Filtering In Fourier Space Research Articles

Fraction of Clumpy Star-forming Galaxies at 0.5 ≤ z ≤ 3 in UVCANDELS: Dependence on Stellar Mass and Environment

High-resolution imaging of galaxies in rest-frame UV has revealed the existence of giant star-forming clumps prevalent in high-redshift galaxies. Studying these substructures provides important information about their formation and evolution and informs theoretical galaxy evolution models. We present a new method to identify clumps in galaxies’ high-resolution rest-frame UV images. Using imaging data from CANDELS and UVCANDELS, we identify star-forming clumps in an HST/F160W ≤ 25 AB mag sample of 6767 galaxies at 0.5 ≤ z ≤ 3 in four fields, GOODS-N, GOODS-S, EGS, and COSMOS. We use a low-passband filter in Fourier space to reconstruct the background image of a galaxy and detect small-scale features (clumps) on the background-subtracted image. Clumpy galaxies are defined as those having at least one off-center clump that contributes a minimum of 10% of the galaxy’s total rest-frame UV flux. We measure the fraction of clumpy galaxies (f clumpy) as a function of stellar mass, redshift, and galaxy environment. Our results indicate that f clumpy increases with redshift, reaching ∼65% at z ∼ 1.5. We also find that f clumpy in low-mass galaxies () is 10% higher compared to that of their high-mass counterparts (). Moreover, we find no evidence of significant environmental dependence of f clumpy for galaxies at the redshift range of this study. Our results suggest that the fragmentation of gas clouds under violent disk instability remains the primary driving mechanism for clump formation, and incidents common in dense environments, such as mergers, are not the dominant processes.

Topological spatial differentiation via complex amplitude filtering in Fourier space.

Various approaches to implementing optical analog differentiation have been studied extensively and applied in edge-based image processing. Here, we report a topological optical differentiation scheme based on complex amplitude filtering, i.e., amplitude and spiral phase modulation in Fourier space. The isotropic and anisotropic multiple-order differentiation operations are demonstrated both theoretically and experimentally. Meanwhile, we also achieve multiline edge detection corresponding to the differential order for the amplitude and phase objects. This proof-of-principle work could open up new avenues for engineering a nanophotonic differentiator and realizing a more compact image-processing system.

Displacement separation analysis from atomic-resolution images

Structural distortions frequently occur in materials, either periodically (ferroelectric or antiferroelectric) or in local areas (domain boundaries, surfaces/interfaces, dislocations). Measuring atomic displacements from an average lattice is of crucial importance for analyzing structural distortions and their connections to physical properties. Conventionally, the displacements are measured atom-by-atom by fitting atomic-resolution images with two-dimensional gaussian functions. Here, we exhibit an efficient method, named Displacement Separation Analysis, DSA in short, to directly separate atomic displacements from an average lattice based on Fourier space filtering. Using antiferroelectric AgNbO3 as a model system, we demonstrate the consistence between DSA and gaussian fitting. The suppression of polarization at interfacial region of h-LuFeO3/α-Al2O3 heterostructure and the emergence of modulation structure in LuFe2O4+x is then revealed using DSA, attesting the implication of DSA in unveiling structural distortions either locally or periodically. Inspired by the simple principle of DSA, such method can be used for any atomic-resolution images, including TEM, STM, and AFM images to exhibit the atomic displacement intuitively.

An uncertainty principle for star formation – IV. On the nature and filtering of diffuse emission

Abstract Diffuse emission is observed in galaxies in many tracers across the electromagnetic spectrum, including tracers of star formation, such as H α and ultraviolet (UV), and tracers of gas mass, such as carbon monoxide (CO) transition lines and the 21-cm line of atomic hydrogen (H i). Its treatment is key to extracting meaningful information from observations such as cloud-scale star formation rates. Finally, studying diffuse emission can reveal information about the physical processes taking place in the interstellar medium, such as chemical transitions and the nature of stellar feedback (through the photon escape fraction). We present a physically motivated method for decomposing astronomical images containing both diffuse emission and compact regions of interest, such as H ii regions or molecular clouds, into diffuse and compact component images through filtering in Fourier space. We have previously presented a statistical method for constraining the evolutionary timeline of star formation and mean separation length between compact star-forming regions with galaxy-scale observations. We demonstrate how these measurements are biased by the presence of diffuse emission in tracer maps and that by using the mean separation length as a critical length-scale to separate diffuse emission from compact emission, we are able to remove its biasing effect. Furthermore, this method provides, without the need for interferometry or ancillary spectral data, a measurement of the diffuse emission fraction in input tracer maps and decomposed diffuse and compact emission maps for further analysis.

Temporal Filtering to Improve Single Molecule Identification in High Background Samples.

Single molecule localization microscopy is currently revolutionizing the life sciences as it offers, for the first time, insights into the organization of biological samples below the classical diffraction limit of light microscopy. While there have been numerous examples of new biological findings reported in the last decade, the technique could not reach its full potential due to a set of limitations immanent to the samples themselves. Particularly, high background signals impede the proper performance of most single-molecule identification and localization algorithms. One option is to exploit the characteristic blinking of single molecule signals, which differs substantially from the residual brightness fluctuations of the fluorescence background. To pronounce single molecule signals, we used a temporal high-pass filtering in Fourier space on a pixel-by-pixel basis. We evaluated the performance of temporal filtering by assessing statistical parameters such as true positive rate and false discovery rate. For this, ground truth signals were generated by simulations and overlaid onto experimentally derived movies of samples with high background signals. Compared to the nonfiltered case, we found an improvement of the sensitivity by up to a factor 3.5 while no significant change in the localization accuracy was observable.

Identification of the acoustic response in the irrotational near-field of an excited subsonic jet

Analysis and understanding of the noise generation processes in high-speed, high-Reynolds number jets are hampered by the broad range of turbulent scales and the disparate fluctuation intensities of the acoustic response hidden under the hydrodynamic source. Towards providing insight into these processes, the irrotational near-field of an unheated, Mach 0.9 jet is decomposed into its constitutive hydrodynamic and acoustic components using three separate filters in the present work. Previous work had decomposed the full near-field pressure signal into its hydrodynamic and acoustic components using a linear filter in Fourier space. The presence of numerical artifacts in the results prompted the current study, in which a new algorithm is developed to filter the pressure field in wavelet space. Results from the new method are then compared against those obtained using the standard Fourier-based algorithm, as well as another algorithm based upon the empirical mode decomposition. The ability of the wavelet-based algorithm to decompose the broadband irrotational pressure field into its constitutive components, as well as to identify and extract individual events, is found to be superior to that of the other two decomposition methods.

Numerical Approximation of the Fractional Laplacian via $$hp$$ h p -finite Elements, with an Application to Image Denoising

The fractional Laplacian operator $$(-\varDelta )^s$$(-Δ)s on a bounded domain $$\varOmega $$Ω can be realized as a Dirichlet-to-Neumann map for a degenerate elliptic equation posed in the semi-infinite cylinder $$\varOmega \times (0,\infty )$$Ω×(0,?). In fact, the Neumann trace on $$\varOmega $$Ω involves a Muckenhoupt weight that, according to the fractional exponent $$s$$s, either vanishes $$(s 1/2)$$(s>1/2). On the other hand, the normal trace of the solution has the reverse behavior, thus making the Neumann trace analytically well-defined. Nevertheless, the solution develops an increasingly sharp boundary layer in the vicinity of $$\varOmega $$Ω as $$s$$s decreases. In this work, we extend the technology of automatic $$hp$$hp-adaptivity, originally developed for standard elliptic equations, to the energy setting of a Sobolev space with a Muckenhoupt weight, in order to accommodate for the problem of interest. The numerical evidence confirms that the method maintain exponential convergence. Finally, we discuss image denoising via the fractional Laplacian. In the image processing community, the standard way to apply the fractional Laplacian to a corrupted image is as a filter in Fourier space. This construction is inherently affected by the Gibbs phenomenon, which prevents the direct application to spliced images. Since our numerical approximation relies instead on the extension problem, it allows for processing different portions of a noisy image independently and combine them, without complications induced by the Gibbs phenomenon.

SU-E-T-164: Clinical Implementation of ASi EPID Panels for QA of IMRT/VMAT Plans.

To investigate various issues for clinical implementation of aSi EPID panels for IMRT/VMAT QA. Six linacs are used in our clinic for EPID-based plan QA; two Varian Truebeams, two Varian 2100 series, two Elekta Infiniti series. Multiple corrections must be accounted for in the calibration of each panel for dosimetric use. Varian aSi panels are calibrated with standard dark field, flood field, and 40×40 diagonal profile for beam profile correction. Additional corrections to account for off-axis and support arm backscatter are needed for larger field sizes. Since Elekta iViewGT system does not export gantry angle with images, a third-party inclinometer must be physically mounted to back of linac gantry and synchronized with data acquisition via iViewGT PC clock. A T/2 offset correctly correlates image and gantry angle for arc plans due to iView image time stamp at the end of data acquisition for each image. For both Varian and Elekta panels, a 5 MU 10×10 calibration field is used to account for the nonlinear MU to dose response at higher energies. Acquired EPID images are deconvolved via a high pass filter in Fourier space and resultant fluence maps are used to reconstruct a 3D dose 'delivered' to patient using DosimetryCheck. Results are compared to patient 3D dose computed by TPS using a 3D-gamma analysis. 120 IMRT and 100 VMAT cases are reported. Two 3D gamma quantities (Gamma(V10) and Gamma(PTV)) are proposed for evaluating QA results. The Gamma(PTV) is sensitive to MLC offsets while Gamma(V10) is sensitive to gantry rotations. When a 3mm/3% criteria and 90% or higher 3D gamma pass rate is used, all IMRT and 90% of VMAT QA pass QA. After appropriate calibration of aSi panels and setup of image acquisition systems, EPID based 3D dose reconstruction method is found clinically feasible.

Control of the spatial emission structure of broad-area vertical-cavity surface-emitting lasers by feedback

The wave number of transverse spatial structures in broad-area vertical-cavity surface-emitting lasers (VCSELs) is controlled via frequency-selective feedback from an external self-imaging cavity in a broad range of wave numbers and emission frequencies. The selected states follow the dispersion curves of the free-running laser. A control range of about 2.5 µm−1 in spatial frequency space and 2.5 nm in emission wavelength was obtained for square VCSELs and of about 3 µm−1 and 8 nm for circular VCSELs having a different dispersion curve. By spatial filtering in Fourier space, the shape of the structures can also be controlled to some extent. It is argued that the feedback techniques are useful to ‘probe’ emission states of the free-running laser.

Action-Spectra of Electrochromic Voltage-Sensitive Dyes in an Intact Excitable Tissue

Voltage-sensitive dyes VSDs provide a spatially resolved optical read-out of electrical signals in excitable tissues. Several com- mon fluorescent VSDs display electrochromic shifts of their emission spectra, making them suitable candidates for ratiometric measure- ments of transmembrane voltages. These advantages of VSDs are tem- pered by tissue-specific shifts to their fluorescence emission. In addi- tion, the optimal electrochromic dye response occurs in wavelength bands distinct from the dye's maximal resting emission. This spectrum can undergo tissue-specific shifts as well. We have devel- oped a technique for in situ measurements of the action spectra of VSDs in intact excitable tissues. Fluorescence emission spectra of VSDs during action-potential depolarization were obtained within a single sweep of a spectrophotometer equipped with a change-coupled device CCD array detector. To resolve the subtle electrochromic shifts in voltage-induced dye emission, fluorescence emission spectra measured right before and during field-induced action-potential de- polarization were averaged over about 100 trials. Removing white- noise contributions from the spectrometer's CCD detector/amplifier via low-pass filtering in Fourier space, the action spectra of all dyes could be readily determined. © 2008 Society of Photo-Optical Instrumentation En-

Action spectra of electrochromic voltage-sensitive dyes in an intact excitable tissue

Voltage-sensitive dyes (VSDs) provide a spatially resolved optical read-out of electrical signals in excitable tissues. Several common fluorescent VSDs display electrochromic shifts of their emission spectra, making them suitable candidates for ratiometric measurements of transmembrane voltages. These advantages of VSDs are tempered by tissue-specific shifts to their fluorescence emission. In addition, the optimal electrochromic dye response occurs in wavelength bands distinct from the dye's maximal resting emission. This "action spectrum" can undergo tissue-specific shifts as well. We have developed a technique for in situ measurements of the action spectra of VSDs in intact excitable tissues. Fluorescence emission spectra of VSDs during action-potential depolarization were obtained within a single sweep of a spectrophotometer equipped with a change-coupled device (CCD) array detector. To resolve the subtle electrochromic shifts in voltage-induced dye emission, fluorescence emission spectra measured right before and during field-induced action-potential depolarization were averaged over about 100 trials. Removing white-noise contributions from the spectrometer's CCD detector/amplifier via low-pass filtering in Fourier space, the action spectra of all dyes could be readily determined.

Instabilities in a One-Dimensional Driven Bistable System under Delayed Feedback Control

We consider the dynamics of a delayed feedback controlled system, which is designed to stabilize an unstable homogeneous symmetric periodic state in a periodically driven bistable system in one dimension. The existence of a finite limit on our ability to measure spatial structure in the feedback system is taken into account by employing Fourier space filtering with a cutoff, which corresponds to the measurement resolution, in the wave number domain. The main purpose of this paper is to clarify the influences of the resolution on the limitation of control and the dynamics in various unstable regimes. First, we give an overview of the dynamics. The characteristic features of the dynamics due to the first and second instabilities, the dynamics in resonant regimes, and the dynamics in a chaotic regime are elucidated. Second, on the basis of a linear stability analysis, we estimate the stability criterion in a conventional control model and an extended control model. Third, we treat the transition from a standing wave state to a vibrating standing wave state in which the mean level of the standing wave undergoes a Hopf bifurcation, and obtain the borders of the transitions for the two controlled models.

Tomographical Imaging and Mathematical Description of Porous Media Used for the Prediction of Fluid Distribution

Flow and transport processes in porous media depend on the geometric properties of their pores, where the diameters typically range from micrometers to millimeters. In this study, we mapped the pore structure of glass bead and sand columns using tomography with X‐rays, thermal neutrons, and synchrotron radiation. Utilizing X‐rays from tubes, we mapped two 2.5‐ and 5.3‐cm‐diam. sand samples that contained particles with sizes ranging from 0.08 to 1.25 mm. The resulting voxels (i.e., the unit of a three‐dimensional image, the smallest distinguishable box‐shaped part of a three‐dimensional image) were cubes of 60‐μm length in the case of microfocus X‐rays, and 70 μm in case of industrial X‐rays. In the latter case, each voxel represented the material density of a rectangular parallelepiped with side lengths of 70 μm and a height of 210 μm. The material density of cubes of 70 μm was reconstructed by applying an optimized filter in Fourier space. Columns with diameters of 4.0 and 5.3 cm containing glass beads with diameters of 3.0 and 2.0 mm were scanned with thermal neutrons. The voxel size was 167 μm. Because this technique is sensitive to the presence of water, it was possible to measure the water table in a partially water‐filled sample. Two sand columns were scanned with synchrotron X‐rays, and the resulting voxel sizes were 11.5 and 3.5 μm. In the first case, the sample with a diameter of 15 mm contained particles of sizes ranging from 300 to 900 μm. In the second case, a sample with a diameter of 5 mm was filled with 100‐ to 200‐μm particles. In a numerical analysis of the sphere packings, we computed various geometric properties of the porous media as a function of the resolution. The pore‐size distribution and the Minkowski functionals (quantities that define the morphology of a structure) were used to describe changes in the imaged pore space as a function of voxel size. We found that the geometric properties of the mapped pore space converged to true values for a voxel size of 10 to 20% of the mean particle radius. Based on this analysis, we postulate that the resolution of a tomographic measurement must be in the range of 10% of the mean particle radius for repacked media to reconstruct the characteristic features of the pore space. This condition was fulfilled for the tomography with synchrotron light. Using the images of the sand samples measured with synchrotron light, we predicted the amount of water and air for a drainage process. For the pore space mapped with tube X‐rays, it was possible to make qualitative predictions of the hysteretic water and air distribution.

Digital removal of power frequency artifacts using a Fourier space median filter

An efficient technique to remove periodic noise from digital images via a novel implementation of the median filter is presented and discussed within this letter. The technique is based on applying the nonlinear filter to the Fourier amplitude spectrum of the image. Since the median filter is normally used to spatially reduce spiky noise in digital images, using this filter in Fourier space is especially useful for removing periodic frequency noise. Provisional experimental results are shown that demonstrate that the proposed filter provides good performance when compared with a similar Fourier filter: the notch filter. This letter, when considering a prototype version of a Fourier-based median filter, defines the set of user-defined options that are available and also defines a possible solution to solve the distortions caused around the dc component due to natural spectrum decay.

Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data

We report on the reconstruction of absorption and reduced scattering coefficients of breast tissue in vivo of a patient with mastopathic disease. Distributions of times of flight of photons through the compressed breast were recorded by paraxial scanning. From data measured at four different source–detector offsets optical properties were reconstructed within the linear Rytov approximation by a fast inverse Fourier space method. Low-pass filtering in Fourier space was employed to remove excessive noise from high spatial frequency components and to reduce the computational efforts by a factor of 3, typically. The mammograms displaying reconstructed absorption and reduced scattering coefficients were compared with projection mammograms either obtained by time-window analysis of experimental data or based on average absorption and reduced scattering coefficients which were derived from measured temporal point spread functions within a simple homogeneous model. All inhomogeneities which were visible in the projection mammograms and which could be associated with specific breast tissue compartments could be correlated with inhomogeneities in the reconstructed absorption coefficient. In particular, the mastopathic disease was detected in the reconstructed absorption mammogram. In order to assess reliability of optical properties reconstructed from data obtained by paraxial scanning, corresponding phantom experiments and reconstructions of phantom optical properties were carried out. Because of the limited angular range sampled by the in vivo and phantom measurements, considerable blurring of the absorption coefficient occurs along the compression direction, compromising longitudinal resolution.

Spatiotemporal image correlation spectroscopy (STICS) theory, verification, and application to protein velocity mapping in living CHO cells.

We introduce a new extension of image correlation spectroscopy (ICS) and image cross-correlation spectroscopy (ICCS) that relies on complete analysis of both the temporal and spatial correlation lags for intensity fluctuations from a laser-scanning microscopy image series. This new approach allows measurement of both diffusion coefficients and velocity vectors (magnitude and direction) for fluorescently labeled membrane proteins in living cells through monitoring of the time evolution of the full space-time correlation function. By using filtering in Fourier space to remove frequencies associated with immobile components, we are able to measure the protein transport even in the presence of a large fraction (>90%) of immobile species. We present the background theory, computer simulations, and analysis of measurements on fluorescent microspheres to demonstrate proof of principle, capabilities, and limitations of the method. We demonstrate mapping of flow vectors for mixed samples containing fluorescent microspheres with different emission wavelengths using space time image cross-correlation. We also present results from two-photon laser-scanning microscopy studies of alpha-actinin/enhanced green fluorescent protein fusion constructs at the basal membrane of living CHO cells. Using space-time image correlation spectroscopy (STICS), we are able to measure protein fluxes with magnitudes of mum/min from retracting lamellar regions and protrusions for adherent cells. We also demonstrate the measurement of correlated directed flows (magnitudes of mum/min) and diffusion of interacting alpha5 integrin/enhanced cyan fluorescent protein and alpha-actinin/enhanced yellow fluorescent protein within living CHO cells. The STICS method permits us to generate complete transport maps of proteins within subregions of the basal membrane even if the protein concentration is too high to perform single particle tracking measurements.

Nanoscale Measurement of Stress and Strain by Quantitative High-Resolution Electron Microscopy

The geometric phase technique (GPA) for measuring the distortion of crystalline lattices from high-resolution electron microscopy (HRTEM) images will be described. The method is based on the calculation of the “local” Fourier components of the HRTEM image by filtering in Fourier space. The method will be illustrated with a study of an edge dislocation in silicon where displacements have been measured to an accuracy of 3 pm at nanometre resolution as compared with anisotropic elastic theory calculations. The different components of the strain tensor will be mapped out in the vicinity of the dislocation core and compared with theory. The accuracy is of the order of 0.5% for strain and 0.1° for rigid-body rotations. Using bulk elastic constants for silicon, the stress field is determined to 0.5 GPa at nanometre spatial resolution. Accuracy and the spatial resolution of the technique will be discussed.

Imaging a dense nanodot assembly by phase retrieval from TEM images

Phase retrieval is a classical inverse problem in many fields dealing with waves that is becoming of increasing interest in transmission electron microscopy (TEM). A non-interferometric approach is here applied to TEM images. Phase retrieval possibilities given by the transport intensity equation are compared to the ones deriving from the weak phase object approximation. In the limit of small angles, both methods lead to a similar equation between the phase and a set of defocus images. This equation can be solved by an image processing equivalent to using a specific filter in Fourier space. This processing leads to phase images with a spatial resolution here essentially limited by the defocus amount between images. A dense assembly of silicon nanodots is used as a model case to illustrate the interest of this approximate phase retrieval method which can be carried out on standard equipment. The dot heights estimated using the phase images are found to be in good agreement with ones measured by atomic force microscopy. Since image noise and large defocus values may strongly affect the solution given by the approximate method, an iterative phase retrieval method is also used as a test for working conditions.

Relationship between spatial resolution and noise in scanning superconducting quantum interference device microscopy

An inverse transformation based on the fast Fourier transform can convert a two-dimensional image of the normal component of magnetic field into a corresponding image of the two-dimensional source currents that generated the field. Applying such a transformation to a magnetic image from a scanning Superconducting Quantum Interference Device (SQUID) microscope reveals that the spatial resolution s in the current image can be over 20 times better than that found in the raw magnetic field image, and up to about 5 times smaller than the SQUID sample separation z. We describe a quantitative theory for the noise and spatial resolution found in such current density images. We find that s is proportional to z and logarithmically related to the magnetic field noise in the image, the current applied to the sample, and the pixel size. We discuss the unusual functional dependence of these parameters and compare our theory to experimental data obtained from a scanning SQUID microscope. Finally, we describe how selective filtering in Fourier space can reduce noise and other artifacts in the current density images.

Investigations of pattern forming mechanisms by Fourier filtering: properties of hexagons and the transition to stripes in an anisotropic system

The properties of patterns in an anisotropic system are studied experimentally and numerically in an optical pattern forming system with single-mirror feedback. A controlled anisotropy is introduced by a slit filter in Fourier space. If the slit width is reduced, a transition between hexagons and stripes via nonequilateral hexagons and rhomboids is observed. The scenario is reproduced in numerical simulations. The bifurcation to stripes is found to be supercritical whereas the one to hexagons is subcritical in accordance with expectation. The results illustrate the potential of Fourier filtering as a tool for investigating mechanisms of pattern formation.