Two-dimensional Fast Fourier Research Articles

Quantitative Image Quality Measurements of a Digital Breast Tomosynthesis System

The aim of this study was to measure the image quality of a digital breast tomosynthesis (DBT) system quantitatively. The signal transfer property (STP), modulation transfer function (MTF), noise power spectrum (NPS), and detective quantum efficiency (DQE) of the Hologic Selenia Dimensions breast tomosynthesis system were measured according to established methods. The NPS was calculated from two-dimensional (2 D) fast Fourier transform (FFT) of flat field images. The presampling MTF of the system was determined for 2 D standard projection mammography and 3 D breast tomosynthesis mode using the edge method. The DQE was derived for different detector air kerma (DAK) values from NPS and MTF measurements. The detector response function was linear for both two-dimensional (2 D) standard projection mammography and three-dimensional (3 D) breast tomosynthesis modes. The gradient of the detector response in the 3 D imaging mode was higher than the gradient in the 2 D imaging mode by a factor of 3.1. The MTF values measured at the Nyquist frequency were 32 % and 39 % in 2 D and 3 D imaging modes, respectively. The DQE was saturated at an air kerma value approximately 3.5 times lower in 3 D mode than in 2 D mode. The measured maximum DQE value was 54 %. The measured DQE values were comparable with breast tomosynthesis systems from other companies (Siemens, GE).

Fabrication of broadband poly(vinylidene difluoride-trifluroethylene) line-focus ultrasonic transducers for surface acoustic wave measurements of anisotropy of a (1 0 0) silicon wafer

This paper investigates a new method for fabrication of broadband line-focus ultrasonic transducers by sol–gel spin-coating the poly(vinylidene difluoride-trifluroethylene) [P(VDF-TrFE)] copolymer film on a concave fine-polished beryllium copper backing. The ferroelectric hysteresis loops of the P(VDF-TrFE) films spin-coated from different molar ratios of VDF/TrFE, 77/23 and 55/45, were measured to select the better mixture. Owing to the better acoustic matching to water, compared with lead zirconate titanate (PZT), the fabricated transducers show relatively wide bandwidth of approximately 50MHz with high central frequency of 60MHz obtained at the focal plane when a fused-quartz acts as a reflecting target. Each one of the two finished transducers has a focal length of 5mm and a full aperture angle of 90°. After applying the specially developed digital signal processing algorithm to the defocusing experiment data, which is called V(f,z) analysis method based on two-dimensional fast Fourier transform (2-D FFT), the operating frequency can extend from several MHz to over 90MHz. Surface acoustic wave (SAW) velocities of a typical (100) silicon wafer was measured along various directions between [100] and [010] to represent the anisotropic features.

Windowed Fourier transform as an essential digital interferometry tool to study coupled heat and mass transfer

Abstract Series of thermodiffusion experiments using optical digital interferometry (ODI) have been conducted onboard the International Space Station. Conventionally, the two-dimensional (2D) fast Fourier transform (FFT) fringe analysis technique has been applied as a fast and reliable technique to extract data. In this study, for the first time, the windowed Fourier transform (WFT) method is used to analyze the same experiments. In this method, a Fourier transformation is applied on the fringes at two different stages: initially, during the filtration of the non-zero peaks and then on the wrapped phase image. We provide a detailed comparison between FFT and WFT results of binary and ternary mixtures for ODI thermodiffusion experiments. The substantial enhancements of this method are presented and discussed for different experiments conducted for both binary and ternary mixtures. We show that while disturbances in the phase fringe pattern can cause significant error in FFT techniques, if the windowed Fourier filtration (WFF) parameters are properly chosen this type of noise can be eliminated during WFF analysis. The importance of replacing the FFT method becomes more pronounced for the ternary system, as this method fails to reconcile reliable concentration profiles. The results of this work can show that the application of the windowed Fourier transform in optical digital interferometry investigations show improved results over the same experiments analyzed using FFT methods, especially for experiments involving very small heat and mass fluxes such as the Soret effect in multicomponent mixtures.

Scattering Characteristics of Targets above a Rough Surface in SAR Images

The modeling, simulation, and analysis of target characteristics are essential to a synthetic aperture radar (SAR) image-based autotarget recognition (ATR) system. The coupling effect between targets and rough surface is also important to the electromagnetic scattering and remote sensing. In this work, the simulations to SAR images of targets above a finite rough surface have been investigated. The effect of rough surface on the target characteristics, or the coupling between the rough surface and targets, is analyzed in details by observing changes of locations and intensities of scattering centers in the SAR images. The SAR images are obtained by taking two-dimensional inverse fast Fourier transforms (FFTs) of the scattered fields, which are computed by the combined high-frequency method of shooting and bouncing ray (SBR) and truncated-wedge incremental-length diffraction coefficients (TW-ILDCs). Simulated results of SAR images for complicated targets above a rough surface are given under the 0.25 × 0.25 m2resolution at the X band, in which the coupling effect between targets and rough surface has been studied in details.

DOA and Doppler Frequency Estimation Based on Sub-aperture MUSIC

Most available algorithms for DOA estimation in monostatic MIMO radar involve the computation of covariance matrix and its inversion or eigendecomposition, of which the computational complexity is expensive, especially in the case that both the number of sensors and snapshots are large. To solve this problem, a high-resolution algorithm for joint direction-of-arrival (DOA) and Doppler Frequency estimation based on sub-aperture MUSIC in monostatic MIMO radar is presented. Firstly, the received data matrix form each transmitter is evenly divided into four sub-blocks. Then two-dimensional fast Fourier transforms (2D-FFTs) is applied to each sub-block in order to achieve coherent integration. By utilizing the data corresponding to the peaks of coherent integration in each sub-block, a reduced-dimensional data vector is constructed for joint DOA and Doppler frequency estimation via root-MUSIC. Since the full-dimensional covariance matrix estimation and eigendecomposition are avoided, the computational complexity is relatively small. Simulation results demonstrate the effectiveness of the proposed method with slightly better performance than that of ESPRIT-based method.

Patellar tendon morphology in volleyball athletes with and without patellar tendinopathy

Appropriate management of patellar tendinopathy requires distinguishing between inflammatory and degenerative conditions, often difficult because tendon thickening can be a normal or pathological adaptation, and micromorphology is not observable on clinical imaging. The purpose of this study was to quantitatively examine patellar tendon micro- and macromorphology in volleyball athletes and relate those findings to reported symptoms. Longitudinal ultrasound images of proximal and distal patellar tendons were acquired from 84 male elite volleyball athletes (44 symptomatic, 40 asymptomatic) and 10 asymptomatic nonathlete controls. Micromorphology was determined using two-dimensional Fast Fourier Transform analysis providing a discriminating peak spatial frequency parameter (PSF). Macromorphology (patellar tendon thickness) was measured using Image J software. All athletes regardless of symptoms had thicker proximal tendons compared to nonathletes, suggesting a normal adaptation to training loads. However, symptomatic athletes demonstrated lower PSF than asymptomatic athletes and nonathletes at the proximal tendon, suggesting greater collagen disorganization, and tendon degeneration rather than inflammation. Only symptomatic athletes had thicker distal tendons than nonathletes, but there was no difference in PSF distally. Diagnostic ultrasound enhances the understanding of the micromorphology of patellar tendons, supporting the rationale for management that remodels the degenerated tendon instead of treating inflammation.

Dimensional stability of electrospun membranes of poly(l-lactide-co-glycolide)/poly(l-lactide-co-glycolide)-b-polyethylene glycol blends under stretch

Control of dimensional stability is crucial for using electrospun membranes in biomedical and tissue engineering applications. In this study, the contraction of electrospun membranes of poly(l-lactide-co-glycolide) (PLLGA) after stretch was investigated. Then, by adding PLLGA-b-polyethylene glycol (PLLGA-PEG), the contraction of the membranes was controlled. In addition, the mechanical properties of the membranes were investigated. On the basis of the strain–stress behavior of the membranes, an elongation of 50 % was used to investigate the orientation degrees of the membrane fibers. On the basis of the morphology of the stretched membranes, the contraction was found to depend on the orientation degree of fibers after stretch. A linear relationship between the contraction and degree of orientation after stretch was confirmed. Two-dimensional fast Fourier transform (2D FFT) analysis of the scanning electron microscopy (SEM) images of the membranes was used to quantify the orientation degree. It was surmised that the different orientation degrees were responsible for the different morphologies and thermal behaviors of the membranes.

Nanoscale structure of type I collagen fibrils: Quantitative measurement of D‐spacing

This article details a quantitative method to measure the D-periodic spacing of type I collagen fibrils using atomic force microscopy coupled with analysis using a two-dimensional fast fourier transform approach. Instrument calibration, data sampling and data analysis are discussed and comparisons of the data to the complementary methods of electron microscopy and X-ray scattering are made. Examples of the application of this new approach to the analysis of type I collagen morphology in disease models of estrogen depletion and osteogenesis imperfecta (OI) are provided. We demonstrate that it is the D-spacing distribution, not the D-spacing mean, that showed statistically significant differences in estrogen depletion associated with early stage osteoporosis and OI. The ability to quantitatively characterize nanoscale morphological features of type I collagen fibrils will provide important structural information regarding type I collagen in many research areas, including tissue aging and disease, tissue engineering, and gene knockout studies. Furthermore, we also envision potential clinical applications including evaluation of tissue collagen integrity under the impact of diseases or drug treatments.

Type I Collagen D-Spacing in Fibril Bundles of Dermis, Tendon, and Bone: Bridging between Nano- and Micro-Level Tissue Hierarchy

Fibrillar collagens in connective tissues are organized into complex and diverse hierarchical networks. In dermis, bone, and tendon, one common phenomenon at the micrometer scale is the organization of fibrils into bundles. Previously, we have reported that collagen fibrils in these tissues exhibit a 10 nm width distribution of D-spacing values. This study expands the observation to a higher hierarchical level by examining fibril D-spacing distribution in relation to the bundle organization. We used atomic force microscopy imaging and two-dimensional fast Fourier transform analysis to investigate dermis, tendon, and bone tissues. We found that, in each tissue type, collagen fibril D-spacings within a single bundle were nearly identical and frequently differ by less than 1 nm. The full 10 nm range in D-spacing values arises from different values found in different bundles. The similarity in D-spacing was observed to persist for up to 40 μm in bundle length and width. A nested mixed model analysis of variance examining 107 bundles and 1710 fibrils from dermis, tendon, and bone indicated that fibril D-spacing differences arise primarily at the bundle level (∼76%), independent of species or tissue types.

Reconstruction of nonstationary sound fields based on the time domain plane wave superposition method

A time-domain plane wave superposition method is proposed to reconstruct nonstationary sound fields. In this method, the sound field is expressed as a superposition of time convolutions between the estimated time-wavenumber spectrum of the sound pressure on a virtual source plane and the time-domain propagation kernel at each wavenumber. By discretizing the time convolutions directly, the reconstruction can be carried out iteratively in the time domain, thus providing the advantage of continuously reconstructing time-dependent pressure signals. In the reconstruction process, the Tikhonov regularization is introduced at each time step to obtain a relevant estimate of the time-wavenumber spectrum on the virtual source plane. Because the double infinite integral of the two-dimensional spatial Fourier transform is discretized directly in the wavenumber domain in the proposed method, it does not need to perform the two-dimensional spatial fast Fourier transform that is generally used in time domain holography and real-time near-field acoustic holography, and therefore it avoids some errors associated with the two-dimensional spatial fast Fourier transform in theory and makes possible to use an irregular microphone array. The feasibility of the proposed method is demonstrated by numerical simulations and an experiment with two speakers.

Evaluation of mechanical stimulation effect on cellular orientation under confluence based on 2D-FFT and principal component analysis

Mechanical stress plays an important role in cellular alignment. Here we evaluated the effect of applying mechanical stimulation to a muscular cell sheet by the combination of two-dimensional fast Fourier transform (2D-FFT) and principal component analysis. In the conventional methods, all the cells must be recognized by a software image analysis program. This means it is difficult to evaluate the cell orientation non-invasively under confluence like in a cell sheet. Our proposed method which treats an image as one pattern is able to evaluate the cellular orientation from only a microscopic image of cells even under confluence. In order to stimulate the cell sheet with arbitrary patterns, we developed a uniaxial multi-pattern stimulation system. C2C12 myoblast cell sheets were stimulated with mechanical stress under various conditions. Each stretch pattern consisted of three cyclic stretches and a subsequent quiescent time. The myoblasts were aligned perpendicularly to the stretch direction as has been reported in a number of previous studies. A highly aligned myoblast sheet was obtained when the cells were stimulated mechanically at a stretch rate of 15 % and a quiescent time of 1 min. Shortened stretches were also applied, but they did not align the cells well compared to the extended stretches. These results indicate that our proposed method based on the image analysis is appropriate to evaluate the cell alignment under confluence.

Saccharomyces cerevisiae Dmc1 and Rad51 Proteins Preferentially Function with Tid1 and Rad54 Proteins, Respectively, to Promote DNA Strand Invasion during Genetic Recombination

The Saccharomyces cerevisiae Dmc1 and Tid1 proteins are required for the pairing of homologous chromosomes during meiotic recombination. This pairing is the precursor to the formation of crossovers between homologs, an event that is necessary for the accurate segregation of chromosomes. Failure to form crossovers can have serious consequences and may lead to chromosomal imbalance. Dmc1, a meiosis-specific paralog of Rad51, mediates the pairing of homologous chromosomes. Tid1, a Rad54 paralog, although not meiosis-specific, interacts with Dmc1 and promotes crossover formation between homologs. In this study, we show that purified Dmc1 and Tid1 interact physically and functionally. Dmc1 forms stable nucleoprotein filaments that can mediate DNA strand invasion. Tid1 stimulates Dmc1-mediated formation of joint molecules. Under conditions optimal for Dmc1 reactions, Rad51 is specifically stimulated by Rad54, establishing that Dmc1-Tid1 and Rad51-Rad54 function as specific pairs. Physical interaction studies show that specificity in function is not dictated by direct interactions between the proteins. Our data are consistent with the hypothesis that Rad51-Rad54 function together to promote intersister DNA strand exchange, whereas Dmc1-Tid1 tilt the bias toward interhomolog DNA strand exchange.

Fast Fourier Transform–Based Analysis of Second-Harmonic Generation Image in Keratoconic Cornea

To qualify and quantify structural alterations in keratoconic corneas ex vivo by the use of second-harmonic generation (SHG) microscopy and two-dimensional fast Fourier transform (2D-FFT) analysis. Two keratoconic and three normal human corneal specimens were imaged with a multiphoton microscope. Forward and backward second-harmonic generation images (FSHG and BSHG) of corneal stroma were obtained at high resolution and at different depths. The SHG images were further analyzed with a 2D-FFT algorithm to quantify the texture and orientation changes of collagen fibers. The results showed that the abnormality of collagen architecture was found through the whole layer of stroma. 2D-FFT analysis of SHG cornea images provided fiber orientation direction and an aspect ratio (AR) as a quantitative measure of fiber direction determination. It was found that for keratoconic cornea the average AR values are statistically greater than those of the normal cornea: 1.66 ± 0.42 (case I keratoconic cornea), 1.72 ± 0.44 (case II keratoconic cornea), and 1.34 ± 0.16 (average of three normal human corneas). Furthermore, the fiber directions determined by 2D-FFT analysis of BSHG and FSHG images were strongly correlated for large AR values (AR > 2). The high correlation between FSHG and BSHG fiber direction for large AR values shows that BSHG imaging can provide qualitative and quantitative information of the extent of structural changes in a keratoconic cornea. The ability to use BSHG for diagnosing and monitoring stroma abnormalities, even when cornea transparency is retained, demonstrates the clinical potential of this method:

On the link between central black holes, bar dynamics and dark matter haloes in spiral galaxies

The discovery of a relationship between supermassive black hole (SMBH) mass and spiral arm pitch angle (P) is evidence that SMBHs are tied to the overall secular evolution of a galaxy. The discovery of SMBHs in late-type galaxies with little or no bulge suggests that an underlying correlation between the dark matter halo concentration and SMBH mass (MBH) exists, rather than between the bulge mass and MBH. In this paper we measure P using a two-dimensional fast fourier transform and estimate the bar pattern speeds of 40 barred spiral galaxies from the Carnegie-Irvine Galaxy Survey. The pattern speeds were derived by estimating the gravitational potentials of our galaxies from Ks-band images and using them to produce dynamical simulation models. The pattern speeds allow us to identify those galaxies with low central dark halo densities, or fast rotating bars, while P provides an estimate of MBH. We find that a wide range of MBH exists in galaxies with low central dark matter halo densities, which appears to support other theoretical results. We also find that galaxies with low central dark halo densities appear to follow more predictable trends in P versus de Vaucouleurs morphological type (T) and bar strength versus T than barred galaxies in general. The empirical relationship between MBH and total gravitational mass of a galaxy (Mtot) allows us to predict the minimum Mtot that will be observationally measured of our fast bar galaxies. These predictions will be investigated in a subsequent paper.

Fourier Transform Analysis of Basal Plane Dislocation Structure in Repeated A-Face Grown Crystals

Morphological features, such as the orientation and linearity of basal plane dislocations (BPDs) in SiC crystals, were analyzed by applying a two-dimensional fast Fourier transform (2D-FFT) to X-ray topographic images of the BPDs. An SiC crystal fabricated by an improved repeated a-face (RAF) method and an SiC crystal fabricated by an conventional RAF method discussed in a previous study were evaluated. In the 2D-FFT images of the improved crystal, streaks along the directions were observed, indicating that the BPDs were highly oriented along the directions. The degree of orientation of the BPDs, which may reflect their linearity, was calculated, and the improved RAF crystal had a much higher degree of orientation than the conventional RAF crystal.

Inspection of reinforced concrete interface delamination using ultrasonic guided wave non-destructive test technique

An ultrasonic-guided wave (UGW) is a very promising tool in the field of structural health monitoring and non-destructive test. Numerical analysis was used to simulate the propagation in the rebar and explore the characteristics of UGW in the steel rebar waveguide. Two-dimensional fast Fourier transform was used to process the numerical results and to evaluate the damage. Subsequently, different UGW test influence factors were investigated. The results clearly showed that both the group velocity and the amplitude of longitudinal modes were not very sensitive to stress and temperature variations. However, the received UGW signal energy decreased with the increasing concrete strength. Finally, the interface condition between the concrete and the rebar was investigated. Time-domain and frequency-domain analyses were used to process the received signals. Different interface delamination lengths of the UGW energy attenuation were analyzed and a relationship was obtained. This study successfully proved that UGW is an effective tool in the non-destructive test of reinforced concrete interface delamination.

MEASUREMENT OF GALACTIC LOGARITHMIC SPIRAL ARM PITCH ANGLE USING TWO-DIMENSIONAL FAST FOURIER TRANSFORM DECOMPOSITION

A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.

NEAR FIELD AND FAR FIELD EFFECTS IN THE TAGUCHI-OPTIMIZED DESIGN OF AN InP/GaAs-BASED DOUBLE WAFER-FUSED MQW LONG-WAVELENGTH VERTICAL-CAVITY SURFACE-EMITTING LASER

Long-wavelength VCSELs (LW-VCSEL) operating in the 1.55 μm wavelength regime offer the advantages of low dispersion and optical loss in fiber optic transmission systems which are crucial in increasing data transmission speed and reducing implementation cost of fiber-to-the-home (FTTH) access networks. LW-VCSELs are attractive light sources because they offer unique features such as low power consumption, narrow beam divergence and ease of fabrication for two-dimensional arrays. This paper compares the near field and far field effects of the numerically investigated LW-VCSEL for various design parameters of the device. The optical intensity profile far from the device surface, in the Fraunhofer region, is important for the optical coupling of the laser with other optical components. The near field pattern is obtained from the structure output whereas the far-field pattern is essentially a two-dimensional fast Fourier Transform (FFT) of the near-field pattern. Design parameters such as the number of wells in the multi-quantum-well (MQW) region, the thickness of the MQW and the effect of using Taguchi's orthogonal array method to optimize the device design parameters on the near/far field patterns are evaluated in this paper. We have successfully increased the peak lasing power from an initial 4.84 mW to 12.38 mW at a bias voltage of 2 V and optical wavelength of 1.55 μm using Taguchi's orthogonal array. As a result of the Taguchi optimization and fine tuning, the device threshold current is found to increase along with a slight decrease in the modulation speed due to increased device widths.

Discrimination of paper-based kraft tapes using Fourier transform of transmitted light images

This study focused on two-dimensional fast Fourier transform (2D-FFT) as a new technique for the discrimination of kraft tapes, which is a kind of adhesive packing tape. The 2D power spectrum (2D-PS) obtained by applying 2D-FFT to an image enables us to obtain information about the spatial periodicity, even if the periodicity is invisible within the image. However, in the case of kraft tape, peaks in the 2D-PS are too unclear to determine its periodicity. We developed novel analytical image processes combined with 2D-FFT. 2D-FFT was applied to 50 randomly selected areas in a transmitted light image of kraft tape. The 2D-PSs were calculated from each area without applying a logarithmic transformation, accumulated, and processed by the removal of the area surrounding the center, and finally normalized for visualization. These processes enhanced the peaks and eliminated local variations. Through an intra-roll comparison, the 2D-PSs collected from a roll were similar in the location of the peaks and in their patterns at low frequency area. Using an inter-roll comparison, the 2D-PSs from 50 commercially available brand-name products were classified into 26 groups based on these peaks and patterns. All results demonstrate that this method, which is convenient, rapid, and non-destructive, could be a valuable tool for the identification of kraft tapes.

Development of regional gravimetric geoid model and comparison with EGM2008 gravity-field model over Korea

We constructed a regional geoid model and compared it with the EGM2008 global gravity-field model to evaluate the performance of EGM2008 for Korea. By using the Remove–Compute–Restore (RCR) technique, we developed an improved gravimetric geoid model JNUGEOID2010 on a 1 × 1′ grid by combining the EIGEN-GL04C global geopotential model (GGM), 8316 land-gravity data, an altimetry-derived marine gravity model DNSC08, and the Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM). The computations were done using a two-dimensional four-band spherical fast Fourier transform (FFT) with 100% zero padding. In addition, we compared the Korean national gravimetric geoid model KGEOID98 to EGM2008. For the comparison, geometric geoid heights derived from 735 GPS-levelling stations were used. The smallest standard deviation of geoid height differences is ± 0.163 m for EGM2008 to degree and order 2190. Thus, we conclude that the new model EGM2008 is superior to the two regional gravimetric geoid models, JNUGEOID2010 and KGEOID98, for Korea. Key words: Regional geoid model, EGM2008, Global geopotential models, GPS-levelling, geoid height, Korea.