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Image restoration in chirp pulse microwave CT (CP-MCT)
Abstract
Chirp-pulse microwave computed tomography (CP-MCT) is a technique for imaging the distribution of temperature variations inside biological tissues. Even if resolution and contrast are adequate to this purpose, a further improvement of image quality is desirable. In this paper, we discuss the blur of CP-MCT images and we propose a method for estimating the corresponding point spread function (PSF). To this purpose we use both a measured and a computed projection of a cylindrical phantom. We find a good agreement between the two cases. Finally the estimated PSF is used for deconvolving data corresponding to various kinds of cylindrical phantoms. We use an iterative nonlinear deconvolution method which assures nonnegative solutions and we demonstrate the improvement of image quality which can be obtained in such a way.
... Chirped pulses, known as frequency-swept pulses have been widely used in radar technologies [1], spread-spectrum communication system [2], chirped pulse microwave computed tomography [3] and also other applications covering military and civilian systems such as communications, surveillance, countermeasures, navigation and imaging equipment [4]. Most radar applications make use of long chirped pulses with wide bandwidth, or pulses with a high time-bandwidth product (TBWP), allowing the detection of targets at long distances with improved range resolution. ...
... Experimental results show low strain measurement uncertainty and larger static measurement range by using the generated high order Kerr pulse with large chirping rate. Beyond that, the proposed method is also a promising alternative for other applications, such as radar [1], ultra-wideband sensing [15], bio-medical imaging [3], and non-contact healthcare monitoring [16]. ...
... When optical waves propagate in dielectric media with molecular inversion symmetry such as optical fibers, changes in the effective refractive index are induced and governed by the third-order susceptibility, (3) . The higher is the intensity of the optical waves, the greater are the changes in the refractive index, a phenomenon known as Kerr effect. ...
A photonic approach for generating low frequency drifting noise, arbitrary and large frequency chirping rate (FCR) optical pulses based on the Kerr effect in the nonlinear optical fiber is theoretically analyzed and experimentally demonstrated. Due to the Kerr effect-induced sinusoidal phase modulation in the nonlinear fiber, high order Kerr pulse with a large chirping rate is generated. In the concept-proof experiments, the FCR of the mth Kerr pulse has been significantly improved by a factor of 2m+1. In addition, dynamic strain measurement along with a random fiber grating array (RFGA) sensor by using different order Kerr pulse is carried out for demonstrating a large strain measurement range with lower uncertainty sensing capability. Benefiting from the use of a single laser source and large FCR Kerr pulse, the system exhibits a 3.9 µɛ static strain measurable range, 0.24 µɛ measurement uncertainty by using −4th order Kerr pulse that has an FCR up to 0.8 GHz/ns. Note that the FCR of the chirped pulse could be further enhanced by using larger FCR chirped pulse seed or choosing higher order Kerr pulses.
... Our main research interest is the development of a new temperature monitoring system, based on UWB radar detection principle, for primary usage in hyperthermia. The methods based on the microwave radar were proposed by Miyakawa et al. [14,15]. The tomographic method is used for the noninvasive detection of the temperature changes in the human body. ...
... The resolution was estimated for all three positions separately, because the standard deviation was different. The dependence of temperature difference on intensity y d used in Equation (13) can be expressed by regression formula (15). ...
... For experiments using the MIMO system, we developed a curved breast phantom with the heating possibility (based on tissue mimicking oil-gelatin phantoms) according to [23]. The phantom was composed of 3 mm thick skin (made from silicon with carbon powder) and was filled by gelatin phantom material (ε r = 68 and σ = 2 S/m for 3 GHz) [15]. Used phantom filling contained only gelatin. ...
... A comparison of CP-MCT with another microwave modality is discussed in [6]. In spite of good results obtained with different kinds of phantoms [4], the CP-MCT images are still affected by a considerable blur due to incomplete discrimination of the straight path joining the two antennas and to their finite aperture size [7]. Moreover, it is not completely clear what the physical parameter imaged by CP-MCT is. ...
... Indeed, it implies not only microwave scattering but also mixing and filtering of the detected signal, as required by MTDS. An attempt to develop an improved 'empirical' model was made in a series of papers789. According to this model, a CP-MCT projection is given by a blurred version of the corresponding Radon transform, the blurring being described by an appropriate point spread function (PSF). ...
... , the signal at the exit of the mixer is given by S(t) = c(t)u θ (d; t) and it is easy to see that it contains the beating term (see [7]): ...
Chirp-pulse microwave computerized tomography (CP-MCT) represents an innovative medical imaging technique. One of the advantages of CP-MCT is that data reduction is based on the standard algorithm of x-ray tomography, namely filtered back-projection and therefore is very fast, even if not very accurate. For this reason we recently proposed a modification of this algorithm based on a linear model, hence on a computationally efficient approach. The method has been validated by means of real data obtained with the Niigata prototype of the CP-MCT scanner. However, the applicability of the underlying model has not yet been completely analysed. In this paper, we first investigate the assumptions leading to the linear model and then we show, by means of numerical simulations, that it can provide quantitative maps of the attenuation constant of the body in the low-contrast case.
... A swept light source is a promising tool, which has been widely used in optical fiber sensing (OFS) [1][2][3][4][5], biomedical imaging [6] and microwave photonics [7]. In distributed OFS systems, the typical application of swept light sources is the application in the optical frequency domain reflectometer (OFDR) system [1,2]. ...
... In a phase-sensitive OTDR (ΦOTDR) system, the linearly chirped pulses and direct detection are used to measure the changes of temperature/strain from trace to trace, and then 1 mK/4 nε resolution is obtained experimentally and theoretically [5]. In biomedical imaging applications, the linearly chirped pulses are used as optical sources for extracting depth of the organization sample, which show great prospects in tumor detection [6]. ...
In this paper, a novel method for generating high-quality chirped pulses with IQ modulator is studied theoretically and experimentally, which is a crucial building block for high-performance coherent optical time-domain reflectometry (COTDR). In order to compensate the nonlinearity of the modulator transfer function, we present a predistortion technique for chirped-pulse coherent optical time-domain reflectometry (CP-COTDR), the arcsin predistortion method and the single sideband with a suppressed carrier analog modulation used to generate the high quality chirped optical pulse. The high order sidebands, due to the large amplitude of the modulation signal and the nonlinear transfer function of the IQ modulator, can be relieved by the predistortion process, which means the power and the quality of the generated chirped pulse has been improved. In the experiment, this method increases the peak power of the chirped pulse by 4.2 dB compared to the case without predistortion process, as for the CP-COTDR system, this method increases the signal-to-noise ratio of the demodulated phase variation by 6.3 dB.
... D'autres propositions de linéarisation du problème ont aussi été faites. Mentionnons l'approximation de Born étendue (extended Born approximation) et l'approximation par tenseur diagonal (diagonal tensor approximation) Tomography [Bertero et al. (2000); Fhager et Persson (2005)]. L'idée est de prétraiter les signaux mesurés (dans le domaine temporel) afin de n'en conserver que les composantes qui ont traversé l'OST en ligne droite. ...
... To overcome these problems, some microwave tomography methods are based on simplified models. This is the case for the chirp-pulse microwave computed tomography method (inspired from X-ray computed tomography) [Bertero et al. (2000); Fhager et Persson (2005)] and Born-type methods [van den Berg et ; Abubakar et van den Berg (2004); Li et al. (2004)]. Both types of methods present a low computational cost, but are only efficient for low and/or small contrasts. ...
This thesis is about microwave tomography applied to breast cancer detection. Both algorithmic aspects and questions related to the configuration of the measurements setup are treated.
The time needed for the reconstruction process is critical if clinical applications of microwave tomography are envisioned. In the first part of the thesis, we suggest new algorithms designed to decrease the calculation time in comparison with the concurrent methods. The “current source inversion” (CSI) method is used as starting point of the reflection. We first identify some of its pitfalls and propose two generalized versions, which are faster and more robust. Then, two new families of methods, which focus on different bottlenecks of the generalized CSIs, are introduced. They are based on two new formulations of the forward problem. The first of these is mathematically equivalent to the one used by CSI while the second one is based on approximations.
Regarding the configuration of the measurements setup, we first show that the resolution of the reconstructed images can be significantly improved by compressing the breast. We also propose a new setup based on the properties of the dielectric waveguides. Measurements can then be performed in the air rather than in a match liquid. This opens the door to the development of more compact setups.
... H IGH-FREQUENCY microwave waveform generation with large time-bandwidth product (TBP) has attracted considerable attention for a wide range of applications, including radar, telecommunications, imaging, and sensing systems [1], [2]. For example, chirped or phase-modulated microwave pulses are used to increase range resolution and detection distance in radar systems [1]. ...
... (8) and (9). As it can be inferred from Eqs. (1)(2)(3)(4)(5)(6)(7)(8)(9), the imperfections of the spectral phase response of the CBG, i.e. the group delay ripples (GDRs), can cause deviations in the instantaneous frequency, and the target central frequency and chirp rate of the generated microwave pulses. This suggests improving the integrated CBG design by using some apodization techniques [15]. ...
We demonstrate an integrated spectral shaper based on a Sagnac loop incorporating a chirped Bragg grating in silicon photonics for photonic generation of chirped microwave pulses. The technique is based on optical spectral shaping combined with linear frequency-to-time mapping. By tuning the central wavelength of the input optical pulse, we obtain chirped microwave pulses with central frequencies ranging from ~10 GHz to ~30 GHz and an RF chirp rate of ~20 GHz/ns with both positive and negative signs.
... The goal of calibration in general is to extract the scattered field from the measurements as accurately as possible. For instance, calibration may: 1) aim to compensate the nonlinearity of the receiver channels [28]; 2) correct mutual coupling and poor isolation [29]; 3) employ measurements of objects the scattered field of which is assumed known [30]; 4) employ direct measurement of the incident field in the volume occupied by the OUT and/or the measurement of the background wavenumber k b [5], [10], [31], [32]; 5) measure the PSF of the imaging system for the purposes of image deblurring [18]; or 6) subtract the signal acquired without the presence of the objects from those acquired when the object is present (performed in most of the above-mentioned approaches). The approach proposed here utilizes the simple background de-embedding of item 6) above in similarity to prior work. ...
... It also employs measurements of the system PSF, in similarity with item 5) above. However, unlike in [18], where the PSF is used in chirp-pulse tomography for image deblurring through deconvolution, here, the system PSF is used directly in the forward scattering model, which is then subjected to holographic inversion in Fourier (or k) space. ...
Microwave holography requires knowledge of the incident field and the Green tensor of the background medium. In near-field imaging, analytical models of these are inadequate and the use of electromagnetic simulations has been previously proposed. In practice, however, the fidelity of such simulations may also be insufficient. Here, we propose a measurement method for the acquisition of this information, thus eliminating the need to estimate it analytically or numerically. We validate the approach through simulated data acquisitions as well as through experiments. It is shown that this approach characterizes the measurement system more reliably than simulations leading to significant improvement of the image quality.
... Subsequently, Bertero worked on seismic tomography [16], microwave tomography obtained with a particular technique based on the use of chirp signals [17] and tomography with a finite set of projections [18]. One of his most persistent passions was astronomical imaging. ...
... The tomographic method uses the backscattered waves in an algorithm to reconstruct an image of the breast, in terms of tissue electrical parameters. The problem is considered an ill-conditioned nonlinear one and normally requires intensive computational work [10][11][12][13][14]. This is so due to the heterogeneous nature of the breast medium. ...
... Pulse compression techniques based on matched filtering method using linearly chirped pulses or phase coded pulses are widely used in modern radar systems and distributed fiber sensing systems for high spatial resolution and large dynamic range [1][2][3][4][5][6]. In some other applications such as biomedical imaging, linearly chirped pulses are used as optical sources for extracting depth of the organization sample, which show a great prospect in tumor detection [7]. In particular for long distance applications such as coherent radar systems and distributed fiber sensing systems, pulse compression techniques allow to transmit long pulses minimizing the transmitted peak power while maintaining a high spatial resolution. ...
Pulse compression technique is a particularly competitive method that enables both high spatial resolution and dynamic range in coherent radar and distributed fiber sensing systems. Up to now, the frequency bandwidths of most pulse compression techniques are restricted to tens of GHz. In this paper, we propose an all-optic sub-THz-range linearly chirped optical source and a large-bandwidth detection system to characterize it. Taking advantage of the chromatic dispersion effect, ultrashort optical pulses are stretched to be ~10 ns linearly chirped pulses with sub-THz range, which yields a large time-bandwidth product of 4500, a high compression ratio of 4167 and a chirp rate of 45 GHz/ns. The generated waveform is characterized with high precision thanks to the large detection bandwidth of linear optical sampling technique. A spatial resolution of 120 μm and an extinction ratio of 20.4 dB is demonstrated by using this technique, which paves the way for ultra-high spatial resolution and long range sensing applications such as LIDAR and optical reflectometry.
... The generation of broad bandwidth linearly or arbitrarily chirped microwave (MW) and sub-THz signals has attracted extensive research interest for a wide range of applications such as frequency-modulated continuous-wave (FMCW) radar [1][2][3], ultra-wideband sensing [4,5], bio-medical imaging [6], physical chemistry [7], noncontact sensing and non-destructive diagnosis [1,8,9]. Frequency-chirped radio-frequency (RF) signals can be generated through electrical approaches such as direct synthesis using electrical oscillators [10], and digital signal processing or direct digital frequency synthesizer [11,12] together with frequency upconversion chains. ...
We present a photonic approach for generating low phase noise, arbitrary chirped microwave waveforms based on heterodyne beating between high order correlated comb lines extracted from frequency-agile optical frequency comb. Using the dual heterodyne phase transfer scheme, extrinsic phase noises induced by the separate optical paths are efficiently suppressed by 42-dB at 1-Hz offset frequency. Linearly chirped microwave waveforms are achieved within 30-ms temporal duration, contributing to a large time-bandwidth product. The linearity measurement leads to less than 90 kHz RMS frequency error during the entire chirp duration, exhibiting excellent linearity for the microwave and sub-THz waveforms. The capability of generating arbitrary waveforms up to sub-THz band with flexible temporal duration, long repetition period, broad bandwidth, and large time-bandwidth product is investigated and discussed.
... More specifically, one of these interesting signals is the chirped microwave pulse with the main characteristic of having a frequency variation along the time duration pulse, which involves a large bandwidth signal processing. Among the diverse applications where chirped microwave pulses are used, spread spectrum communications, pulsed compression radars or tomography for medical imaging [9][10][11] can be highlighted. ...
We experimentally demonstrate, for the first time, a chirped microwave pulses generator based on the processing of an incoherent optical signal by means of a nonlinear dispersive element. Different capabilities have been demonstrated such as the control of the time-bandwidth product and the frequency tuning increasing the flexibility of the generated waveform compared to coherent techniques. Moreover, the use of differential detection improves considerably the limitation over the signal-to-noise ratio related to incoherent processing.
... Chirped microwave filters are typically employed due to their ability to compress or expand the bandwidth occupied by the signal, with the achievable RF group delay slope referred to as the chirp parameter. They have extensive application in high performance radar [5], antenna phase distortion compensation for ultra-wide band (UWB) radio systems [6], radio over fibre systems [7], real-time spectral analysis [8] and clinical diagnosis for microwave computed tomography systems [9]. Whilst applications typically require a large in-band chirp, electronic chirped filter structures have been limited in the maximum achievable group delay slope, operating bandwidth and reconfigurability of both the amplitude and phase response [10]. ...
A novel chirped microwave photonic filter (MPF) capable of achieving a large radio frequency (RF) group delay slope and a single passband response free from high frequency fading is presented. The design is based upon a Fourier domain optical processor (FD-OP) and a single sideband modulator. The FD-OP is utilized to generate both constant time delay to tune the filter and first order dispersion to induce the RF chirp, enabling full software control of the MPF without the need for manual adjustment. An optimized optical parameter region based on a large optical bandwidth >750 GHz and low slicing dispersion < ± 1 ps/nm is introduced, with this technique greatly improving the RF properties including the group delay slope magnitude and passband noise. Experimental results confirm that the structure simultaneously achieves a large in-band RF chirp of −4.2 ns/GHz, centre frequency invariant tuning and independent reconfiguration of the RF amplitude and phase response. Finally, a stochastic study of the device passband noise performance under tuning and reconfiguration is presented, indicating a low passband noise <−120 dB/Hz.
... This is because in most cases (e.g., far-field regime), the output intensity TBP remains unchanged during TS-DFT operation. It would be highly desirable to increase the output bandwidth or expand the output TBP for various applications of microwave waveform generation such as radar systems [13], spread-spectrum communications [14], microwave computed tomography [15], and modern instrumentation [11], [12]. ...
We experimentally demonstrate, for the first time, a method for arbitrary waveform generation (AWG) with time-bandwidth product (TBP) expansion beyond the limitations set by a spectral encoder. We show that, by using an anamorphic stretch transform with a specific group delay (GD) profile, one can boost the TBP of the generated electrical waveform in time-stretch AWG. In particular, we show that the TBP expansion can be achieved, depending on the signal sparsity and proper choice of the warped GD dispersion profile. The new waveform generation system is implemented here using a nonlinearly chirped fiber Bragg grating with a warped GD profile. Experimental demonstrations in this paper show a TBP expansion of more than three times above the maximum achievable using conventional methods. Details of the signal dependence and spectral redundancy/sparsity requirement for time-bandwidth compression and expansion are also studied.
... The basic principle of their projects is similar to our proposal. To obtain finer resolution less than 1 cm, pulse signals and multiple antennas for transmitting and receiving were implemented [11][12][13][14]. Because attenuation in the human body at the microwave frequency range is remarkable, an electromagnetic darkroom is necessary to prevent interference of an electromagnetic wave along indirect paths as well as to suppress emission of the microwave to the outside environment. ...
The authors are developing a technique for conducting measurements inside the human body by applying a weak electric field at a radio frequency (RF). Low RF power is fed to a small antenna, and a similar antenna located 15-50 cm away measures the electric field intensity. Although the resolution of the method is low, it is simple, safe, cost-effective, and able to be used for biomedical applications. One of the technical issues suggested by the authors' previous studies was that the signal pattern acquired from measurement of a human body was essentially different from that acquired from a phantom. To trace the causes of this difference, the accuracy of the phase measurements was improved. This paper describes the new experimental system that can measure the signal phase and amplitude and reports the results of experiments measuring a human body and a phantom. The results were analyzed and then discussed in terms of their contribution to the phase measurement.
... Bertero et.al. [20]) or Born approximations (Bulyshev et.al. [21]). ...
Microwave tomography is a promising method for the breast cancer imaging. Dielectric properties of the healthy tissue and the tumor have a high contrast under microwave investigation. To determine the dielectric properties from antenna measurements it is necessary to solve the inverse electromagnetic problem. This inverse problem is ill-posed, its solution is not stable. Regularization is used to achieve stability. Ordinary Tikhonov regularization usually makes the solution too smooth. Edge-preserving regularization is investigated to obtain a stable solution without oversmoothing the solution. Tikhonov and Edge-preserving regularizations are compared. It is found that edge-preserving reg-ularization decreases the smoothness of the reconstruction but has the same robustness against the noise compared to Tikhonov regularization.
... I N RECENT years, pulsed radio-frequency (RF) technology has attracted considerable attention due to potential applications in modern radars, spread-spectrum communications and microwave computed tomography [1]- [3]. Specifically, in a modern radar system, pulsed transmitted signals are desirable to obtain range information. ...
Based on the frequency-to-time mapping approach, we generate frequency-modulated millimeter-wave (MMW) pulses with central frequencies up to the W-band by a shaped optical pulse excitation of an MMW photonic transmitter with an ultrawide band photodiode as its key component. A coherent detection is achieved via a terahertz time-domain spectroscopic setup. Two different kinds of chirped MMW waveforms are generated; one is a linearly chirped sinusoidal pulse and the other is produced by a frequency-stepped modulation. Through appropriate optical spectral design, the frequency-chirped MMW pulses with instantaneous frequencies sweeping from 120 to 60 GHz, and a time-bandwidth product of ~ 25 is experimentally demonstrated.
... The frequency modulated continuous wave (FMCW) radar has also shown its advantage over the CW Doppler radar in the application of contactless sensing, because it can monitor the user motor activity as well as the cardiac activity and respiration [2]. In biomedical imaging, chirp-pulse microwave computed tomography (CP-MCT) in which the linearly chirped microwave pulse is used to extract the straight path from multiple paths has been demonstrated in noninvasive thermometry [3] and shown great promise in breast tumor detection [4]. In physical chemistry, broadband chirped pulse Fourier transform microwave (CP-FTMW) spectrometer is also widely used for measuring the rotational spectrum for molecular structure determination of gas phase samples [5]. ...
Based on the heterodyne beating between the pre-chirped optical pulse and the continuous wave (CW) light in a wideband photodetector (PD), linearly chirped microwave pulse with time duration of 3.2ns and bandwidth of 33GHz, which yields a large time-bandwidth product (TBWP) of 106 and high compression ratio of 160, is generated in our experiment. Dispersion compensation fiber (DCF) with uniform response across broad bandwidth is used for providing the original linear chirp in our method, which shows the promise to generate linearly chirped microwave pulse with bandwidth of up to THz. The flexibility of the center frequency and the stability of the time-frequency performance are demonstrated by generating different types of linearly chirped microwave pulses. The range resolution of our generated microwave pulse is also verified by off-line processing.
... Contrast agent uptake Diagnosis Screening (Allen et al. , 1999), (Edel & Eisen, 1999), (Stuntz et al. , 1999) , , (Suzuki et al. , 1996), (Fantini et al. , 1997) continued on next page continued from previous page (Faupel et al. , 1997), (Cuzick et al. , 1998) Positron emission tomography Forms images using emission from annihilation of positrons from radioactive pharmaceuticals increased metabolic activity Screening, diagnosis (Phelps, 2000), (Stuntz et al. , 1999), (Edel & Eisen, 1999) Elastography Uses ultrasound or MRI to infer the mechanical properties of tissue Difference of tissue elasticity Screening, diagnosis (Gao et al. , 1996), (Sarvazyan, 1995), (Plewes et al. , 2000), (Lorenzen et al. , 2002) Magnetic resonance spectroscopy Analyzes tissues's chemical makeup using radio emission from nuclear spin Increased water content Screening, diagnosis (Merchant, 1994), (Mountford et al. , 2000) Thermoacoustic and photoacoustic computed imaging Generates short sound pulses within breast using radio-frequency or nearinfrared light energy and construct a 3-D image from them increased blood or water concentration Screening, diagnosis (Kruger et al. , 1999a), (Oraevsky et al. , 1998) Microwave imaging View breast using scattered microwaves Increased water content data not available yet (Fear et al. , 2002), (Bertero et al. , 2000), (Meaney et al. , 2000) Hall-effect imaging Picks up the sonic vibrations of charged particles exposed to a magnetic field difference of tissue conductivity data not available yet (Wen et al. , 1998) Magnetomammography Senses magnetic contrast agents collected in tumor Contrast agent uptake data not available yet (Clarke, 1994) At present, X-ray mammography is the only technology sufficiently well developed for screening of the general population for breast cancer. It therefore serves as a "gold standard" with which new technology will be compared. ...
This research deals with developing the photoacoustic imaging technique
for breast cancer detection. Photoacoustics brings together the strong aspects of ultrasound and optical imaging. Medical imaging with photoacoustics is relatively new, and promising for a lot of applications, one of which is breast cancer detection.
... M ICROWAVE signal synthesis in the optical domain is an interesting topic which can find many applications such as in radar, communications, and microwave tomography [1]- [3]. In the past few years, numerous techniques have been proposed [4]- [7]. ...
We propose and demonstrate a new and simple method for achieving continuously tunable microwave frequency multiplication using an unbalanced temporal pulse shaping (TPS) system incorporating two linearly chirped fiber Bragg gratings (LCFBGs) written in erbium/ytterbium co-doped fibers. By optically pumping the LCFBGs with different pumping power, the dispersion of the LCFBGs is tuned. The incorporation of the LCFBGs in an unbalanced TPS system would enable the generation of a frequency tunable microwave waveform. The operation of the system is discussed which is then verified by an experiment. Continuously tunable microwave frequency multiplication with a multiplication factor from 5.14 to 11.9 is experimentally demonstrated. The impact of the ripples in the magnitude and group delay responses of the LCFBGs on the performance of the microwave generation is also studied.
Application of THz radiation is attractive and promising in biology and medicine, in particular, in order to remove ionizing X-rays in imaging test and to enhance the nuclear magnetic resonance (NMR) signal. At present the problem of lack of powerful and compact-style sources of THz radiation in the frequency range from 300 GHz to 1 THz still exists. Especially for high sensitive and high-resolution dynamic nuclear polarization (DNP) NMR spectroscopy, the increase of the operating frequency and output power of THz sources is a key issue. In this chapter, we will analyze the physical principles of classical electromagnetic (EM) sources of THz radiation those are widely applied in THz imaging systems and in DNP-enhanced NMR Spectroscopy. The advantages of solid-state oscillators (Gunn, impact ionization avalanche transit-time (IMPATT) and TUNNET diodes together with multipliers), vacuum electron devices (VEDs) (backward wave oscillators (BWOs), clinotrons, diffraction radiation oscillators (DROs), orotrons, extended interaction klystrons and oscillators (EIKs and EIOs), gyrotrons), and combined systems for different THz applications have been discussed. State-ofthe-art of compact frequency-tunable sources and up-to-date research and development activities on high-frequency medium power VEDs have been presented. Special attention is paid to THz-imaging and spectroscopy schemes and modules based on existing sources. The examples of THz-image processing of the biological objects and its application in medical diagnostics are presented.
This letter studies the problem of ultrawideband (UWB) tomographic imaging for unknown building layouts where the multipath-rich condition is considered. Specifically, first, the multiple propagation paths of the UWB signal are analyzed, and a delay estimation algorithm is proposed to estimate the direct path (DP) delay from the multipath signal. Then, a tomographic projection model is established by mapping the relationship between the delay of the DP and the relative permittivity of the unknown layout. Besides, a modified total variation method is developed to reconstruct the building layout, which shows significant performance in preserving the edges of the structure. Finally, the effectiveness of the proposed algorithm is verified using both simulated and real data.
Progress in microwave and millimeter-wave technologies has made possible advanced diagnostics for application to various fields, including radio astronomy, alien substance detection, plasma diagnostics, airborne and space-borne imaging radars called as synthetic aperture radars, and living body measurements. Transmission, reflection, scattering, and radiation processes of electromagnetic waves are utilized as diagnostic principles. The diagnostics are classified as active and passive systems. Specifically, active radar reflectometry has become of importance in various applications due to the possibility of high localization and accessibility of the measurements as well as the non-invasive nature of the systems. In this paper, recent development and application of radar reflectometers are described. The key words are profile reflectometry, fluctuation reflectometry, imaging radar (optics imaging and synthetic aperture imaging), and radio-optics fusion technology in order to improve the spatial resolution.
The development of communications technologies has led to an ever-increasing demand for a higher speed and wider bandwidth of microwave signal processors. To overcome the inherent electronic speed limitations, photonic techniques have been developed for processing of ultrabroadband microwave signals. A dispersive delay line (DDL) is a key photonic device that can be used to implement signal processing functions, such as time reversal, time delay, dispersion compensation, Fourier transformation, and pulse compression. Compared with an electrical delay line, a photonic DDL has a much wider bandwidth and can be used for processing a microwave signal with a much wider bandwidth. In this paper, we review our recent work using photonic DDLs for processing of broadband microwave signals. Two types of DDLs are to be discussed, a linearly chirped fiber Bragg grating-based DDL and an optical dispersive loop-based DDL. Signal processing functions including microwave time reversal, microwave temporal convolution, time-stretched sampling, microwave waveform generation with an extended temporal duration, and wideband true-time delay beamforming are discussed.
An opto-electronic oscillator (OEO) scheme which operates at “chirp oscillation” mode and generates low-phase-noise, frequency-swept microwave is proposed and experimentally demonstrated. This frequency-swept OEO is achieved by embedding a rapidly frequency-scanning microwave filter in an opto-electronic cavity. The filter has fixed passband while its center frequency scans rapidly and periodically at cavity round-trip time, covering a large frequency range (~GHz). Experimentally, the generated frequency-swept microwave is linear frequency-modulated continuous wave (FMCW) which centers at 7 GHz with 1-GHz bandwidth. Its instantaneous frequency varies linearly from 6.5 GHz to 7.5 GHz, back and forth, in a period of 12.8 μs, resulting in a frequency scanning rate of ~156 MHz/μs. The single-side-band (SSB) noise of the generated FMCW is −104 dBc/Hz at 10 kHz offset frequency, which is much lower than that from a commercial electronic arbitrary waveform generator (E-AWG). Improvement as large as 23 dB is experimentally reported.
We propose and experimentally demonstrate a fully reconfigurable generator of chirped microwave pulses based on the processing of an incoherent optical signal by means of a dispersive element with a non-uniform optical spectral shaping. The system performance has been proven by the generation of different chirped microwave pulses. Different capabilities of the system has been experimentally demonstrated as frequency tunability and TBWP control by means of the dispersive element and optical source power distribution. Furthermore, the possibility for generating chirped microwave pulses with positive and negative chirp characteristic has been shown achieving similar chirps in terms of magnitude but opposite sign. For it, the chirp characteristic is introduced by proper shaping of the optical source signal power distribution.
A photonic approach for generating an arbitrary chirp microwave waveform using optical coupler of different length is proposed and experimentally demonstrated. The chirp microwave waveform can be used in Radar system to improve its range Doppler resolution. The paper give the specific details about various performance parameters like input signal frequency and power, output signal parameters viz output frequency, chirp rate, chirp bandwidth and time bandwidth product etc. In this proposed approach two single mode optical fibers of different lengths are used to create the phase variation of the light coming from the continuous wave laser. The overall model and its performance parameters are computed on optiwave software and compared with experimental results carried out in lab which shows the validity of our experimental setup.
A photonic approach to linearly chirped microwave waveform generation with an extended temporal duration is proposed and experimentally demonstrated. The linearly chirped microwave waveform generation is realized based on spectral-shaping and wavelength-to-time mapping, in which a Fabry-Perot (FP) interferometer with a linearly increasing or decreasing free spectral range is used to as a spectral shaper, and the wavelength-to-time mapping is realized using a recirculating dispersive loop with a large equivalent dispersion coefficient realized by allowing the spectrally shaped optical pulse to travel in the dispersive loop multiple times. The generation of two linearly chirped microwave waveforms at two different frequency bands with two temporal durations of 25 and 42 ns and a time-bandwidth product (TBWP) of 210 is experimentally demonstrated.
In Chirp-Pulse Microwave Computed Tomography (CP-MCT) the images are affected by the blur which is inherent to the measurement principle and is described by a space-variant Point Spread Function (PSF). In this paper we investigate the PSF of CP-MCT including the space dependence both experimentally and computationally. The experimental evaluation is performed by measuring the projections of a target consisting of a thin low-loss dielectric rod surrounded by a saline solution and placed at various positions in the measuring region. On the other hand, the theoretical evaluation is obtained by computing the projections of the same target via a numerical solution of Maxwell's equations. Since CP-MCT uses a chirp signal, the numerical evaluation is carried out by the use of a FD-TD method. The projections of the rod could be obtained by computing the field during the sweep time of the chirp signal for each position of the receiving antenna. Since this procedure is extremely time consuming, we compute the impulse response function of the system by exciting the transmitting antenna with a wide-band Gaussian pulse. Then the signal transmitted in CP-MCT is obtained by computing the convolution product in time domain of the input chirp pulse with the impulse response function of the system. We find a good agreement between measured and computed PSF. The rationality of the computed PSF is verified by three distinct ways and the usefulness of this function is shown by a remarkable effect in the restoration of CP-MCT images. Knowledge on the space-variant PSF will be utilized for more accurate image deblurring in CP-MCT.
We have been investigating microwave imaging system which visualizes biological functions of a human body. The striking feature of our method is use of chirp pulse microwaves for detecting the wave components which transmit on the straight path between two antennas. One of the developed prototype systems performs it in frequency domain and another one does it in time domain. The former is referred to as Chirp Pulse Microwave Computed Tomography (CP-MCT) and the latter is Direct Current Voltage-based Microwave Computed Tomography (DC-MCT). Regardless of the difference in the measuring techniques, both systems provide similar but useful images on biological function. In this study, feasibility of clinical application of the developed imaging systems has been demonstrated by showing the tomograms of tumorembedded breast phantom and forearm phantom developed in our laboratory.
This chapter focuses only on qualitative approaches, which are less ambitious because they either attempt to provide less complete characterization of the scatterers or can be applied only to a particular class of targets. Both the approaches are discussed. However, since many qualitative methods lead to resolution of linear ill-posed problems, some preliminary theory and tools useful in dealing with this class of problems are presented. In particular, the concepts of generalized inverse operators and generalized solutions are addressed, along with one of the most commonly used and powerful tools in linear inverse scattering, the singular value decomposition (SVD). Some basic concepts regarding regularization theory are also briefly introduced, without cumbersome mathematical details. It should be noted that the linear sampling method is only one of the qualitative techniques able to provide the shapes of unknown scatterers. electromagnetic wave scattering; image reconstruction; image sampling; singular value decomposition
We have developed the method for improvement in the receiver dynamic range and signal processing technique of image reconstruction in demodulated direct current voltage-based microwave CT (DC-MCT). By using standard signal generator with the low phase noise and phase synchronization of signal source, the reconstructed amplitude- and phase-images were obtained. Improvement in receiver dynamic range was attempted on the distributed system gains to radio- and low-frequencies. By removing unwanted components of the received signal, the receiver dynamic range was expanded. Two methods for removing unwanted components from the received signal were attempted by using time domain filters to remove all receiver noises from the measurement data. By removing unwanted components, the reconstructed definite tumor images of the breast-and biological-phantoms were obtained. At the result, this paper shows usefulness of the new method that improves the receiver dynamic range and reconstructed images.
We show for the first time that a chirped fiber Bragg grating with specially engineered nonlinear group delay profile can be used to significantly increase the time-bandwidth product of a microwave waveform.
In an earlier paper [E. Beretta, E. Francini and M. S. Vogelius, J. Math. Pures Appl. (9) 82, No. 10, 1277–1301 (2003; Zbl 1089.78003)] we derived an asymptotic formula for the steady state voltage potentials in the presence of thin inhomogeneities. In this paper we extend this result to time harmonic transverse electric Maxwell equations.
A general framework for the development and application of environmental models is reviewed. The problem of the identification of model parameters is described within this framework, and great attention is devoted to specific issues that arise in the application of models whose aim is to answer practical questions for environmental protection or management of natural resources. In particular the stability issue is discussed for discrete models and a definition of ill-conditioning of the inverse problem is given and linked to the time and space scale lengths of the model. Finally, the importance of multiple data sets to limit the uncertainty of the inverse method is shortly discussed.
Frequency-chirped sub-THz pulses are photonically generated by shaped optical pulses (λ=1550 nm) propagating over tens of kMs of optical fiber. The carrier frequency of the sub-THz (MMW) pulse can be frequency swept over 68-130 GHz is demonstrated.
This study is concerned with a technique used for developing a new modality of microwave imaging aiming at noninvasive imaging of biological functions. The paper describes a new technique for transmission analysis of electromagnetic waves in high-loss media. For this purpose, we have combined the equivalent multi-transmission line method in which ion conduction is taken into consideration with the moment method. As a typical problem, this technique has been applied to validate the sandwiched dipole antennas used in microwave imaging by Chirp Pulse Microwave Computed Tomography (CP-MCT). The measurement is done in saline solution to minimize the scattering effects at the body surface. Characteristics of sandwiched dipole antennas developed by trial and error-based learning have been validated almost perfectly by the developed technique. In conclusion, it has been proved that the developed technique is successfully used to find ideal parameters of the antennas which improve the quality in images of CP-MCT.
We have developed demodulated direct current voltage-based microwave CT
(DC-MCT) which is composed on the basis of chirp-pulse microwave CT.
DC-MCT was used time domain measurement technique to determine the
shortest propagation path between the transmitting-and
receiving-antennas. By using standard signal generator with the low
phase noise and phase synchronization of signal source, the
reconstructed amplitude-and phase-images can be obtained. A study of
high speed imaging, the method of measurement and the influence of
overshoot characteristics from the low pass filter were examined, then
these images were evaluated for the number of rotary scanning of 50 and
72. In addition, for the purpose of improvement of resolution, pursuing
a time domain spectrum which gives the max value of amplitude was showed
the possibility to improve receiver dynamic range. At the result, this
paper shows usefulness of new method for microwave imaging.
In this paper we present the integration of multimedia contents in the teaching of Digital Electronic Circuits and Computer Structure, of the first course of Computer Engineering at the University of Seville. Different tools for screenshot and video recording have been used for the preparation of audiovisual material, integrated in the learning platform currently used at the University of Seville. Feedback on the prepared material was collected in a survey, showing the interest and utility found by students in the preparation of theoretical and experimental classes with the videos. Successful results have been obtained in the evaluation of students. Suggestions of improvement and further work to be carried out are also described in the paper.
We propose and demonstrate an optical fiber-based scheme for GHz-frequency microwave pulse generation with full frequency and linear chirp reconfigurability. The scheme incorporates a balanced photodetection strategy to achieve dc-free microwave pulses with significantly improved noise figures.
We propose and demonstrate a microwave chirped pulse generator which is based on the effects of the dispersion slope over the propagation of an optical broadband signal. A complete reconfigurability of the generated signal waveform is easily achieved by a suitable adjustment of the optical source power distribution profile. Moreover, large frequency tuning range and TBWP control of the pulse generated have been also experimentally demonstrated.
Two image reconstruction algorithms for microwave tomography are compared and contrasted. One is a general, gradient-based minimization algorithm. The other is the chirp pulse microwave computed tomography (CP-MCT) method, which is a highly computationally efficient reconstruction method but also a method best suited for low contrasts. The results of the simulations show that when imaging high-contrast objects, such as a breast cancer tumor, reconstructions made are comparable to results from the minimization algorithm below a contrast of about 10%. The simulations, however, show that the reconstructions made by the CP-MCT method are very robust to noise. The reconstruction of the conductivity using the minimization algorithm, on the other hand, is very sensitive to the level of noise. In spite of a strong degradation in the conductivity reconstructions, the corresponding permittivity reconstructions do not show the same sensitivity to the noise level.
Chirp Pulse Microwave Computed Tomography (CP-MCT) that was originally developed for noninvasive imaging of a human body was applied to visualize sugar distribution inside a fruit. It can visualize not only permittivity distribution itself of a fruit but also various physical- or chemical-quantities relating to the permittivity value. Almost all fruits are dielectric materials containing much water, sugar, acids and so on. But for water, the principal ingredient of a fruit is sugar. Most of the fruits contain sugar from 8% to 22% by weight at the harvest time. Therefore sugar content distribution should be measured by CP-MCT nondestructively. By using apples and Japanese pears, feasibility of sugar distribution imaging has been evaluated by comparing the gray level of CP-MCT and sugar content of the cross section. The averaged correlation coefficients of the apple and pear are 0.793 and 0.681.
This paper considers chirp pulse microwave CT (CP-MCT), in which the chirp pulse and signal processing technology are used to estimate the internal structure and temperature variation of biological objects. A method is developed in which the CT image to be acquired by actual measurement can be derived by numerical computation. The aftereffect function between the transmitting and receiving antennas is calculated by a Gaussian pulse and the FDTD method. After convolution of the function with the input chirp pulse signal on the time axis, the measured signal at a point is constructed by the same signal processing as in real measurement. This computation is repeated for each point on the translation-scanning axis. The projection data are acquired and the CT image is generated. The validity of this computation procedure, which is called the aftereffect function method, is demonstrated by comparing the resolution and the measured temperature variation in actual measurements with the results of a simulation computation. Using the aftereffect function method, the point-spread function of an imaging system which is difficult to measure, can be derived. An analytical model for the human head is constructed. Simulations are performed for the attenuation distribution and the temperature variation distribution. Based on the results, the feasibility of the biological imaging by CP-MCT is discussed. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(9): 53–63, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20190
A new 3-D holographic microwave imaging technique is proposed to reconstruct targets in the near-field range. It is based on the Fourier analysis of the wideband transmission and reflection signals recorded by two antennas scanning together along two rectangular parallel apertures on both sides of the inspected region. The complex scattering parameters of the two antennas are collected at several frequencies and then processed to obtain a representation of the 3-D target in terms of 2-D slice images at all desired range locations. No assumptions are made about the incident field and Green's function, which are derived either by simulation or by measurement. Furthermore, an approach is proposed to reduce the image artifacts along range. To validate the proposed technique, predetermined simulated targets are reconstructed. The effects of random noise, number of sampling frequencies, and dielectric contrast of the targets are also discussed.
A new radar technique has been developed that provides a solution for the conflicting requirements of simultaneous long-range and high-resolution performance in radar systems. This technique, called Chirp at Bell Telephone Laboratories, recognizes that resolution depends on the transmitted pulse bandwidth. A long high-duty-factor transmitted pulse, with suitable modulation (linear frequency modulation in the case of Chirp), which covers a frequency interval many times the inherent bandwidth of the envelope, is employed. The receiver is designed to make optimum use of the additional signal bandwidth. This paper contains many of the important analytical methods required for the design of a Chirp radar system. The details of two signal generation methods are considered and the resulting signal waveforms and power spectra are calculated. The required receiver characteristics are derived and the receiver output waveforms are presented. The time-bandwidth product is introduced and related to the effective increase in the performance of Chirp systems. The concept of a matched filter is presented and used as a reference standard in receiver design. The effect of amplitude and phase distortion is analyzed by the method of paired echoes. One consequence of the signal design is the presence of time side lobes on the receiver output pulse analogous to the spatial side lobes in antenna theory. A method to reduce the time side lobes by weighting the pulse energy spectrum is explained in terms of paired echoes. The weighting process is described, and calculated pulse envelopes, weighting network characteristics and deleterious effects are presented. The effects of quadratic phase distortion are analyzed and the resultant pulse envelopes are presented. The receiver response characteristics in the presence of Doppler-shifted signals from moving targets are examined. Schematic ambiguity diagrams are presented for current signal designs.
A microwave tomographic scanner for biomedical applications is presented. It consists of a 64-element circular array with a useful diameter of 20 cm. Electronically scanning the transmitting and receiving antennas allows multiview measurements with no mechanical movement. Imaging parameters-a spatial resolution of 7 mm and a contrast resolution of 1% for a measurement time of 3 s-are appropriate for medical use. Measurements on tissue-simulating phantoms and volunteers, together with numerical simulations, are presented to assess the system for absolute imaging of tissue distribution and for differential imaging of physiological, pathological, and induced changes in tissues.
It is now well demonstrated that hyperthermia can constitute an efficient adjuvant to radiotherapy and chemotherapy in cancer treatment. The precondition of successful results is that hyperthermia treatments are carefully controlled according to more or less well-defined clinical protocols stipulating the most efficient treatment sequences. These protocols imply some constraints concerning the temperature distribution tolerances to be satisfied in the heated volumes in order simultaneously to obtain therapeutic efficiency inside tumoral tissues and to avoid any undesirable burning effect in surrounding healthy tissues.
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This chapter explains super-resolution using case examples, and discusses the classical Rayleigh resolution limit and defines it in terms of the overlap between the images of two-point sources. It is shown that, in the framework of modern Fourier optics, the resolving power is characterized instead by specifying the spatial-frequency band associated with the instrument. Some important features of inversion methods are discussed to the extent that they relate to the assessment of resolution limits. The main difficulty encountered in solving inverse problems is their sensitivity to noise in the data, which can be the source of major instabilities in the solutions. The role of regularization is to prevent such instabilities from occurring. The chapter explains the problem of extrapolating the object spectrum outside the band or the effective band under the assumption that the object vanishes outside some finite known domain. The case of scanning microscopy is considered. The chapter also focuses on confocal microscopy and shows how the use of data inversion techniques allows enhancing the resolving power of such microscopes. The problem of inverse diffraction from plane to plane, which consists of back-propagating toward the source plane a field propagating in free space, is considered.
Minimization problems in Hilbert space with quadratic objective function and closed convex constraint set C are considered. In case the minimum is not unique we are looking for the solution of minimal norm. If a problem is ill-posed, i.e. if the solution does not depend continuously on the data, and if the data are subject to errors then it has to be solved by means of regularization methods. The regularizing properties of some gradient projection methods—i.e. convergence for exact data, order of convergence under additional assumptions on the solution and stability for perturbed data—are the main issues of this paper.
Details the reconstruction of a function from line or plane integrals, with special emphasis on applications in science, radiology and engineering. Both the relevant mathematical theory of the Radon transform and related transforms, and practical questions such as sampling, resolution, stability, and accuracy, are covered. Much space is given to the derivation, analysis and practical examination of reconstruction algorithms, for both standard problems and problems with incomplete data.
A method is described which overcomes the problems of multipath propagation and range ambiguity that is suffered by the single-frequency continuous-wave microwave-imaging system described in part I. This technique is essentially a variation of chrip radar techniques, which have been adapted to time delay and attenuation measurements through a target. The feasibility of discriminating between paths whose differential time delay is on the order of 100 ps is demonstrated. Further, the need for small physical aperture in the transmitting and receiving antennas is demonstrated.
The chirp radar-type microwave computed tomograph (CT) measures the temperature change in a human body noninvasively. The paper examines its feasibility. A chirp pulse signal between 1 and 2 GHz is radiated from the transmitting antenna to the phantom. The transmitted waves are detected by the receiving antenna, which is placed on the opposite side of the object, and the beat signal between the incident wave and the transmitted wave is produced by the mixer. By spectral analysis of the beat signal, only those signals transmitted on the straight line between the transmitting antenna and the receiving antenna are discriminated from multipath signals. The microwave tomogram can therefore be reconstructed easily using the conventional algorithms for an X-ray CT image. The microwave CT can use the chirp signal to remove the influence of multipath signals caused by diffraction and reflection. The imaging of dielectric materials with complicated structures is thus possible. The experimental results using phantoms show that the spatial resolution of this microwave CT is about 10 mm and that a two-dimensional distribution of temperature change can be measured.
The goal of this work is to develop a microwave-based imaging system for hyperthermia treatment monitoring and assessment. Toward this end, a four transmit channel and four receive channel hardware device and concomitant image reconstruction algorithm have been realized. The hardware is designed to measure electric fields (i.e., amplitude and phase) at various locations in a phantom tank with and without the presence of various heterogeneities using standard heterodyning principles. Particular attention has been paid to designing a receiver with better than 115 dB of linear dynamic range which is necessary for imaging biological tissue which often has very high conductivity, especially for tissues with high water content. A calibration procedure has been developed to compensate for signal loss due to three-dimensional radiation in the measured data, since the reconstruction process is only two-dimensional at the present time. Results are shown which demonstrate the stability and accuracy of the measurement system, the extent to which the forward computational model agrees with the measured field distribution when the electrical properties are known, and image reconstructions of electrically unknown targets of varying diameter. In the latter case, images of both the reactive and resistive component of the electrical property distribution have been recoverable. Quantitative information on object location, size, and electrical properties results when the target is approximately one-half wavelength in size. Images of smaller objects lack the same level of quantitative information, but remain qualitatively correct.
A prototype microwave imaging system is evaluated for its ability to recover two-dimensional (2-D) electrical property distributions under transverse magnetic (TM) illumination using multitarget tissue equivalent phantoms. Experiments conducted in a surrounding lossy saline tank demonstrate that simultaneous recovery of both the real and imaginary components of the electrical property distribution is possible using absolute imaging procedures over a frequency range of 300-700 MHz. Further, image reconstructions of embedded tissue-equivalent targets are found to be quantitative not only with respect to geometrical factors such as object size and location but also electrical composition. Quantitative assessments based on full-width half-height criteria reveal that errors in diameter estimates of reconstructed targets are less than 10 mm in all cases, whereas, positioning errors are less than 1 mm in single object experiments but degrade to 4-10 mm when multiple targets are present. Recovery of actual electrical properties is found to be frequency dependent for the real and imaginary components with background values being typically within 10-20% of their correct size and embedded object having similar accuracies as a percentage of the electrical contrast, although errors as high as 50% can occur. The quantitative evaluation of imaging performance has revealed potential advantages in a two-tiered receiver antenna configuration whose measured field values are more sensitive to target region changes than the typical tomographic type of approach which uses reception sites around the full target region perimeter. This measurement strategy has important implications for both the image reconstruction algorithm where there is a premium on minimizing problem size without sacrificing image quality and the hardware system design which seeks to economize on the amount of measured data required for quantitative image reconstruction while maximizing its sensitivity to target perturbations.
Microwave tomographic imaging is one of the new technologies which has the potential for important applications in medicine. Microwave tomographically reconstructed images may potentially provide information about the physiological state of tissue as well as the anatomical structure of an organ. A two-dimensional (2-D) prototype of a quasi real-time microwave tomographic system was constructed. It was utilized to reconstruct images of physiologically active biological tissues such as an explanted canine perfused heart. The tomographic system consisted of 64 special antennae, divided into 32 emitters and 32 receivers which were electronically scanned. The cylindrical microwave chamber had an internal diameter of 360 mm and was filled with various solutions, including deionized water. The system operated on a frequency of 2.45 GHz. The polarization of the incident electromagnetic field was linear in the vertical direction. Total acquisition time was less than 500 ms. Both accurate and approximation methods of image reconstruction were used. Images of 2-D phantoms, canine hearts, and beating canine hearts have been achieved. In the worst-case situation when the 2-D diffraction model was used for an attempt to "slice" three-dimensional (3-D) object reconstruction, we still achieved spatial resolution of 1 to 2 cm and contrast resolution of 5%.
A numerical analysis of the tomographic imaging of the chirp radar-type microwave computed tomography̵Computation of the projected data based on a transfer function method
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