse in a first path through the object and transmitting the optical probe pulse in a second path not through the object; (c) modulating the optical probe pulse with the transmitted THz pulse in an electro- optic crystal to create a modulated optical pulse; (d) detecting the modulated optical pulse with a two-dimensional CCD imaging system and storing information corresponding thereto; (e) repeating steps (a)-(d) for a plurality of delay times between the THz pulse and the optical pulse sufficient to characterize a full waveform of the THz pulse; (f) repeating steps (a)-(e) for a plurality of projection angles relative to the object.; (g) constructing at least one image of the object using data collected during steps (a)-(f).

10. The method according to claim 9 wherein in step (a) said optical pulse is a chirped optical probe pulse.

11. The method according to claim 9 wherein the step of constructing at least one image of the object comprises constructing said at least one image representing a cross sectional slice of said object.

12. The method according to claim 9 wherein in step (g) the image constructed is a 3D representation of the object.

13. The method of claim 12 comprising using a filtered backprojection algorithm in step (g) to construct tlie three-dimensional image.

14. The method of claim 9 wherein step (g) comprises measuring a phase and amplitude of the transmitted THz pulses and reconstructing the complex refractive index of the object using said measured phase and amplitude as the input to an algorithm which inverts the Radon transform to reconstruct the complex refractive index of the object.

15. The method of claim 14 wherein there are transmitted a plurality of THz pulses and wherein the phase measurement comprises a phase delay and is estimated by interpolating the transmitted THz pulses and interpolating a reference THz pulse, cross-correlating the interpolated reference pulse with the transmitted pulses and using a timing of a peak of the cross correlation as the estimated phase delay.

16. The method of claim 14 where the amplitude and phase are estimated at a plurality of frequencies by Fourier transforming the time domain THz pulses and calculating a phase and amplitude of the complex Fourier coefficients at each given frequency.

17. The method of claim 9 comprising detecting the modulated optical pulse using a spectrometer and a CCD camera.

18. The method of claim 12 wherein said three-dimensional image comprises voxels and wherein a Fourier frequency-dependent refractive index and absorption coefficient for each voxel in the three- dimensional image is constructed using a Fourier transform of the information.

19. The method of claim 9, wherein the THz pulse comprises an expanded THz pulse, the optical probe pulse comprises an expanded optical probe pulse, and detecting the modulated optical probe pulse comprises using a two-dimensional charge coupled device (CCD) camera and the information corresponding thereto includes diffraction information.

20. The method of claim 19, wherein step (e) comprises repeating steps (a)-(d) for a plurality of delay times between the THz pulse and the optical pulse sufficient to characterize a full wavelength of the THz pulse.

21. The method of claim 20, wherein step (g) comprises constructing the three-dimensional image using a mathematical algorithm selected from the group consisting of: an algorithm based on a linearization of the wave equation, an algorithm that inverts the non-linear wave equation using iterative finite difference techniques, an iterative algorithm based on the contrast source inversion algorithm, or an algorithm based upon reconstruction of 2D profiles of the object using Fresnel Diffraction.

22. The method of claim 21, wherein the linearization algorithm comprises a Born or Rytov approximation.

23. The method of claim 21, wherein the iterative finite difference technique comprises a propagation-back propagation (PBP) algorithm.

24. The method of claim 9, further comprising using a dynamic subtraction technique to increase the signal to noise ratio.

25. A system for performing T-ray tomography, the system comprising: means for providing a THz pulse and an optical pulse; means for directing the THz pulse in a first path through an object; means for directing the optical pulse through a second path not through the object; an electro-optic crystal at a point of conversion of the first path and second path, for modulating the optical pulse with the THz pulse to create a modulated optical pulse; means for detecting the modulated optical pulse; means for storing information relating to the detected modulated optical pulse; means for obtaining the stored information for the temporal profile of the THz pulse for a plurality of pixels along an x-axis of the object and a y-axis of the object for a plurality of projection angles; means for rotating the object relative to the THz pulse along a z-axis to obtain the plurality of projecting angles; means for constructing a three-dimensional image of the object using the information obtained for the plurality of pixels for the plurality of projection angles.

26. The system of claim 25 wherein the means for obtaining the stored information for a THz pulse comprises means for providing a chirped optical pulse.

27. The system of claim 26wherein the means for detecting the modulated optical pulse comprises a spectrometer and a CCD camera.

28. The system of claim 26 wherein the means for obtaining the stored information for a full wavelength comprises a delay stage for providing a plurality of delays between the THz pulse and the optical probe pulse and the means for detecting the modulated optical pulse comprises one of a two- dimensional CCD imaging system or single photo-detector.

29. The system of claim 28, wherein the means for providing a THz pulse and an optical pulse comprises means for providing an expanded THz pulse and an expanded optical pulse, the means for obtaining the stored information for the temporal profile comprises a delay stage for providing a plurality of delays between the THz pulse and the optical probe pulse, and the means for detecting the modulated optical pulse comprises a two-dimensional CCD imaging system.

30. The system according to claim 29 further comprising an optical system placed in said first path at a point between said object and said point of conversion, said optical system comprising at least a focusing lens and a limiting aperture means at a focal point of the focusing lens to attenuate scattered radiation components of said expanded THz pulse.

31. The system of claim 28, wherein the information stored by the means for storing information includes diffraction information.

32. A system for performing T-ray tomography, the system comprising: means for simultaneously providing a THz pulse and an optical pulse; means for directing the THz pulse in a first path through an object; means for directing the optical pulse through a second path not through the object; a conversion point for said first and said second paths a photoconductive antenna at said point of conversion of the first path and second path for generating a photocurrent proportional to the instantaneous THz field; means for detecting the generated photocurrent; means for storing information relating to the generated photocurrent; means for obtaining the stored information for the temporal profile of the THz pulse for a plurality of pixels along an x-axis of the object and a y-axis of the object for a plurality of projection angles; means for rotating the object relative to tlie THz pulse along a z-axis to obtain the plurality of projecting angles; means for constructing a three-dimensional image of the object using the information obtained for the plurality of pixels for the plurality of projection angles.

33 A method for performing T-ray imaging on an object, the method comprising the steps of: (a) emitting a THz pulse and an optical probe pulse; (b) transmitting the THz pulse in a first path through the object and transmitting the optical probe pulse in a second path not through the object; (c) modulating tlie optical probe pulse with the transmitted THz pulse in an electro-optic crystal to create a modulated optical pulse; (d) detecting the modulated optical pulse and storing information corresponding thereto; (e) repeating steps (a)-(d) from a plurality of locations relative to the object sufficient to characterize the object; (f) constructing a three-dimensional image of the object using the information collected during steps (a)-(e).

34. The method of claim 33 comprising detecting the modulated optical pulse using a CCD camera.

35. The method of claim 34 comprising detecting the modulated optical pulse using a spectrometer and a CCD camera.

36. The method of claim 35 comprising using a filtered backprojection algorithm in step (f) to construct the three-dimensional image.

37. The method of claim 35 wherein said three dimensional image comprises voxels the method further comprising using a Fourier transform of the information to construct a frequency-dependent refractive index and absorption coefficient for each voxel in the three-dimensional image.

38. The system of claim 37 further comprising means for performing a dynamic subtraction technique to improve signal-to-noise ratio in the detected information relating to the modulated expanded optical pulse.

39. A method for providing a two-dimensional profile image of an object, the method comprising the steps of: (a) emitting an expanded THz pulse and an expanded optical probe pulse; (b) transmitting the expanded THz pulse in a first path through the object and transmitting the expanded optical probe pulse in a second path not through the object; (c) modulating the expanded optical probe pulse with the transmitted expanded THz pulse in an electro-optic crystal to create a modulated expanded optical pulse; (d) detecting the modulated expanded optical pulse with a charge coupled device (CCD) camera and storing information corresponding thereto, including diffraction information; (e) constructing a two-dimensional profile image of the object using a mathematical algorithm based upon the time-reversal of the Huygen-Fresnel Diffraction integral.