Frequency division transmission imaging and synthetic aperture reconstruction

In synthetic transmit aperture imaging only a few transducer elements are used in every transmission, which limits the signal-to-noise ratio (SNR). The penetration depth can be increased by using all transmitters in every transmission. In this paper, a method for exciting all transmitters in every transmission and separating them at the receiver is proposed. The coding is done by designing narrow-band linearly frequency modulated signals, which are approximately disjointed in the frequency domain and assigning one waveform to each transmitter. By designing a filterbank consisting of the matched filters corresponding to the excitation waveforms, the different transmitters can be decoded at the receiver. The matched filter of a specific waveform will allow information only from this waveform to pass through, thereby separating it from the other waveforms. This means that all transmitters can be used in every transmission, and the information from the different transmitters can be separated instantaneously. Compared to traditional synthetic transmit aperture (STA) imaging, in which the different transmitters are excited sequentially, more energy is transmitted in every transmission, and a better signal-to-noise-ratio is attained. The method has been tested in simulation, in which the resolution and contrast was compared to a standard synthetic transmit aperture system with a single sinusoid excitation. The resolution and contrast was comparable for the two systems. The method also has been tested using the experimental ultrasound scanner RASMUS. The resolution was evaluated using a string phantom. The method was compared to a conventional STA using both sinusoidal excitation and linear frequency modulated (FM) signals as excitation. The system using the FM signals and the frequency division approach yielded the same performance concerning both axial (of approximately equal to 3 wavelengths) and lateral resolution (of approximately equal to 4.5 wavelengths). A SNR measurement showed an increase in SNR of 6.5 dB compared to the system using the conventional STA method and FM signal excitation.     

Conformal ultrasound imaging system for anatomical breast inspection

Ultrasound tomography has considerable potential as a means of breast cancer detection because it reduces the operator-dependency observed in echography. A half-ring transducer array was designed based on breast anatomy, to obtain reflectivity images of the ductolobular structures using tomographic reconstruction procedures. The 3-MHz transducer array comprises 1024 elements set in a 190-degree circular arc with a radius of 100 mm. The front-end electronics incorporate 32 independent parallel transmit/receive channels and a 32-to-1024 multiplexer unit. The transmit and receive circuitries have a variable sampling frequency of up to 80 MHz and 12-bit precision. Arbitrary waveforms are synthesized to improve the signal-to-noise ratio and to increase the spatial resolution when working with low-contrast objects. The setup was calibrated with academic objects and a needle hydrophone to develop the data correction tools and specify the properties of the system. The backscattering field was recorded using a restricted aperture, and tomographic acquisitions were performed with a pair of 0.08-mm-diameter steel wires, a low-contrast 2-D breast phantom, and a breast-shaped phantom containing inclusions. Data were processed with dedicated correction tools and a pulse compression technique. Objects were reconstructed using the elliptical back-projection algorithm.     

Directional velocity estimation using a spatio-temporal encoding technique based on frequency division for synthetic transmit aperture ultrasound

This paper investigates the possibility of flow estimation using spatio-temporal encoding of the transmissions in synthetic transmit aperture imaging (STA). The spatial encoding is based on a frequency division approach. In STA, a major disadvantage is that only a single transmitter (denoting single transducer element or a virtual source) is used in every transmission. The transmitted acoustic energy will be low compared to a conventional focused transmission in which a large part of the aperture is used. By using several transmitters simultaneously, the total transmitted energy can be increased. However, to focus the data properly, the signals originating from the different transmitters must be separated. To do so, the pass band of the transducer is divided into a number of subbands with disjoint spectral support. At every transmission, each transmitter is assigned one of the subbands. In receive, the signals are separated using a simple filtering operation. To attain high axial resolution, broadband spectra must be synthesized for each of the transmitters. By multiplexing the different waveforms on different transmitters over a number of transmissions, this can be accomplished. To further increase the transmitted energy, the waveforms are designed as linear frequency modulated signals. Therefore, the full excitation amplitude can be used during most of the transmission. The method has been evaluated for blood velocity estimation for several different velocities and incident angles. The program Field II was used. A 128-element transducer with a center frequency of 7 MHz was simulated. The 64 transmitting elements were used as the transmitting aperture and 128 elements were used as the receiving aperture. Four virtual sources were created in every transmission. By beamforming lines in the flow direction, directional data were extracted and correlated. Hereby, the velocity of the blood was estimated. The pulse repetition frequency was 16 kHz. Three different setups were investigated with flow angles of 45, 60, and 75 degrees with respect to the acoustic axis. Four different velocities were simulated for each angle at 0.10, 0.25, 0.50, and 1.00 m/s. The mean relative bias with respect to the peak flow for the three angles was less than 2%, 2%, and 4%, respectively.     

Pulse-inversion-based fundamental imaging for contrast detection

Pulse-inversion-based fundamental imaging was experimentally investigated for the enhancement of contrast detection. The pulse-inversion technique involves two firings with inverted waveforms. When the returning echoes from the two firings are summed, the residue signal is limited to even-order harmonics for tissue. However, when the returning echoes are from microbubbles, the fundamental signal is not completely cancelled because the reaction of the bubbles under compression is different from that under rarefaction. Thus, with the application of pulse-inversion technique, the fundamental signal can be used to enhance the contrast-to-tissue ratio. In this paper, B-mode, pulse-inversion-based fundamental images were constructed with various transmit waveforms. Motion artifacts also were studied. The results indicate that the contrast-to-tissue ratio was significantly enhanced compared to that obtained using either conventional, fundamental imaging or second-harmonic imaging. Longer transmit pulses resulted in a better signal-to-noise ratio, but did not noticeably affect the nonlinear response of the bubbles. In addition, the optimal ratio of the magnitude of the positive pulse to that of the negative pulse was unity, in terms of avoiding the uncancelled, third-order response in the fundamental frequency range. It also was found that the pulse-inversion fundamental technique is highly sensitive to tissue motion because the fundamental tissue signal is not cancelled when motion is present.     

Optimization of a phased-array transducer for multiple harmonic imaging in medical applications: frequency and topology

Second-harmonic imaging is currently one of the standards in commercial echographic systems for diagnosis, because of its high spatial resolution and low sensitivity to clutter and near-field artifacts. The use of nonlinear phenomena mirrors is a great set of solutions to improve echographic image resolution. To further enhance the resolution and image quality, the combination of the 3rd to 5th harmonics--dubbed the superharmonics--could be used. However, this requires a bandwidth exceeding that of conventional transducers. A promising solution features a phased-array design with interleaved low- and high-frequency elements for transmission and reception, respectively. Because the amplitude of the backscattered higher harmonics at the transducer surface is relatively low, it is highly desirable to increase the sensitivity in reception. Therefore, we investigated the optimization of the number of elements in the receiving aperture as well as their arrangement (topology). A variety of configurations was considered, including one transmit element for each receive element (1/2) up to one transmit for 7 receive elements (1/8). The topologies are assessed based on the ratio of the harmonic peak pressures in the main and grating lobes. Further, the higher harmonic level is maximized by optimization of the center frequency of the transmitted pulse. The achievable SNR for a specific application is a compromise between the frequency-dependent attenuation and nonlinearity at a required penetration depth. To calculate the SNR of the complete imaging chain, we use an approach analogous to the sonar equation used in underwater acoustics. The generated harmonic pressure fields caused by nonlinear wave propagation were modeled with the iterative nonlinear contrast source (INCS) method, the KZK, or the Burger's equation. The optimal topology for superharmonic imaging was an interleaved design with 1 transmit element per 6 receive elements. It improves the SNR by ~5 dB compared with the interleaved (1/2) design reported in literature. The optimal transmit frequency for superharmonic echocardiography was found to be 1.0 to 1.2 MHz. For superharmonic abdominal imaging this frequency was found to be 1.7 to 1.9 MHz. For 2nd-harmonic echocardiography, the optimal transmit frequency of 1.8 MHz reported in the literature was corroborated with our simulation results.     

Mutual interference and low probability of interception capabilities of noise radar

Recently, there has been considerable interest in noise radar over a wide spectrum of applications, such as through-wall surveillance, tracking, Doppler estimation, polarimetry, interferometry, ground penetrating or subsurface profiling, detection, synthetic aperture radar (SAR) imaging, inverse SAR imaging, foliage penetration imaging etc. Major advantages of using noise in the transmit signal are its inherent immunity from radio frequency and electromagnetic interference, improved spectrum efficiency, and hostile jamming as well as being very difficult to detect. The basic theory of digital signal processing in noise radar design is treated. The theory supports the use of noise waveforms for radar detection and imaging in such applications as covert military surveillance and reconnaissance. It is shown that by using wideband noise waveforms, one can achieve high resolution and reduced range estimation ambiguity. Mutual interference and low probability of interception capabilities of noise radar are also evaluated. The simulation results show the usefulness of the noise radar technology to improve on conventional radars.     

Design of chirp excitation waveform for dual-frequency harmonic contrast detection

Tissue background suppression is essential for harmonic detection of ultrasonic contrast microbubbles. To reduce the tissue harmonic amplitude for improvement of contrast-to-tissue ratio (CTR), the method of third harmonic (3f₀) transmit phasing uses an additional 3f₀ transmit signal to provide mutual cancellation between the frequency-sum component and the frequency-difference component of tissue harmonic signal. Chirp excitation can further improve the SNR in harmonic imaging without requiring an excessive transmit pressure and thus reduce potential bubble destruction. However, for effective suppression of tissue harmonic background in 3f₀ transmit phasing, the 3f₀ chirp waveform has to be carefully designed for the generation of spectrally matched cancellation pairs over the entire second harmonic band. In this study, we proposed a chirp waveform suitable for the method of 3f₀ transmit phasing, the different-bandwidth chirp signal (DBCS). With the DBCS waveform, the frequency-difference component of tissue harmonic signal becomes a chirp signal similar to its frequency-sum counterpart. Thus, the combination of the DBCS waveform with the 3f₀ transmit phasing can markedly suppress the tissue harmonic amplitude for CTR improvement together with effective SNR increase of contrast harmonic signal. Our results indicate that, as compared with the conventional Gaussian pulse, the DBCS waveform can provide 6-dB improvement of SNR in 3f₀ transmit phasing with a CTR increase of 3 dB. Nevertheless, the limitation of available transmit bandwidth and the frequency-dependent attenuation can degrade the performance of the DBCS waveform in tissue suppression. The design of the DBCS waveform is also applicable to other dual-frequency imaging techniques that rely on the harmonic generation at the difference frequency.     

Transmit beamforming for optimal second-harmonic generation

A simulation study of transmit ultrasound beams from several transducer configurations is conducted to compare second-harmonic imaging at 3.5 MHz and 11 MHz. Second- harmonic generation and the ability to suppress near field echoes are compared. Each transducer configuration is defined by a chosen f-number and focal depth, and the transmit pressure is estimated to not exceed a mechanical index of 1.2. The medium resembles homogeneous muscle tissue with nonlinear elasticity and power-law attenuation. To improve computational efficiency, the KZK equation is utilized, and all transducers are circular-symmetric. Previous literature shows that second-harmonic generation is proportional to the square of the transmit pressure, and that transducer configurations with different transmit frequencies, but equal aperture and focal depth in terms of wavelengths, generate identical second-harmonic fields in terms of shape. Results verify this for a medium with attenuation f1. For attenuation f1.1, deviations are found, and the high frequency subsequently performs worse than the low frequency. The results suggest that high frequencies are less able to suppress near-field echoes in the presence of a heterogeneous body wall than low frequencies.     

Golay-encoded excitation for dual-frequency harmonic detection of ultrasonic contrast agents

Golay-encoded excitation in combination with the third harmonic (3f?) transmit phasing is examined for both signal-to-noise ratio (SNR) and contrast-to-tissue ratio (CTR) improvements in harmonic imaging of contrast microbubbles. To produce the cancellation pair of tissue harmonic signal in 3f? transmit phasing, the phase of the bit waveform is properly designed for both the fundamental and the 3f? transmit signals to provide the Golay encoding of the received harmonic responses. Results indicate that the proposed Golay excitation can effectively suppress the tissue harmonic amplitude to increase CTR. Meanwhile, the SNR of the contrast harmonic signal also improves because of the elongated waveform of Golay excitation. Nevertheless, the generation of marked range side-lobes of the bubble region would degrade the achievable SNR improvement and the image contrast, especially when the bit of Golay excitation increases. The range side-lobes could result from the nonlinear resonance of the microbubbles that interferes with the phase modulation of the Golay encoding.     

Synthetic aperture imaging for small scale systems

Multi-element synthetic aperture imaging methods suitable for applications with severe cost and size limitations are explored. Array apertures are synthesized using an active multi-element receive subaperture and a multi-element transmit subaperture defocused to emulate a single-element spatial response with high acoustic power. Echo signals are recorded independently by individual elements of the receive subaperture. Each method uses different spatial frequencies and acquisition strategies for imaging, and therefore different sets of active transmit/receive element combinations. Following acquisition, image points are reconstructed using the complete data set with full dynamic focus on both transmit and receive. Various factors affecting image quality have been evaluated and compared to conventional imagers through measurements with a 3.5 MHz, 128-element transducer array on different gel phantoms. Multielement synthetic aperture methods achieve higher electronic signal to noise ratio and better contrast resolution than conventional synthetic aperture techniques, approaching conventional phased array performance     

Evaluation of the radiation pattern of a split aperture linear phased array for high frequency imaging

Developing transducer arrays for high frequency medical imaging is complicated because of the extremely small size and spacing of the array elements. For example, a 50 MHz linear phased array requires a center-to-center spacing of only 15 mum (one-half wavelength in water) to avoid the formation of grating lobes in the radiation pattern of the array. Fabricating an array with these dimensions is difficult using conventional technology. A split aperture design that permits much larger element spacing (3 to 4 times) while avoiding the formation of grating lobes is described. The 3-D radiation pattern of a 1.9x1.4 mm, 50-MHz split aperture linear phased array with 33 transmit elements and 33 receive elements has been evaluated theoretically. The azimuthal beam width is 90 mum at a distance of 4.0 mm. Grating lobes are suppressed by at least 60 dB at distances >4.0 mm (~f/2). The elevation beam width is 220 mum at 4.0 mm, and a useful depth of field over the axial range from 4 to 10 mm is obtained.     

Spatial encoding using a code division technique for fast ultrasound imaging

This paper describes a method for spatial encoding in synthetic transmit aperture ultrasound imaging. This allows several ultrasonic sources to be active simultaneously. The method is based on transmitting pseudorandom sequences to spatially encode the transmitters. The data can be decoded after only one transmission using the knowledge of the transmitted code sequences as opposed to other spatial encoding techniques, such as Hadamard or Golay encoding. This makes the method less sensitive to motion, and data can be acquired using fewer transmissions. The aim of this paper is to analyze the underlying theory and to test the feasibility in a physical system. The method has been evaluated in simulations using Field II in which the point-spread functions were simulated for different depths for a 7 MHz linear array transducer. A signal-to-noise ratio (SNR) simulation also was included in the study in which an improvement in SNR of approximately 1.5 dB was attained compared to the standard synthetic transmit aperture (STA) firing scheme. Considering the amount of energy transmitted, this value is low. A plausible explanation is given that is verified in simulation. The method also was tested in an experimental ultrasound scanner and compared to a synthetic transmit aperture ultrasound imaging scheme using a sinusoidal excitation. The performance of the proposed method was comparable to the reference with respect to axial and lateral resolution, but it displayed poorer contrast with sidelobe levels at approximately - 40 dB compared to the mainlobe.     

Reducing inter-element acoustic crosstalk in capacitive micromachined ultrasound transducers

The inter-element acoustic crosstalk problem in capacitive micromachined ultrasound transducer (CMUT) arrays is discussed in this paper. A transfer function matrix approach was used to derive modified transmit waveforms on adjacent elements to reduce the apparent acoustic crosstalk. The significance of this is that this technique relies on programmable waveforms, so that it yields a reduced crosstalk effect with no additional fabrication complexity if the requisite programmable waveform transmit circuits are available. The crosstalk reduction achieved by this method also was examined in combination with conventional (physical separation-based) crosstalk reduction approaches. A CMUT transducer array structure was simulated in a two-dimensional (2-D) model using finite element analysis (FEA), and the crosstalk reduction method was tested for both small and large alternating current (AC) (ultrasonic) excitation conditions. A 25 dB crosstalk reduction was achieved for small AC excitation conditions in which approximately linear operation is encountered. When the AC excitation amplitude was large compared to the direct current (DC) bias, an "iterative harmonic cancellation" approach (also based on programmable waveform techniques) could be applied in combination with the crosstalk reduction method to minimize the inherently transmitted harmonics, and a similar crosstalk reduction effect of 25.5 dB was achieved. This method also can be combined with other structure-modification based crosstalk reduction approaches.     

A study of synthetic-aperture imaging with virtual source elements in B-mode ultrasound imaging systems

We propose an all point transmit and receive focusing method based on transmit synthetic focusing combined with receive dynamic focusing in a linear array transducer. In the method, on transmit, a virtual source element is assumed to be located at the transmit focal depth of conventional B-mode imaging systems, and transmit synthetic focusing is used in two half planes, one before and the other after the transmit focal depth, using the RF data of each scanline, together with all other relevant RF scanline data previously stored. The proposed new method uses the same data acquisition scheme as the conventional focusing method while maintaining the same frame rate via high-speed signal processing, but it is not suitable for imaging moving objects. It improves upon the lateral resolution and sidelobe level at all imaging depths. Also, it increases the transmit power and image signal-to-noise ratio (SNR), due to transmit field synthesis, and extends the image penetration depth as well. Evaluations with simulation and experimental data show much improvement in resolution and SNR at all imaging depths.     

Use of modulated excitation signals in medical ultrasound. Part III: High frame rate imaging

This paper, the last from a series of three papers on the application of coded excitation signals in medical ultrasound, investigates the possibility of increasing the frame rate in ultrasound imaging by using modulated excitation signals. Linear array-coded imaging and sparse synthetic transmit aperture imaging are considered, and the trade-offs between frame rate, image quality, and SNR are discussed. It is shown that FM codes can be used to increase the frame rate by a factor of two without a degradation in image quality and by a factor of 5, if a slight decrease in image quality can be accepted. The use of synthetic transmit aperture imaging is also considered, and it is here shown that Hadamard spatial encoding in transmit with FM emission signals can be used to increase the frame rate by 12 to 25 times with either a slight or no reduction in signal-to-noise ratio and image quality. By using these techniques a complete ultrasound-phased array image can be created using only two emissions.     

Coherent array imaging using phased subarrays. Part II: simulations and experimental results

The basic principles and theory of phased subarray (PSA) imaging imaging provides the flexibility of reducing the number of front-end hardware channels between that of classical synthetic aperture (CSA) imaging--which uses only one element per firing event--and full-phased array (FPA) imaging-which uses all elements for each firing. The performance of PSA generally ranges between that obtained by CSA and FPA using the same array, and depends on the amount of hardware complexity reduction. For the work described in this paper, we performed FPA, CSA, and PSA imaging of a resolution phantom using both simulated and experimental data from a 3-MHz, 3.2-cm, 128-element capacitive micromachined ultrasound transducer (CMUT) array. The simulated system point responses in the spatial and frequency domains are presented as a means of studying the effects of signal bandwidth, reconstruction filter size, and subsampling rate on the PSA system performance. The PSA and FPA sector-scanned images were reconstructed using the wideband experimental data with 80% fractional bandwidth, with seven 32-element subarrays used for PSA imaging. The measurements on the experimental sector images indicate that, at the transmit focal zone, the PSA method provides a 10% improvement in the 6-dB lateral resolution, and the axial point resolution of PSA imaging is identical to that of FPA imaging. The signal-to-noise ratio (SNR) of PSA image was 58.3 dB, 4.9 dB below that of the FPA image, and the contrast-to-noise ratio (CNR) is reduced by 10%. The simulated and experimental test results presented in this paper validate theoretical expectations and illustrate the flexibility of PSA imaging as a way to exchange SNR and frame rate for simplified front-end hardware.     

Adaptive ultrasonic measurement of blood vessel diameter and wall thickness: theory and experimental results

An adaptive ultrasonic technique for measuring blood vessel diameter and wall thickness is presented. This technique allows one to use a target-specific transmitted waveform/receiver filter to obtain a larger signal-to-noise ratio (SNR) in the received signal than conventional techniques. Generally, SNR of a received wave increases as the intensity of the transmit wave increases; however, because of the FDA limitations placed on the amount of transmit energy, it is important to be able to make the most efficient use of the energy that is available to obtain the best possible SNR in the received signal. Adaptive ultrasonic measurement makes the most efficient use of the energy that is available by placing the maximum amount of energy in the largest target scattering mode. This results in more energy backscatter from a given target, which leads to a higher SNR in the received waveform. Computer simulations of adaptive ultrasonic measurement of blood vessel diameter show that for a SNR of 0 dB in the transmitted waveform, the standard deviation of the diameter measurements for a custom-designed transmitted waveform is about two orders of magnitude less than the standard deviation of the diameter measurements using more conventional waveforms. Diameter and wall thickness measurement experiments were performed on a latex tube and a bovine blood vessel using both custom-made and conventionally used transmitted waveforms. Results show that the adaptively designed waveform gives a smaller uncertainty in the measurements. The adaptive ultrasonic blood vessel diameter and wall thickness measuring technique has potential applications in examining vessels which are either too deep inside the body or too small for conventional techniques to be used, because of the low SNR in the received signal.     

Probing acoustic fields of clinically relevant transducers: the effect of hydrophone probes' finite apertures and bandwidths

The influence of finite aperture and frequency response of piezoelectric ultrasonic hydrophone probes on the free-field pulse intensity integral (PII) and mechanical index (MI) was investigated using a comprehensive acoustic wave propagation model. The model developed was capable of predicting the true pressure-time waveforms at virtually any point in the field. The input to the model used pressure amplitude data measured in the immediate vicinity of the acoustic source or transducer considered. The experimental verification of the model was obtained using a commercially available, 8 MHz, dynamically focused linear array and a single element, 5 MHz, focused rectangular source. The verification was performed at low and high excitation levels, corresponding to linear and nonlinear acoustic wave propagation, respectively. The pressure-time waveforms were recorded using piezoelectric polymer hydrophone probes that had different sensitivities, frequency responses, bandwidths, and active element diameters. The nominal diameters of the probes ranged from 50 to 500 microm, and their useable bandwidths varied between 55 and 100 MHz. The PII, used to calculate the thermal index (TI), was found to increase with increasing bandwidth and decreasing effective aperture of the probes. The MI, another safety indicator, also was affected, but to a lesser extent. The corrections predicted using the model were used to reduce discrepancies as large as 30% in the determination of PII. The results of this work indicate that, by accounting for hydrophones' finite aperture and correcting the value of PII, all intensities derived from the PII can be corrected for spatial averaging error. The results also point out that caution should be exercised when comparing acoustic output data. In particular, hydrophone's frequency characteristics of the effective diameter and sensitivity are needed to correctly determine the MI, TI, and the total acoustic output power produced by an imaging transducer.     

A 256 x 256 2-D array transducer with row-column addressing for 3-D rectilinear imaging

We present simulation and experimental results from a 5-MHz, 256times256 2-D (65536 elements, 38.4times38.4 mm) 2-D array transducer with row-column addressing. The main benefits of this design are a reduced number of interconnects, a modified transmit/receive switching scheme with a simple diode circuit, and an ability to perform volumetric imaging of targets near the transducer with transmit beamforming in azimuth and receive beamforming in elevation. The final dimensions of the transducer were 38.4 mm times 38.4 mm times 300 mum. After a row-column transducer was prototyped, the series resonance impedance was 104 Omega at 5.4 MHz. The measured -6 dB fractional bandwidth was 53% with a center frequency of 5.3 MHz. The SNR at the transmit focus was measured to be 30 dB. At 5 MHz, the average nearest neighbor crosstalk was -25 dB. In this paper, we present 3-D images of both 5 pairs of nylon wires embedded in a clear gelatin phantom and an 8 mm diameter cylindrical anechoic cyst phantom acquired from a 256 times 256 2-D array transducer made from a 1-3 composite. We display the azimuth and elevation B-scans as well as the C-scan for each image. The cross-section of the wires is visible in the azimuth B-scan, and the long axes can be seen in the elevation B-scan and C-scans. The pair of wires with 1-mm axial separation is discernible in the elevational B-scan. When a single wire from the wire target phantom was used, the measured lateral beamwidth was 0.68 mm and 0.70 mm at 30 mm depth in transmit beamforming and receive beamforming, respectively, compared with the simulated beamwidth of 0.55 mm. The cross-section of the cyst is visible in the azimuth B-scan whereas the long axes can be seen as a rectangle in the elevation B-scan and C-scans.     

Simulation of Transient Response of Ir-TES for Position-Sensitive TES with Waveform Domain Multiplexing

We are developing a new x-ray microcalorimeter based on a superconducting transition edge sensor (TES) as an imaging sensor. Our measurement shows unique waveforms which we consider as an expression of thermal nonuniformity of TES films. This arises from the different thermal responses, so that response signal shapes would vary according to the position of the incident x-ray. This position dependency deteriorate the measured energy resolution, but with appropriate waveform analysis, this would be useful for imaging device. For more inspection, we have developed a simulation code which enables a dynamic simulation to obtain a transient response of the TES by finite differential method. Temperature and electric current distributions are calculated. As a result, we successfully obtained waveform signals. The calculated signal waveforms have similar characteristics to the measured signals. This simulation visualized the transition state of the device and will help to design better detector.