Frequency Fourier Components Research Articles

Temporal light modulation: A phantom array visibility measure

At temporal light modulation (TLM) frequencies between 80 Hz and 20 000 Hz observers may perceive a series of repeated images called the phantom array effect (PAE) when they move their eyes in large saccades across a modulating light source or across a scene lit by the modulating light source. To date, there is no well-established measure for quantifying PAE visibility, but there is growing awareness of the need for one among design professionals and sensitive populations. This paper documents a new measure, the phantom array visibility measure (PAVM), which is based on the results of recent human factors experiments. The measure follows the mathematical underpinning used by the flicker visibility measure and the stroboscopic visibility measure, where the time-domain TLM waveform is converted into its Fourier frequency components; each component is evaluated through a threshold curve of modulation depth, then summed through an equation employing a Minkowski exponent. This scales the PAVM so that a value of 1 indicates a waveform at a threshold visibility in the conditions of the underlying experiment.

A pseudo-spectral based efficient volume penalization scheme for Cahn–Hilliard equation in complex geometries

In this paper, we have developed an efficient volume penalization based diffuse-filtering scheme to solve variable mobility based Cahn–Hilliard equation in complex geometries. The main novelty of the work is that a dealiased pseudo-spectral scheme with immersed interface method (IIM) is proposed for solving any generalized concentration-dependent mobility function-based Cahn–Hilliard (CH) equation in complicated computational domains. An indicator function based mobility parameter is introduced to perform simulation of binary spinodal decomposition problem at a lower computational expense in complex geometries by solving a single phase field equation. Due to the smooth removal of high frequency Fourier components, the solution of the present RK4 based diffuse-filtering scheme does not display spurious currents when suitable low-pass filtering strategy and adequately resolved mobility indicator are incorporated. The traditional and memory optimized zero padding schemes are also implemented to show the comparative performance of different dealiasing schemes for the variable mobility based Cahn–Hilliard equation. It is found that the diffuse-filtering scheme displays reasonable accuracy similar to the zero padding based schemes but its average CPU time is significantly lower, which indicates better computational performance of the scheme for the variable mobility Cahn–Hilliard equation. Time variation of the characteristic length scale during spinodal decomposition of a binary mixture agrees well with the analytical prediction. The optimal three stage SSPRK3 temporal scheme is employed and it is found that time step size can be increased approximately 1.4 times than the classical RK4 scheme reducing total CPU time. Oscillation free numerical solution and conservation of order parameter are obtained for the complex geometry based spinodal decomposition problem. A radially-averaged structure factor is introduced to quantify resolution issues of the dealiasing schemes for the spinodal decomposition problem in different complex geometries.

A Sparse Approximation Based Algorithm to Detect Aortic Valve Opening from HVAD Waveforms Acquired via Monitor Snapshot

<h3>Purpose</h3> The HeartWare HVAD monitor displays a real-time waveform of the flow provided by the LVAD. However, there are no commercially available methods to obtain this flow waveform data. We describe a novel algorithm that leverages sparse approximation with Gaussian dictionary to estimate aortic valve opening status from HVAD flow waveform data acquired via monitor snapshot. <h3>Methods</h3> Stable adult patients receiving MCS therapy with an HeartWare HVAD were included. Aortic valve opening status was determined during routine echocardiography ("Open" = opens in ≥8/10 beats vs "Closed" = opens in ≤2/10 beats) and a photo of the HVAD monitor was taken with a smartphone at the same time. The flow waveform graph was digitized and interpolated using low frequency Fourier components for the purpose of low pass filtering and standardization of sampling frequency (Figure 1). Sparse approximations (SA) with Gaussian dictionary were generated for each signal using orthogonal matching pursuit (OMP). Waveforms with a closed Ao valve are better aligned with SA (Figure 2: 2a, 2b). Therefore, residual sum of squares (RSS) -which is a marker of deviation from SA- was used to estimate Ao valve status. <h3>Results</h3> 54 waveforms were acquired. Area under the ROC curve for RSS' capacity to estimate the status (open/closed) of a single beat was .766 (± .021) (p: .000). The SA-based algorithm had 83.33% overall accuracy for detecting aortic valve opening (sensitivity: 86.67%, specificity: 79.17%) from a 10 sec. signal (Figure 2). <h3>Conclusion</h3> We describe a method for reliable data acquisition and estimation of aortic valve opening from a HVAD monitor snapshot.

Damage to the rat cerebrum under in vitro sinusoidal translational shear deformation

Blast waves, which induce sinusoidal shear waves within brain tissue, may cause mild traumatic brain injury (mTBI). To identify damage from a shear deformation wave, sagittal slices of rat cerebra are subjected to 50 cycles of translational shear deformation at six fixed frequencies between 25 Hz and 125 Hz and displacement amplitudes of 10% or 25% of the original length of the specimen. Each deformation frequency produces transient and apparent steady shear stress states that frequency analysis describes by their harmonic wavelet and Fourier frequency components. The dominant frequency components are integer multiples of the applied deformation frequency. The morphology of the shear stress versus time curve, and probably the type of damage, changes with deformation frequency. Damage at the lower frequencies appears to be diffuse bond breaking. Imaging and histology do not clearly detect mild damage due to bond breaking that underlies mTBI, which the analysis of the shear stress response captures. Major transitions in the morphology of the stress response in the two regions occur at about 75 Hz deformation frequency, possibly due to minor damage to cerebral substructures. An increase in deformation frequency increases the drag force between the extracellular fluid and solid matter. The deformation frequency dependence of the shear stress response makes protection against blast mTBI more difficult because the frequency content of a blast wave is not known a priori.

Venturing beyond the ISCO: detecting X-ray emission from the plunging regions around black holes

ABSTRACT We explore how X-ray reverberation around black holes may reveal the presence of the innermost stable circular orbit (ISCO), predicted by general relativity, and probe the dynamics of the plunging region between the ISCO and the event horizon. Being able to directly detect the presence of the ISCO and probe the dynamics of material plunging through the event horizon represents a unique test of general relativity in the strong field regime. X-ray reverberation off of the accretion disc and material in the plunging region is modelled using general relativistic ray tracing simulations. X-ray reverberation from the plunging region has a minimal effect on the time-averaged X-ray spectrum and the overall lag-energy spectrum, but is manifested in the lag in the highest frequency Fourier components, above $0.01\, c^{3}\, (GM)^{-1}$ (scaled for the mass of the black hole) in the 2–4 keV energy band for a non-spinning black hole or the 1–2 keV energy band for a maximally spinning black hole. The plunging region is distinguished from disc emission not just by the energy shifts characteristic of plunging orbits, but by the rapid increase in ionization of material through the plunging region. Detection requires measurement of time lags to an accuracy of 20 per cent at these frequencies. Improving accuracy to 12 per cent will enable constraints to be placed on the dynamics of material in the plunging region and distinguish plunging orbits from material remaining on stable circular orbits, confirming the existence of the ISCO, a prime discovery space for future X-ray missions.

Super-resolution spatial frequency differentiation of nanoscale particles with a vibrating nanograting

We propose a scheme for detecting and differentiating deeply subwavelength particles based on their spatial features. Our approach combines scattering from an ultrasonically modulated nanopatterned grating with heterodyne techniques to enable far-field detection of high spatial frequency Fourier components. Our system is sensitive to spatial features commensurate in size to the patterning scale of the grating. We solve the scattering problem in Born approximation and illustrate the dependence of the signal amplitude at modulation frequency on grating period, which allows to differentiate between model nanoparticles of size λ/20.

The Atacama Compact Array (ACA)

Abstract For realizing high fidelity of imaging with mosaicing observations, the Atacama Large Millimeter/submillimeter Array (ALMA) consists of a homogeneous array of 12 m antennas (12 m Array) and the Atacama Compact Array (ACA) in order to cover all spatial frequency Fourier components of the brightness distribution of observed sources. The array is located at an altitude site of about 5000 m with an operating wavelength range of 0.3 to 3 mm. ACA is an array composed of four 12 m dishes [TP (Total Power) Array] and twelve 7 m dishes (7 m Array). The 7 m Array has a very compact configuration to take short-baseline data corresponding to the low spatial frequency Fourier components. The 7 m Array has two configurations extended over 30-50 m to avoid shadowing at low elevation. The scientific importances and operation concepts of ACA, and the system design of ACA and its performance are presented in this paper.

Principles of calculating the dynamical response of misaligned complex resonant optical interferometers

In the long-baseline laser interferometers for measuring gravitational waves that are now under construction, understanding the dynamical response to small distortions such as angular alignment fluctuations presents a unique challenge. These interferometers comprise multiple coupled optical resonators with light storage times approaching 100 m. We present a basic formalism to calculate the frequency dependence of periodic variations in angular alignment and longitudinal displacement of the resonator mirrors. The electromagnetic field is decomposed into a superposition of higher-order spatial modes, Fourier frequency components, and polarization states. Alignment fluctuations and length variations of free-space propagation are represented by matrix operators that act on the multicomponent state vectors of the field.

Search for the Most Stable Structures on Potential Energy Surfaces

Smoothing techniques for global optimization in search for the most stable structures (clusters or conformers) have been a novel possibility for the last decade. The techniques turned out to be related to a variety of fundamental laws: Fick's diffusion equation, time-dependent and time-independent Schrodinger equations, Smoluchowski dynamics equation, Bloch equation of canonical ensemble evolution with temperature, Gibbs free-energy principle. The progress indicator of global optimization in those methods takes different physical meanings: time, imaginary time, Planck constant, or the inverse absolute temperature. Despite this large spectrum of physical phenomena, the resulting global optimization procedures have a remarkable common feature. In the case of the Gaussian Ansatz for the wave function or density distribution, the underlying differential equations of motion for the Gaussian position and width are similar for all these phenomena. In all techniques the smoothed potential energy function plays a central role rather than the potential energy function itself. The smoothed potential results from a Gaussian convolution or filtering out high frequency Fourier components of the original potential energy function. During the minimization, the Gaussian position moves according to the negative gradient of the smoothed potential energy function. The Gaussian width is position dependent through the curvature of the potential energy function, and evolves according to the following rule. For sufficiently positive curvatures (close to minima of the smoothed potential) the width decreases, thus leading to a smoothed potential approaching the original potential energy function, while for negative curvatures (close to maxima) the width increases leading eventually to the disappearance of humps of the original potential energy function. This allows for crossing barriers separating the energy basins. Some methods result in an additional term, which increases the width, when the potential becomes flat. This may be described as a feature allowing hunting for distant minima.

On the rate equation approximation for free-running multimode lasers

We generalize the Tang, Statz and deMars rate equations by retaining low spatial frequency Fourier components of the population inversion. For homogeneous pumping, the new terms barely influence the results of the usual TSD equations. However, for strongly inhomogeneous pumping, the new rate equations predict an instability leading to a breakup of the CW intensity into pulses which can be either periodic or chaotic.

A Systematic Error in Surface Residence Time Measurements by Molecular Beam Relaxation Method.

During the mean surface residence time measurements by means of molecular beam relaxation method it is often found that an error starts to appear as the mean residence time becomes comparable to the molecular beam modulation period. An analysis has been made to clarify that this is due to a systematic error which occurs during data processing using Fast Fourier Transform software. Fourier transform is usually performed in a single period of the desorbed molecular beam time-of-flight signal, while the resultant signal is a sum of the signals at present period and those initiated in the past periods. This signal overlapping creates a systematic error especially at high frequency components of Fourier transform.

Quantitative deformation studies using electron back scatter patterns

The diffuseness of electron back scatter patterns (EBSPs) is observed to increase with plastic strain. The application of this technique to deformation studies has been limited by the lack of a general method of measuring the pattern quality. The degradation of EBSPs by cold work was thus thoroughly investigated using the A1 6061 alloy for the purpose. Methods of enhancing the Kikuchi band contrast by removal of the background intensity variation from digital images of 〈112〉 zone axes present in the EBSP have been developed. The contrast of the Kikuchi bands was quantified using the root mean square intensity of averaged band profiles, while the sharpness of the patterns was assessed by the attenuation of high frequency components of Fourier transforms of the enhanced images and of the averaged band profiles. Tilt was found to effect contrast but not sharpness, while cold work reduced both. However, surface contamination produced effects that were very similar to those of specimen deformation. A method is presented for quantitative determination of EBSP quality, which is independent of grain orientation and is based on the first moment of power spectra (the square of the Fourier transform) of features common to all patters to be compared.

Direct digital-to-analog conversion of acoustic signals using a solid dielectric transducer/filter system

This paper describes the theory, construction, and operation of a transducer that is capable of transmitting an analog acoustic signal when driven by a digital input signal. The digital signal drives a capacitive dielectric transducer whose active surface area is proportional to the magnitude of the digital signal. The output of the transducer contains the original digitized analog signal in addition to higher frequency Fourier components that result from the sampling process. The unwanted additional signal is attenuated by coupling the transducer output into an acoustic low-pass filter whose response is determined by using electrical circuit analysis techniques. The results indicate that the experimental transducer system is useful for generating acoustic signals that have an upper frequency limit of 8 kHz. With suitable modifications, wider frequency performance is attainable.

Digital-to-analog conversion of acoustic signals

This paper describes the theory, construction, and operation of a transducer that is capable of transmitting an analog acoustic signal when driven by a digital input signal. The digital signal drives a capacitive dielectric transducer whose active surface area is proportional to the magnitude of the digital signal. The output of the transducer contains the original analog signal in addition to higher frequency Fourier components that result from the sampling process. The unwanted additional signal is attenuated when the transducer output is fed into an acoustic low-pass filter whose response is determined by using electrical circuit analysis techniques. Results indicate that this system is useful for signals that have an upper frequency limit that does not exceed 8 kHz.

Quantitative limitations imposed by atmospheric turbulence and the quantum nature of light on image quality

The turbulent atmosphere of the Earth limits the resolution of conventional astrography to about 1 arcsec. This resolution is much lower than the theoretical diffraction limit of a large telescope. The quantitative limitations imposed by atmospheric turbulence on image quality for both short- and long-exposure images using statistical methods are developed in order to quantify this problem. The limitations were studied in terms of the transfer function of the telescope-atmosphere system, and the Fourier frequency components of an image of a binary star. The quantitative limitations imposed by the quantum nature of light on image quality are also studied.

A High-Resolution Proportional Chamber Positron Camera and Its Applications

A positron camera consisting of two high density proportional chambers is described. It provides a spatial resolution of 2.4 mm FWHM, a maximum data rate of 3000 c.p.s. and a sensitivity of 25 c.p.s. per μCi. Results of its application to angular correlation studies of condensed matter and to phantom and in vivo medical imaging are presented. A Fourier deconvolution technique is described for obtaining three-dimensional medical images. It uses a generalized matrix inversion by singular value decomposition to modify the low frequency Fourier components.

Electric and Magnetic Fields at the Earth's Surface Due to Auroral Currents

The horizontal components of the electric and magnetic fields due to auroral atmospheric currents are calculated at the surface of the earth. For sinusoidal changes in the earth's magnetic field (Fourier frequency components of actual nonsinusoidal variations), a lower limit of the corresponding earth-surface potential is obtained by considering a line-type auroral current over a nonuniform stratified earth. An upper limit of the earth-surface potential is obtained by considering a current-sheet model of the auroral current, and the same model of the earth. A diagram is constructed that allows calculation of the earth-surface potential for given variations in the earth's magnetic field. Finally, the influence of the earth-surface potential on electric power systems is discussed.