Spatial Coherence Of Source Research Articles

The Application of a Linear Microphone Array in the Quantitative Evaluation of the Blade Trailing-Edge Noise Reduction

This paper concerns the application of a linear microphone array in the quantitative evaluation of blade trailing-edge (TE) noise reduction. The noise radiation from the blades with straight and serrated TEs is measured in an indoor open-jet wind tunnel. The array data are processed using the inverse method based on the Clean algorithm based on spatial source coherence (Clean-SC). In order to obtain correct application and achieve the best effect for the microphone array test, the computing software for array data reduction is firstly developed and assessed by Sarradj’s benchmark case. The assessment results show that the present array data processing method has a good accuracy with an error less than 0.5 dB in a wide frequency range. Then, a linear array with 32 microphones is designed to identify the noise source of a NACA65(12)-10 blade. The performance of the Clean-SC algorithm is compared with the Clean algorithm based on point spread functions (Clean-PSF) method for experimentally identifying the noise sources of the blade. The results show that there is about a 2 dB error when using the Clean-PSF algorithm due to the interference of different aerodynamic noise sources. Experimental studies are conducted to study the blade TE noise reduction using serrated TEs. The TE noise for the blade with and without sawtooth configurations is measured with the flow speeds from 20 m/s to 70 m/s, and the corresponding Reynolds numbers based on the chord are from 200,000 to 700,000. Parametric studies of the sawtooth amplitude and wavelength are conducted to understand the noise reduction law. It is observed that the TE noise reduction is sensitive to both the amplitude and wavelength. The flow speed also affects the noise reduction in the serrated TEs. To obtain the best noise suppression effect, the sawtooth configuration should be carefully designed according to the actual working conditions and airflow parameters.

Effects of source spatial partial coherence on intensity statistics of optical beams in mono-static turbulent channels.

We investigate, via both experimental measurements and wave-optics computer simulations, the statistical characteristics of the fluctuating intensity, such as the average intensity, the beam wander and the scintillation index, of the Gaussian Schell-model (GSM) beams on passing through double-pass, monostatic turbulence channels with either a retro-reflector (RR) or a flat mirror (FM). Our experimental results reveal that the enhanced backscatter (EBS) gradually weakens as the spatial coherence of the GSM source decreases, and eventually disappears for the sufficiently low source spatial coherence states. The r.m.s beam wander remains practically invariant with the variation of the source coherence width in the range from 0.2 to 6.0 mm both in the case of the RR and the FM, which formed the RR case being much smaller. In addition, it is found that the long-term scintillation index of the untracked beam with the RR is smaller than that with the FM, while the situation is reversed for the short-term scintillation index of the tracked beam. In both cases, the scintillation index decreases as the spatial coherence of the GSM source decreases. The obtained computer simulation results agree reasonably well with the experimental results. In addition, the effects of spatial coherence on statistical characteristics of the GSM beams along a 1 km propagation distance through the double-pass monostatic turbulence are also investigated using wave-optics simulation. We also carry out evaluation and comparison of the intensity probability density functions for the RR and FM cases and for various source coherence states that are of utmost importance for free-space optical communications in retro-reflection modulation regime. In addition, our findings will be beneficial for the development of remote sensing and directed energy laser applications in the presence of air turbulence.

Coherent artifact suppression in line-field reflection confocal microscopy using a low spatial coherence light source.

Line-field reflection confocal microscopy (LF-RCM) has the potential to add a dimension of parallelization to traditional confocal microscopy while reducing the need for two-axis beam scanning. LF-RCM systems often employ light sources with a high degree of spatial coherence. This high degree of spatial coherence potentially leads to unwanted coherent artifact in the setting of nontrivial sample scattering. Here, we (a) confirm that a coherent artifact is a nontrivial problem in LF-RCM when using spatially coherent light, and (b) demonstrate that such a coherent artifact can be mitigated through the use of reduced spatial coherence line-field sources. We demonstrate coherent noise suppression in a full-pupil line-field confocal microscope using a large number of mutually incoherent emitters from a vertical-cavity surface-emitting lasers (VCSEL) array. The coherent noise from a highly scattering sample is significantly suppressed by the use of this synthesized reduced spatial coherence light source compared to a fully coherent light source. Lastly, with scattering samples, the axial confocality of line-field confocal microscopy is compromised independent of the source spatial coherence, as demonstrated by our experimental result. Our results highlight the importance of spatial coherence engineering in parallelized reflection confocal microscopy.

Vector-valued Lambertian fields and their sources

The electromagnetic field within an aperture in the wall of a blackbody cavity is a known example of a Lambertian source producing a far field which is unpolarized in all directions. In this work we show that in the electromagnetic context other Lambertian sources exist whose far fields, while obeying the cosine law for the radiant intensity, differ by their polarization states and degrees. For example, the far field may be azimuthally, radially, or circularly polarized, or the polarization state may vary depending on the direction. For specific Lambertian fields generated by quasihomogeneous sources it is possible to calculate explicitly the $3\ifmmode\times\else\texttimes\fi{}3$ electric cross-spectral density matrix of the nonevanescent part of the source. This enables one to assess the source's spatial coherence and partial polarization properties. In all cases, the coherence length turns out to be roughly half a wavelength, whereas the polarization characteristics of the sources may differ significantly. Our results could find uses, for instance, in radiometry and photometry, lighting applications, and remote sensing.

Effects of non-Kolmogorov turbulence on the orbital angular momentum of Hankel–Bessel–Schell beams

Abstract We model the effects of the turbulence on the spread and crosstalk of the spiral spectrum of the orbital angular momentum (OAM) states for Hankel–Bessel–Schell (HBS) beams in paraxial and weak non-Kolmogorov turbulence channel. Our results show that HBS beam is a better light source which has the ability to weaken turbulence spreading of the beams and can mitigate the effects of turbulence on the detection probability of the signal OAM state due to its nondiffraction property. The detection probability of the signal OAM state for HBS beams in the non-Kolmogorov turbulence decreases with the increase of propagation distance, the generalized refractive-index structure parameters, OAM quantum number and non-Kolmogorov turbulence-parameters and with the decrease of the source spatial coherence and the wavelength of the beams. The crosstalk probability is symmetrical and has an opposite trend of the detection probability of the signal OAM state for HBS beams, and the spatial incoherence of the source increases the crosstalk effect of atmospheric turbulence among the OAM states and the spread of the spiral spectrum. Our results also show that increasing the values of non-Kolmogorov parameter and quantum number l0, will increase the spread of the spiral spectrum of the OAM states for HBS beams.

Effects of multi-Schell beams on orbital angular momentum of entangled signal photons in low-order turbulence aberration channels

We model the detection and crosstalk probability of orbital angular momentum (OAM) states of the entangled signal photon in the Kolmogorov channels of the low-order turbulence aberrations and by the Rytov approximation. The results show that lower OAM mode number of signal photons and larger sub-beam number of multi-Gaussian Schell-model pump beam, the less susceptible of the detection probability of the signal photon to spatial coherence of source and turbulence aberrations is achieved. The maximum crosstalk probability is decrease as the decreasing of the sub-beam number of multi-Gaussian Schell-model. Enlarging OAM difference value or decreasing sub-beam number of multi-Gaussian Schell-model pump beam results in a lower crosstalk probability of the OAM of entangled signal photons.

Automatic 3D scanning surface generation for microphone array acoustic imaging

This work presents a new technique for automatically generating the 3D scanning surface for acoustic imaging using microphone arrays. Acoustic images, or maps, of sound coming from spatially distributed sources, may be generated from microphone array data using algorithms such as beamforming. Traditional 2D acoustic maps can contain errors in the near-field if the object being imaged has a 3D shape. It has been shown that using the 3D surface geometry of an object as a scanning surface for beamforming can provide more accurate results. The methods used previously to generate this 3D scanning surface have either required existing CAD (Computer-Aided Design) models of the object being acoustically imaged or have required separate equipment which is generally bulky and expensive. The new method uses one or more cameras in the array, a data projector, and structured light code to automatically generate the 3D scanning surface. This has the advantage that it is inexpensive, can be incorporated as an add-onto existing microphone arrays, has short scan time, and is capable of being extended to imaging dynamic scenes. This technique is tested using beamforming and CLEAN-SC (CLEAN based on spatial Source Coherence) algorithms for a spherical array and an Underbrink multi-arm spiral array. For sound sources located about 1.2m from the array, the mean position errors obtained are 6mm. This is a quarter of the diameter of the mini-speakers being used as a sound sources.

Far-zone polarization distributionproperties of partially coherent beams with non-uniform source polarization distributions inturbulent atmosphere

It has already been found that, in turbulent atmosphere, many partially coherent electromagnetic beams with uniform source polarization distributions can regain these distribution patterns in the far field. However, the far-zone polarization properties of beams with non-uniform source polarization distributions are not sufficiently studied and the condition for an electromagnetic beam to reconstruct its source polarization distribution in the far zone is not established. Using a type of electromagnetic anisotropic Gaussian Schell-model (GSM) beams which can have non-uniform polarization distributions on the source plane, we find that, under the influence of turbulent atmosphere, the transverse polarization distribution will finally become uniform starting with a non-uniform source polarization distribution, and the far-field degree of polarization is affected by the source intensity parameters, but not by the source spatial coherence parameters. We also find that, electromagnetic anisotropic GSM beams can regain their source polarization patterns in the far field when propagating through atmospheric turbulence if and only if, the two intensity distributions corresponding to the two orthogonal field components on the source plane are the same, or are different only for a constant parameter. The validity of this condition is unaffected by the intensity and spatial coherence profiles on the source plane.

Spreading of partially coherent Hermite–Gaussian beams through a non-Kolmogorov turbulence

Abstract Based on extended Huygens–Fresnel principle, an analytical expression for beam width of partially coherent Hermite–Gaussian (PCHG) beam through non-Kolmogorov turbulence is derived. The effects of inner scale l 0, outer scale L 0, exponent value α, beam order m and degree of source spatial coherence on the spreading of PCHG beam through non-Kolmogorov turbulence are examined in detail. Results show that the smaller inner scale l 0 and bigger outer scale L 0 give rise to the bigger beam spreading of PCHG beam through non-Kolmogorov turbulence. In the far field, the beam spreading of PCHG is independent of the degree of source spatial coherence, which has potential applications in long-distance free-space optical communications.

Extension of deconvolution algorithms for the mapping of moving acoustic sources

Several deconvolution algorithms are commonly used in aeroacoustics to estimate the power level radiated by static sources, for instance, the deconvolution approach for the mapping of acoustic sources (DAMAS), DAMAS2, CLEAN, and the CLEAN based on spatial source coherence algorithm (CLEAN-SC). However, few efficient methodologies are available for moving sources. In this paper, several deconvolution approaches are proposed to estimate the narrow-band spectra of low-Mach number uncorrelated sources. All of them are based on a beamformer output. Due to velocity, the beamformer output is inherently related to the source spectra over the whole frequency range, which makes the deconvolution very complex from a computational point of view. Using the conventional Doppler approximation and for limited time analysis, the problem can be separated into multiple independent problems, each involving a single source frequency, as for static sources. DAMAS, DAMAS2, CLEAN, and CLEAN-SC are then extended to moving sources. These extensions are validated from both synthesized data and real aircraft flyover noise measurements. Comparable performances to those of the corresponding static methodologies are recovered. All these approaches constitute complementary and efficient tools in order to quantify the noise level emitted from moving acoustic sources.

Comparison of Microphone Array Processing Techniques for Aeroacoustic Measurements

This paper presents a systematic comparison of several prominent beamforming algorithms developed for aeroacoustic measurements. The most widely used delay-and-sum (DAS) beamformer is known to suffer from high sidelobe level and low resolution problems. Therefore, more advanced methods, in particular the deconvolution approach for the mapping of acoustic sources (DAMAS), sparsity constrained DAMAS (SC-DAMAS), covariance matrix fitting (CMF) and CLEAN based on spatial source coherence (CLEAN-SC), have been considered to achieve improved resolution and more accurate signal power estimates. The performances of the aforementioned algorithms are evaluated via experiments involving a 63-element logarithmic spiral microphone array in the presence of a single source, two incoherent sources with similar strengths and with different strengths, and two coherent sources. It is observed that DAMAS, SC-DAMAS and CMF provide the most reliable source location estimates, even at relatively low frequencies. Furthermore, the integrated levels obtained with the array processing algorithms are shown to agree with what a single reference microphone placed at the center of the array measures when the array is appropriately calibrated. It is also shown that, as expected, the aforementioned algorithms are unsuccessful in distinguishing coherent acoustic sources unless the frequency is relatively high. DAS and CLEAN-SC are shown to be around 2 to 90 times faster than the other three algorithms.

CLEAN Based on Spatial Source Coherence

To obtain higher resolution acoustic source plots from microphone array measurements, deconvolution techniques are becoming increasingly popular. Deconvolution algorithms aim at identifying Point Spread Functions (PSF)in source plots, and may therefore fall short when actual beam patterns of measured noise sources are not similar to synthetically obtained PSF's. To overcome this, a new version of the classical deconvolution method CLEAN is proposed here: CLEAN-SC. By this new method, which is based on spatial source coherence, side lobes can be removed of actually measured beam patterns. Essentially, CLEAN-SC iteratively removes the part of the source plot which is spatially coherent with the peak source. A feature of CLEAN-SC is its ability to extract absolute sound power levels from the source plots. The merits of CLEAN-SC were demonstrated using array measurements of airframe noise on a scale model of the Airbus A340 in the 8 ×6 m2 closed test section of DNW-LLF.

Visibility in differential phase-contrast imaging with partial coherence source

This paper gives theoretical analysis of visibility of fringes, which is influenced by distances, temporal and spatial coherence of source, in hard x-ray differential phase-contrast imaging with microfocus x-ray source. According to the character of longitudinal periodicity of the interferogram, the setup is insensitive to mechanical drift and vibrations. The effect of temporal coherence of x-ray source is investigated and its related bandwidth is derived. Based on the theory of partially coherent light, it shows that the requirement for the spatial coherence of x-ray source is not strict and can be met by the general microfocus x-ray tube for x-ray differential phase-contrast imaging.

On the possibility of aperture synthesis with a single mobile antenna in radio astronomy

The classic aperture synthesis widely used in radio astronomy, synthetic aperture radar, and remote sensing is based on the measurement of the degree of spatial coherence in the diffraction pattern of a radio emission source. All these applications imply correlation with a coherent reference signal. The possibility of obtaining the same information from the autocorrelation of a signal recorded on a single, mobile antenna is considered. Comparison of the output of an ordinary cross-correlation two-element radio interferometer and the autocorrelation output of a mobile antenna shows a similarity that allows extraction of information about the radio source spatial coherence in the latter case. The limitations of this method of aperture synthesis are considered.

Atmospheric optical communication with a Gaussian Schell beam.

We consider a wireless optical communication link in which the laser source is a Gaussian Schell beam. The effects of atmospheric turbulence strength and degree of source spatial coherence on aperture averaging and average bit error rate are examined. To accomplish this, we have derived analytic expressions for the spatial covariance of irradiance fluctuations and log-intensity variance for a Gaussian beam of any degree of coherence in the weak fluctuation regime. When spatial coherence of the transmitted source beam is reduced, intensity fluctuations (scintillations) decrease, leading to a significant reduction in the bit error rate of the optical communication link. We have also identified an enhanced aperture-averaging effect that occurs in tightly focused coherent Gaussian beams and in collimated and slightly divergent partially coherent beams. The expressions derived provide a useful design tool for selecting the optimal transmitter beam size, receiver aperture size, beam spatial coherence, transmitter focusing, etc., for the anticipated atmospheric channel conditions.

Optimizing synchroton-based x-ray lithography for 0.1 μm lithography

Abstract Of the many factors affecting the image intensity distribution, the variables that can be controlled are source spectrum, source spatial coherence, proximity gap, mask linewidth bias, and absorber thickness. To obtain the highest quality aerial image, all of these parameters must be optimized simultaneously. We describe an optimization of the spectrum of the Helios synchrotron, located at IBM's Advanced Lithography Facility (ALF) [1]. To obtain a spectrum better suited to 0.1 μm-linewidth x-ray lithography, the vacuum window should be changed from Be to 2 μm of Si. We present experimental results on the strength of SiN x windows for use as vacuum windows and propose a fabrication procedure for making beamline windows. Using the determined optimum spectrum, we summarize the results of a previous optimization study [2] of the x-ray aerial image. This optimization is performed using a rigorous electromagnetic model that accounts for diffraction in the absorber, source partial coherence, and diffraction in the proximity gap. The aerial image of 0.1 μm features at a gap of 10 μm is optimized.

Simultaneous optimization of spectrum, spatial coherence, gap, feature bias, and absorber thickness in synchrotron-based x-ray lithography

Of the many factors affecting the x-ray intensity distribution, the variables that can be controlled are the source spectrum, the proximity gap, the source spatial coherence, the mask linewidth bias, and the absorber thickness. To obtain the highest quality aerial image, all of these parameters must be optimized simultaneously. An optimization of the spectrum of the synchrotron Helios, located at IBM’s Advanced Lithography Facility is described. The optimum parameter space for proximity x-ray lithography at 0.1 μm minimum linewidth is then determined using the optimized spectrum by adjusting the free parameters. For maximum accuracy, a rigorous electromagnetic model that accounts for the dielectric properties of the absorber, the source partial coherence, and diffraction in the proximity gap is used to calculate the x-ray aerial image at the wafer. Descriptive figures-of-merit (FOMs) of the aerial image are the image contrast [(Imax−Imin)/(Imax+Imin)] and the exposure latitude. These two FOMs are maximized with respect to source spectrum, gap, source spatial coherence, feature size and bias, and mask absorber thickness. The global maximum of these FOMs is coarsely located in parameter space by determining the dependence of the FOMs on two variables at a time. The feature bias is then determined so that all feature types (gratings, lines, spaces) can be printed at the same dose with maximum average contrast and exposure latitude.

The effect of spatial coherence of sources on synthetic aperture mapping

The interferometric mapping of astronomical objects relies on the van-Cittert Zernike theorem, one of the major results of the theory of partially coherent light [see, Bom and Wolf (1980), chapter 10]. This theorem states that the degree of spatial coherence of the field from a distant spatially incoherent source is proportional to the Fourier transform of the intensity distribution across the source. Measurement of the degree of spatial coherence, by, for example, measuring the visibility of interference fringes, allows the object to be mapped by making an inverse Fourier transform. (For a full description of this technique see Thompson, Moran and Swenson, 1986.)In this paper I present a summary of the results an investigation into what happens when the distant source is not spatially coherent (James, 1990). Using a heuristic model of a spherically symmetric partially coherent source, an analytic expression for the error in the measurement of the effective radius, expressed as a function of coherence area, can be obtained.

Field correlations within a Bessel-correlated spherical source

The spatial field correlations within a Bessel-correlated spherical source with large size parameter (radius much greater than the wavelength) are investigated. Exact expressions for the field spectral density, in terms of a partial-wave series, as well as for the magnitude of the complex degree of spectral coherence (correlating the field at an arbitrary internal point with that at the center of the sphere), are obtained. Asymptotic approximations for a large size parameter are found by applying complex angular-momentum techniques. The results are discussed and plotted for a wide range of values of the ratio between the source spatial coherence length and the wavelength. The asymptotic approximations are found to be quite accurate. The field ranges from extreme incoherence to full spatial coherence. The latter is attained only when the source’s coherence length becomes much larger than its Fresnel radius. Results previously obtained in the limit of an unbounded source are verified. Features arising from finite size and boundary effects are discussed.

Beam properties of partially coherent curved beam waves in the turbulent atmosphere

The mutual intensity function at a distance from a spatially partially coherent beam wave source is calculated including the effects of intervening atmospheric turbulence using the extended Rayleigh–Sommerfeld integral technique. The source spatial coherence function consists of a coherent contribution and a Schell-model partially coherent contribution simulating the random phase distortion of a coherent curved beam wave resulting from rough-surface reflection or diffuser transmission. The calculated mutual intensity function consists of two Schell-model coherence functions having differing amplitude radii, intensities, coherence length, and phase front curvatures. Calculated results for the special case of a perfectly coherent beam wave agree with previous numerical calculations using the Markov approximation of the parabolic wave equation in both weak and strong turbulence. Graphical results illustrate the effects of the source coherence parameters and turbulence on the beam properties at a distance.