An effective terahertz (THz) imaging technology is presented for achieving tomographic image. A THz pulse reflective focal-plane imaging system is built up and the tomographic image of a metallic cross hidden by a high resistivity Si wafer is achieved. Using the reflected pulses from each interface, the thickness of each layer can be calculated with calculation error below 2.5%. This work demonstrates that the THz pulse focal-plane tomography can be used to analysis interior configuration of the object.
©2007 Optical Society of America
Terahertz (THz) sensing and imaging technologies have been rapidly developed over the latest decade because of their potential applications [1, 2, 3, 4, 5, 6]. According to the mode of measument, THz pulse imaging technologies can be divided into two types: transmission imaging and reflection imaging. Although the transmission imaging can ensure clear image, the reflection technology has attracted more attentions since it is more practicable. Researches on THz pulse reflective tomography have already been reported [7, 8, 9, 10]. However, most of these imaging geometries are achieved using the raster scanning method by focusing the THz beam onto the sample surface. The advantages of this method are the high signal-to-noise-rate (SNR) and good reflected signal collective efficiency, but it is limited to the experimental research since the image is achieved point by point.
One solution of this problem is using THz focal-plane imaging technology [11, 12, 13, 14]. In this kind of configuration, both THz and probe beams are expanded and the target to be imaged is illuminated by the THz quasi-plane wave. The probe beam is overlapped by the THz beam reflected from the target on the sensor crystal. Therefore, the information about the whole target has been transferred from the THz beam to the probe beam. Then the wave front of the probe beam is captured by a CCD camera, thus a two-dimensional (2D) image of the target can be achieved directly and the experimental time can be obviously reduced. For instance, acquiring an image of 256 by 256 pixels may require more than 20 hours using the conventional point by point scanning method; however, it takes only 20 minutes to obtain an image with same quality using the focal-plane imaging technology. The THz pulse focal plane imaging system in reflection geometry has been reported and the system was used to successfully identify different types of explosives . However, the relative report on the important application of this kind of technology, tomography, has not been seen.
In this paper, the tomographic image of a metallic cross hidden behind a high resistivity silicon (Si) wafer is achieved by using the THz pulse reflective focal-plane imaging system. Using the reflected pulses at each interface, the thicknesses of each layer of the sample are accurately calculated. The work will greatly benefit the development of THz imaging technology in analysis of the interior configuration of the object.
2. Experimental setup
The schematic layout of the experimental system is illustrated in Fig. 1. The laser used is a Spectra Physics Spitfire amplifier with 1 kHz repetition rate, 50fs pulse duration, 920mW output power, and 10mm spot diameter. The THz beam is generated by a 2.5mm thick ZnTe crystal and is expanded to 40mm. The sample, which is close to a gold plated mirror, is illuminated by the THz beam with 15° incident angle. A parabolic mirror with 101.6mm focal length is used as an imaging lens. The object distance is 320mm and the image distance is 150mm. Therefore, the obtained THz image is a reduced inverted real image of the sample. The probe beam is not expanded because a small THz sensor crystal (10 by 10 by 1 mm3) is used. The THz signal is detected by using the conventional electro-optic sampling method [12, 13, 14]. The polarization of the probe beam is modulated by the THz electric field inside the sensor crystal via the Pockels effect, then the polarization change is converted into the intensity distribution with an polarization analyzer P2. A CY-DB1300A CCD (1030 by 1300 pixels, ChongQing ChuangYu optoelectronics technology company) is used to capture the intensity distribution of the probe beam. Only 1024 by 1024 pixels of the captured image are extracted and combined to 256 by 256 pixels for simplification of the data-processing. It should be pointed that a mechanical chopper is inserted in the optical path of the pump pulse. The CCD camera is synchronized with the chopper for achieving two images of the probe beam with and without THz modulation, the subtraction of two images gives the near-zero bias image of the object. Furthermore, 50 frames have been averaged for improving the SNR.
For demonstrating the validity of the system, a metallic cross hidden by a high resistivity Si wafer, as shown in Fig. 2, is chosen as the imaged target. The thickness of the Si wafer is approximately 0.4mm and its diameter is 50mm. The cross is put between the Si wafer and metallic mirror. Parameters of the cross are 2.5mm wide, 25mm long, and 0.3mm thick. The cross is made of aluminum, so the THz beam cannot pass through it.
The refractive index of each layer of the sample in the THz frequency range should be known for calculating the thickness of each layer. The medium among the Si wafer, cross, and metallic mirror are air, so the refractive index of these two layers is 1. The refractive index of the Si wafer is measured by a standard THz-TDS system, as shown in Fig. 3. Its refractive index is approximately 3.26 at 0.2 to 2.0 THz, which is consistent with the reported literature well .
3. Expermental results
3.1. THz time domain signals
The THz time domain waveforms of the reference (averaged all over the pixels), reflected signals from the cross and metallic mirror are presented in Fig. 4. The waveforms are normalized and shifted for clarity. In Fig. 4(b) and Fig. 4(c), the first two pulses correspond to the THz signal reflected from the front and back surfaces of the Si wafer. Since the THz wave propagates from the medium with high refractive index into the medium with low refractive index, the half wave loss happens for the signal reflected from the back surface of the Si wafer, and the phase of the pulse changed π. The third pulse in Fig. 4(b) is caused by the reflection of the metallic cross and the third one in Fig. 4(c) corresponds to the reflection of the metallic mirror. Since the Si wafer is put at front of the metallic mirror, so the reflected pulses from the Si wafer are ahead of the reference signal. Nevertheless, the reflected THz pulses from the cross and the metallic mirror pass through the Si wafer twice, thus these pulses are behind of the reference signal.
It should be noted that there are some small pulses appear around 23.2ps, 26.3ps, and 27.6ps behind three primary pulses in Fig. 4(b) and Fig. 4(c). These are caused by the multiple reflections of THz pulses among the back surface of the Si wafer, cross, and mirror. The fourth pulse around 23.2ps in Fig. 4(b) is caused by the multiple reflections between the cross and back surface of the Si wafer, i.e. the pulse reflected by the cross is reflected by the back surface of the Si wafer and cross again. The pulse around 26.3ps in Fig. 4(b) is caused by the signal reflected by the cross, back surface of the Si wafer, and metallic mirror in order or caused by the signal reflected by the metallic mirror, back surface of the Si wafer, and cross due to the diffraction of the THz wave. The pulse around 27.6ps in Fig.4(c) is caused by the multiple reflections between the back surface of the Si wafer and metallic mirror. Comparing the relative time delay between these pulses, the thicknesses of each layer of the sample can be accurately calculated.
3.2. Two-dimensional transverse THz images
The THz pulse reflective focal-plane tomography can present the information about the sample layer by layer. Fig. 5 shows the 2D transverse images of the sample at three layers with fixed delay time of 3.7ps, 17.7ps, and 19.6ps, respectively. Fig. 5(a) presents the 2D image of the Si wafer front surface, which is a Gaussian distribution since the incident THz beam is Gaussian. Fig. 5(b) presents the 2D image of the cross, which is a bright cross since the THz pulses are reflected at the surface of the cross and pass though the air at other positions. Fig. 5(c) presents the 2D image of the metallic mirror, which is a dark cross since THz pulses cannot pass through the metallic cross. The asymmetry of the cross in Fig. 5(b) and Fig. 5(c) is due to the decline of the incident light. It can be drawn that the interior configuration of the sample can be acquired using the reflected THz pulses from each layer.
3.3. Spatial-temporal imaging
The longitudinal information about the object can also be presented by the THz pulse reflective focal-plane tomography. The spatial-temporal image of the sample in the y-t plane is drawn in Fig. 6. It is obtained by extracting the 200th row of each image recorded with different delay time. The first bright line around t = 4ps corresponds to the THz pulses reflected from the front surface of the Si wafer. The dark line around t = 12ps is the THz pulses reflected from the back surfaces of the Si wafer. The bright lines around t = 18ps and t = 20ps are caused by the THz pulses reflected from the cross and the metallic mirror. It should be noted that there are also reflected THz pulses from the metallic mirror behind the cross. Appearance of these pulses is considered as the diffraction of the THz wave since the width of the cross is 2.5mm and the wavelength of the THz wave is also in millimeter range. Furthermore, there are also some horizontal fringes in Fig. 6, which is caused by the non-uniformity of the sensor crystal.
3.4. Calculation of the thickness of each layer
where d is the thickness of each layer, Δt is the time delay between two adjacent THz pulses, c is the speed of light in vacuum, and n is the refractive index of corresponding layer. The thicknesses of each layer in the sample are given in the Table 1.
The real thickness of the Si wafer is 0.40mm and the calculated value is 0.390mm, the calculation error is only 2.5%. Since the metallic cross reflects the THz wave totally, it is quite difficult to measure the thickness of the cross. However, the distance between the cross and metallic mirror is approximately equal to the thickness of the cross. Therefore, the distance between the Si wafer and cross and that between the Si wafer and mirror are used to obtain the distance between the cross and mirror. The real thickness of the cross is 0.34mm and the calculated distance between the cross and metallic mirror is 0.339mm, the corresponding error is 0.2%. Since the cross is not so close to the metallic mirror, the measured value is larger than the thickness of the cross. The uncertainty for three measurements are 0.002, 0.010, and 0.013, respectively. These results demonstrate that the thickness of each layer of the sample can be accurately measured by using the THz reflective pulse focal-plane imaging system.
4.1. Effect of the surface roughness
The roughness of the sample’s surface will severely influence the SNR of the THz signal. It will broaden the THz pulse and weaken the high frequency components . The rough surface can be considered as a lot of small reflection planes. The reflected THz pulse can be expressed as :
where A 0(ω) is the complex amplitude of the incident pulse, A(ω) is the complex amplitude of the reflected pulse, ω is the angular frequency of pulses, 〈τ〉 is the average value of all time delays of reflected pulses from the rough surface, σ2 τ is the variance of the time delays caused by the reflection from the rough surface. It can be drawn that due to rough surface, the Gaussian THz pulse has been expanded.
For improving the accuracy of experiment, the aluminum, which can reflect THz pulses well, is picked as the material of the cross. The surface of the cross is smooth as far as possible in its making. In the experiment, the cross should be close to the metallic mirror so that it can reflect THz pulses well. Improvement of the power of the THz source and the SNR of the detected signal will be helpful to solve this problem.
4.2. Calculation error of the thickness
A main reason of the calculation error of the thickness for each layer is that THz pulses illuminate the sample with 15° incident angles rather than the normal incidence. When they transmit through the sample, THz pulses are reflected and refracted for many times. However, only the normal incidence is considered in Eq. (1), therefore, the calculation of the thickness is greatly simplified, which will bring the deviation between the real and measured value. Due to the dispersion of the medium, the uncertainty increases with the depth into the object increase . Our next step is to build a THz pulse normal reflective focal-plane imaging system for achieving better result.
The THz pulse reflective focal-plane tomography system is build up and the image of a layered sample is achieved. The experimental results demonstrate that this technology can be used to achieve interior images of a multiple layers sample. Meanwhile, the thickness of each layer can be accurately calculated using the reflected pulses from each interface. Over the past years, the application of THz imaging technology in medical field have been demonstrated [7, 9, 18]. It is expected that this technology can be used for medical imaging in the near furture.
This work is supported by the Beijing Science Nova Program (No. 2004B35), the National Natural Science Foundation of China (Grant 10674038), and the National Basic Research Program of China (Grant 2007CB310408).
References and links
1. L. Guo, Y. Hu, Y. Zhang, C. Zhang, Y. Chen, and X.-C. Zhang, “Vibrational spectrum of γ - HNIW investigated using terahertz time-domain spectroscopy],” Opt. Express 14, 3654–3659 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-8-3654. [CrossRef] [PubMed]
2. N. Li, J. Shen, J. Sun, L. Liang, X. Xu, M. Lu, and Y. Jia, “Study on the THz spectrum of methamphetamine,” Opt. Express 13, 6750–6755 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-6750. [CrossRef]
3. P. Y. Han, G. C. Cho, and X.-C. Zhang, “Time-domain transillumination of biological tissues with terahertz pulses,” Opt. Lett. 25, 242–244 (2000). [CrossRef]
4. H.-B. Liu, Y. Chen, G. J. Bastiaans, and X.-C. Zhang, “Detection and identification of explosive RDX by THz diffuse reflection spectroscopy,” Opt. Express 14, 415–423 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-1-415. [CrossRef] [PubMed]
5. Y. Chen, H.-B. Liu, M. J. Fitch, R. Osiander, J. B. Spicer, M. Shur, and X.-C. Zhang, “THz Diffuse Reflectance Spectra of Selected Explosives and Related Compounds,” in Terahertz for Military and Security Applications III, R. J. Hwu, D. L. Woolard, and M. J. Rosker, eds, Proc. SPIE 5790, 19–24 (2005). [CrossRef]
7. D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, “T-Ray Imaging,” IEEE. J. Sel. Top. Quant. 2, 679–692 (1996). [CrossRef]
9. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999). [CrossRef]
10. H. Zhong, J. Xu, X. Xie, T. Yuan, R. Reightler, E. Madaras, and X.-C. Zhang, “Nondestructive Defect Identification With Terahertz Time-of-Flight Tomography,” IEEE. Sens. J. 5, 203–208 (2005). [CrossRef]
11. Z. Jiang and X.-C. Zhang, “2D measurement and spatio-temporal coupling of few-cycle THz pulses,” Opt. Express 5, 243–248 (1999), http://www.opticsinfobase.org/abstract.cfm?URI=oe-5-11-243. [CrossRef] [PubMed]
12. M. Usami, M. Yamashita, K Fukushima, C. Otani, and K. Kawase, “Terahertz wideband spectroscopic imaging based on two-dimensional electro-optic sampling technique,” Appl. Phys. Lett. 86, 141109 1-3 (2005). [CrossRef]
13. Z. Jiang, X. G. Xu, and X.-C. Zhang, “Improvement of terahertz imaging with a dynamic subtraction technique,” Appl. Optics 39, 2982–2987 (2000). [CrossRef]
14. Q. Wu, T. D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996). [CrossRef]
15. H. Zhong, A. R. Sanchez, and X.-C. Zhang, “Identification and classification of chemicals using terahertz reflective spectroscopic focal plane imaging system,” Opt. Express 14, 9130–9141 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-20-9130. [CrossRef] [PubMed]
16. M. Exter and D. Grischkowsky, “Optical and electric properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett. 56, 1694–1696 (1990). [CrossRef]
17. Y. Dikmelik, J. B. Spicer, M. J. Fitch, and R. Osiander, “Effects of surface roughness on reflection spectra obtained by terahertz time-domain spectroscopy,” Opt. Lett. 31, 3653–3655 (2006). [CrossRef] [PubMed]
18. J. Nishizawa, T. Sasaki, K. Suto, T. Yamada, T. Tanabe, T. Tanno, T. Sawai, and Y. Miura, ”THz imaging of nucleobases and cancerous tissue using a GaP THz-wave generator,” Opt. Commun. 244, 469–474 (2005). [CrossRef]