Measurement Of Spatial Coherence Research Articles

Two-dimensional spatial coherence measurement of X-ray sources using aperture array mask.

Fourth-generation synchrotron radiation delivers x-ray sources with unprecedented coherence and brilliance, which enables the development of many advanced coherent techniques taking advantage of the inherent high coherence of the x-ray beams. Simple and accurate measurement of two-dimensional (2D) coherence is of utmost importance for the applications of these coherent experimental techniques. Here, we propose a novel approach based on diffraction of aperture array mask (AAM) to obtain accurate 2D spatial coherence with a single-shot measurement. We utilize a coherent mode decomposition algorithm to simulate the diffraction of AAM illuminated by Gaussian-Schell model beam and demonstrate that spatial coherence function of the incident light beam can be accurately and robustly retrieved. We expect that this new approach will be applied into transverse coherence measurements for the new-generation synchrotron radiation source and relevant coherent experimental techniques.

Image plane digital holography for simultaneous measurement of temporal and spatial coherence

In this work, we propose and validate the Image Plane Digital Holography (IPDH) with laminar illumination technique for measuring the complete coherence degree, the temporal coherence length and the spatial coherence area (transversal coherence radius), of a light source at the same time and from a single measurement. This holographic technique has been used before as a fluid velocimetry technique that allows measuring the three components of the fluid velocity in a plane. Since its performance is limited by the temporal and spatial coherence of the laser, we can take advantage of this and make IPDH with laminar illumination a means of obtaining these laser properties. The proposed method could be of interest for the optics community since it could be used for any type of light source, presenting some advantages by comparing it with other well-established techniques. It has been tested by using a high repetition rate laser commonly used in velocimetry and the results have been compared to those obtained with other standard techniques, verifying the well-functioning of the IPDH-based technique.

Full-beam spatial coherence measurements of supercontinuum generation in multimode fibers

We study experimentally the spatial coherence across the full spatial beam profile of supercontinuum light generated in both in graded-index and step-index multimode fibers. We observe a decrease of the coherence area with an increase of the injected pump power. Numerical simulations based on linearly polarized modes and mode coupling theory are in good agreement with our experiments and indicate that the decrease of coherence area is strongly related to a change in the modal amplitude distribution.

Measurement of spatial coherence of light [Invited

The most frequently used experimental techniques for measuring the spatial coherence properties of classical light fields in the space-frequency and space-time domains are reviewed and compared, with some attention to polarization effects. In addition to Young's classical two-pinhole experiment and several of its variations, we discuss methods that allow the determination of spatial coherence at higher data acquisition rates and also permit the characterization of lower-intensity light fields. These advantages are offered, in particular, by interferometric schemes that employ only beam splitters and reflective elements, and thereby also facilitate spatial coherence measurements of broadband fields.

Fast and reliable technique for spatial coherence measurement with a temporally modulated nonredundant slit array.

We propose a method of measuring the spatial coherence of light by means of a temporally modulated nonredundant slit array implemented on a digital micromirror device. We first formulate the theory of the spatial coherence measurement to incorporate a general case when the observation plane is not necessarily placed in the far field of the slit array. We then demonstrate experimentally that a single measurement determines the spatial coherence for 15 different slit separations accurately, even if background light is unavoidable, under the condition that a nonredundant array of six slits is illuminated evenly. These results clearly show that fast and highly reliable spatial coherence measurement is achievable with the proposed method without any difficulties.

Deep learning-based image reconstruction for photonic integrated interferometric imaging.

Photonic integrated interferometric imaging (PIII) is an emerging technique that uses far-field spatial coherence measurements to extract intensity information from a source to form an image. At present, low sampling rate and noise disturbance are the main factors hindering the development of this technology. This paper implements a deep learning-based method to improve image quality. Firstly, we propose a frequency-domain dataset generation method based on imaging principles. Secondly, spatial-frequency dual-domain fusion networks (SFDF-Nets) are presented for image reconstruction. We utilize normalized amplitude and phase to train networks, which reduces the difficulty of network training using complex data. SFDF-Nets can fuse multi-frame data captured by rotation sampling to increase the sampling rate and generate high-quality spatial images through dual-domain supervised learning and frequency domain fusion. Furthermore, we propose an inverse fast Fourier transform loss (IFFT loss) for network training in the frequency domain. Extensive experiments show that our method improves PSNR and SSIM by 5.64 dB and 0.20, respectively. Our method effectively improves the reconstructed image quality and opens a new dimension in interferometric imaging.

Broadband sound speed and attenuation of a mud layer from acoustic propagation experiments in the New England Mud Patch

A series of Seabed Characterization Experiments (SBCEX) have been conducted in the New England Mud Patch area, where a top mud layer overlays a sand sediment. Using broadband acoustic signals from the SBCEX, the sound speed and attenuation of the mud layer as a function of frequency (from a few tens of Hz up to around 1 kHz) have been estimated by various inversion algorithms based on (1) modal dispersion curves and transmission loss [reported at the ASA Spring meeting, 2016], (2) Airy phase [Spring, 2017], (3) modal amplitude [Fall, 2017], (4) spatial coherence measurements [Spring, 2018], (5) mid-frequency modal dispersion analysis [Fall, 2019], and (6) ground waves [Fall, 2022]. This paper summarizes these inverted sound speed and attenuation, which are obtained at various frequencies independently (without using the frequency dependent constraints from any geo-acoustic models), therefore the inverted results could be used to verify the validity of geo-acoustic models. The performances of these inversion methods are evaluated. The performance assessment is helpful for one to select appropriate inversion algorithms and to choose optimal acoustic data for geo-acoustic inversion. [Work supported by ONR Ocean Acoustics.]

Spatial coherence of vertical atmospheric sound propagation

Atmospheric turbulence causes the amplitude and phase of sound waves to fluctuate, which reduces the coherence of acoustic signals. Spatial coherence describes the similarity of two signals at different points in space, and a better understanding of acoustic coherence could lead to improved target detection, tracking, and identification. This presentation compares theoretical predictions and measurements of the acoustic spatial coherence. The theoretical coherence is derived by combining sound propagation theory with turbulence models that include the effects of atmospheric shear and buoyancy instabilities. To be applicable to vertical and slanted propagation, the turbulence models use height-dependent variances and length scales for the fluctuations in temperature, shear-produced velocity, and buoyancy-produced velocity. Instrumentation on a 135-m meteorological tower at the National Wind Technology Center (Boulder, CO) provided the required model input data. The coherence measurements used a ground-based source and nine microphones attached to the same meteorological tower. Overall, the theoretical model accurately approximated the measured spatial coherences, especially when the atmospheric turbulence was fully developed (e.g., in the afternoon on sunny days). The largest disagreement occurred for measurements taken at dawn. For a source frequency of 3.4 kHz and microphones that are 130 m high and 1.5 m apart, the measured coherence was 0.3–0.6 for sunny conditions and 0.8–0.9 for cloudy conditions.

Imaging Through Random Scatterer with Spatial Coherence Structure Measurement

Optical coherence is becoming an efficient degree of freedom for light field manipulations and applications. In this work, we show that the image information hidden a distance behind a random scattering medium is encoded in the complex spatial coherence structure of a partially coherent light beam that generates after the random scatterer. We validate in experiment that the image information can be well recovered with the spatial coherence measurement and the aid of the iterative phase retrieval algorithm in the Fresnel domain. We find not only the spatial shape but also the position including the lateral shift and longitudinal distances of the image hidden behind the random scatterer can be reconstructed, which indicates the potential uses in three-dimensional optical imaging through random scattering media.

Spatial Coherence Adaptive Clutter Filtering in Color Flow Imaging-Part II: Phantom and In Vivo Experiments.

Conventional color flow processing is associated with a high degree of operator dependence, often requiring the careful tuning of clutter filters and priority encoding to optimize the display and accuracy of color flow images. In a companion paper, we introduced a novel framework to adapt color flow processing based on local measurements of backscatter spatial coherence. Through simulation studies, the adaptive selection of clutter filters using coherence image quality characterization was demonstrated as a means to dynamically suppress weakly-coherent clutter while preserving coherent flow signal in order to reduce velocity estimation bias. In this study, we extend previous work to evaluate the application of coherence-adaptive clutter filtering (CACF) on experimental data acquired from both phantom and in vivo liver and fetal vessels. In phantom experiments with clutter-generating tissue, CACF was shown to increase the dynamic range of velocity estimates and decrease bias and artifact from flash and thermal noise relative to conventional color flow processing. Under in vivo conditions, such properties allowed for the direct visualization of vessels that would have otherwise required fine-tuning of filter cutoff and priority thresholds with conventional processing. These advantages are presented alongside various failure modes identified in CACF as well as discussions of solutions to mitigate such limitations.

Spatial Coherence Adaptive Clutter Filtering in Color Flow Imaging-Part I: Simulation Studies.

The appropriate selection of a clutter filter is critical for ensuring the accuracy of velocity estimates in ultrasound color flow imaging. Given the complex spatio-temporal dynamics of flow signal and clutter, however, the manual selection of filters can be a significant challenge, increasing the risk for bias and variance introduced by the removal of flow signal and/or poor clutter suppression. We propose a novel framework to adaptively select clutter filter settings based on color flow image quality feedback derived from the spatial coherence of ultrasonic backscatter. This framework seeks to relax assumptions of clutter magnitude and velocity that are traditionally required in existing adaptive filtering methods to generalize clutter filtering to a wider range of clinically-relevant color flow imaging conditions. In this study, the relationship between color flow velocity estimation error and the spatial coherence of clutter filtered channel signals was investigated in Field II simulations for a wide range of flow and clutter conditions. This relationship was leveraged in a basic implementation of coherence-adaptive clutter filtering (CACF) designed to dynamically adapt clutter filters at each imaging pixel and frame based on local measurements of spatial coherence. In simulation studies with known scatterer and clutter motion, CACF was demonstrated to reduce velocity estimation bias while maintaining variance on par with conventional filtering.

Classification of volcanic tremors and earthquakes based on seismic correlation: application at Sakurajima volcano, Japan

SUMMARY Classification of volcanic tremors and earthquakes is an important part of volcano monitoring. Conventional classification technique relies on visual characterization of the amplitudes, frequency, or duration of seismic signals. In some cases, such classification is difficult to be maintained continuously, especially during high eruptive activities. In the present study, we develop a classification technique based on analyses of seismic wave correlation. The technique is based on a measure of spatial coherence using the distribution width of eigenvalues from the seismic covariance matrix that is referred to as ‘spectral width’. We use the spectral width characteristics to extract the frequencies where the seismic signals are the most spatially coherent. We analyse 6-month continuous seismic data at six seismic stations deployed on Sakurajima volcano, Japan. The classification is performed every 10 min to recognize volcanic tremor and B-type earthquakes, both of which show unclear onsets and are dominant at around 1–4 Hz. Their frequencies of high spatial coherence are different from each other, providing a basis for automatic classification of both types of seismic events. Our classification results show that an increase in seismic activity, particularly volcanic tremors, occurred during high eruptive activity and is well matched with the events that are routinely determined by the Japan Meteorological Agency (JMA) based on visual examination of the data. We discuss the volcanic activities by combining our classification results with those from detections and location methods based on seismic correlation. Most of the source locations of volcanic tremor and B-type earthquakes are distributed at the same region with depths of less than 4 km beneath the active craters, which are almost consistent with the source locations of explosion earthquakes and B-type earthquakes determined from P-wave onsets in the previous studies. Also, the distribution of horizontal locations is spatially elongated at shallow depths above a dyke that is inferred to extend from Aira caldera at a depth of 7–9 km. We obtain deep and shallow sources for the tremor that occurred before and after an explosive eruption, respectively. We also obtain shallow sources beneath the active crater during a continuous tremor that accompanies increasing eruptive activity. The source locations of the classified volcanic tremor and B-type earthquakes may represent the movement of magma and gas from the shallow magma chamber at 5 km depth to the active craters.

Quantitative measurement of spatial coherence of electron beams emitted from a thermionic electron gun

In this study, quantitative measurement of the spatial coherence of electron beams emitted from a thermionic-emission gun was achieved for the first time, to our knowledge. For the measurement, Airy patterns were formed using a specially fabricated aperture with an effective diameter of approximately 10 nm at the specimen plane in a 200 kV transmission electron microscope. Subsequently, from the fitting analysis of the Airy patterns recorded with beam diameters ranging from 2.0 to 6.9 µ m , spatial coherence lengths from 7 to 19 nm were successfully measured in proportion to the beam diameters. In addition, considering time evolution of the total beam current measured at the specimen plane, the relation between the on-axis current density and the coherence length is shown, where the former is inversely proportional to the square of the latter. Compared with the result using a Schottky-type field emission gun measured in a previous study, the spatial coherence length in the L a B 6 thermionic-emission gun transmission electron microscope is one to two orders of magnitude shorter when a similar beam intensity is formed at the specimen plane.

Dual measurements of temporal and spatial coherence of light in a single experimental setup using a modified Michelson interferometer.

An experimental technique is developed to simultaneously measure both temporal and spatial coherences of a light source by altering a standard Michelson interferometer, which has been primarily used for measuring temporal coherence only. Instead of using simple plane mirrors, two retroreflectors and their longitudinal and lateral movements are utilized to incorporate spatial coherence measurement using this modified Michelson interferometer. In general, one uses Young's double slit interferometer to measure spatial coherence. However, this modified interferometer can be used as an optical setup kept at room temperature outside a cryostat to measure the spatiotemporal coherence of a light source placed at cryogenic temperatures. This avoids the added complexities of modulation of interference fringe patterns due to single slit diffraction as well. The process of mixing of spatial and temporal parts of coherences is intrinsic to existing methods for dual measurements. We addressed these issues of spatiotemporal mixing, and we introduced a method of "temporal filtering" in spatial coherence measurements. We also developed a "curve overlap" method that is used to extend the range of the experimental setup during temporal coherence measurements without compromising the precision. Together, these methods provide major advantages over plane mirror based standard interferometric systems for dual measurements in avoiding systematic errors, which lead to inaccuracies, especially for light sources with low coherences.

Spatial coherence measurement via a digital micromirror device based spatiotemporal light modulation.

We propose a method for measuring the spatial coherence of light by means of temporal modulation of a double slit displayed on a digital micromirror device. It is demonstrated theoretically and experimentally that the technique is generally insensitive to background light, and thus its suppression or subtraction is not necessary. Moreover, the visibility of the interference fringe pattern can be enhanced by modulating only either one of the two slits. These favorable features enable one to measure the spatial coherence of even faint light more conveniently and accurately.

Low threshold incoherent random lasing with spectral overlap optimization of size-tuned plasmonic nanorods

Plasmonic random lasers continue to generate significant interest in the fields of optics and photonics due to their improved performance. This owes to the greater scattering strength and enhanced local field offered by the plasmonic scatterers. However, absorption losses and fluorescence quenching are the major setbacks to plasmonic random lasers. Design of plasmonic random lasers with low threshold and enhanced emission intensity continues to be a challenging area of research. This paper demonstrates that the use of one-dimensional anisotropic plasmonic structures can help to overcome these limitations to a great extent by manipulating the spectral overlap between the scatterers and gain medium. A low threshold random lasing system has been experimentally realized in this context, using Ag nanorods with aspect ratio tuned to give optimal scattering and field enhancement. The optimal aspect ratios were deduced using FDTD simulations and incoherent random lasing was experimentally demonstrated at a low threshold of 116 µJ/cm2 or 0.023 MW/cm2. We also demonstrate through spatial coherence measurements that the bright emission from the plasmonic random laser enables speckle contrast reduction upto 0.034 with single pulse illumination.

Spatial coherence characterization of light: An experimental study using digital micromirror devices

We present spatial coherence measurements of partially coherent light in the far-field of incoherent sources with an experimental setup based on the Thompson–Wolf and Partanen–Turunen–Tervo experiments, to be performed in the context of a possible solar coherence measurement space instrument. The optical setup consists of a telescope to collimate light from a source, to diffract it by a digital micromirror device implementing a Young double-aperture interferometer in retroreflection mode, and finally to image the source into a two-dimensional sensor. Two multimode optical fibers with different diameters were used as incoherent sources and the results obtained for the spectral degree of coherence are compared to those expected from the van Cittert–Zernike theorem.

Enabling time-resolved 2D spatial-coherence measurements using the Fourier-analysis method with an integrated curved-grating beam monitor.

Direct 2D spatial-coherence measurements are increasingly gaining importance at synchrotron beamlines, especially due to present and future upgrades of synchrotron facilities to diffraction-limited storage rings. We present a method to determine the 2D spatial coherence of synchrotron radiation in a direct and particularly simple way by using the Fourier-analysis method in conjunction with curved gratings. Direct photon-beam monitoring provided by a curved grating circumvents the otherwise necessary separate determination of the illuminating intensity distribution required for the Fourier-analysis method. Hence, combining these two methods allows for time-resolved spatial-coherence measurements. As a consequence, spatial-coherence degradation effects caused by beamline optics vibrations, which is one of the key issues of state-of-the-art X-ray imaging and scattering beamlines, can be identified and analyzed.

Mirror-based scanning wavefront-folding interferometer for coherence measurements.

We demonstrate a modification to the traditional prism-based wavefront-folding interferometer that allows the measurement of spatial and temporal coherence, free of distortions and diffraction caused by the prism corners. In our modified system, the two prisms of the conventional system are replaced with six mirrors. The whole system is mounted on a linear XY-translation stage, with an additional linear stage in the horizontal arm. This system enables rapid and exact measurement of the full four-dimensional degree of coherence, even for relatively weak signals. The capabilities of our system are demonstrated by measuring the spatial coherence of two inhomogeneous and non-Schell model light sources with distinct characteristics.

Spatial coherence measurement through Fourier transform of intensity of diffraction fringes of a 1D step in reflection

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