Degree Of Spatial Coherence Research Articles

Effect of spatial coherence on damage occurrence in multimode optical fibers.

We investigate the influence of spatial coherence on damage occurrence in highly multimode optical fibers using ultraviolet (UV) nanosecond pulses, with the aim of delivering high fluence in the UV. In some cases, the optical damage is initiated below the fiber facet damage threshold and takes place along the propagation path; such damage is believed to be caused by local constructive interference, creating "hot spots." In order to reduce the degree of spatial coherence, we used a large-diameter core (1.5mm) fiber as a mode scrambler. Different lengths of this large core fiber were used to deliver energy to a fiber core with a smaller diameter (0.6mm), in which the damage occurrence was observed. The experimental results indicate that there is a correlation between the degree of spatial coherence and the occurrence of optical damages, typically observed a few millimeters from the fiber facet. Numerical simulations, based on the beam-propagation method, support the degradation of spatial coherence, due to the excitation of high-order modes. Finally, by degrading the spatial coherence of the beam, we establish a new record by delivering more than 100mJ via a 1.5mm core diameter fiber in the UV, corresponding to ∼26 times the critical power for self-focusing. Our work sheds light on the ability to deliver high energies of nanosecond-pulsed UV laser radiation through multimode optical fibers.

Spatial coherence of sunlight and its implications for light management in photovoltaics

New technologies are emerging that capture and redirect sunlight inside solar cells. This type of light management can significantly increase efficiency, but the device behavior will fundamentally depend on the spatial coherence of the incoming light. This dependence calls for a complete characterization of the spatial coherence of sunlight. Here, we present the first spectral measurements of the spatial degree of coherence of direct, diffuse, and simulated sunlight. An expression is derived for both the cross-spectral density and the spatial degree of coherence in an arbitrarily oriented device plane, including the effects of overcast skies. Implications of the present work are discussed and may lead to a better understanding of light-managing components in solar cells as well as a new class of solar simulator that provides both the same spectrum and spatial coherence as direct sunlight.

大功率VCSEL三角列阵的空间相干性

The spatial coherence properties of high power vertical cavity surface emitting lasers( VCSELs) triangle-arrays were studied based on the theorem of Hermitian-Gaussian beams and spatial coherence. The far-field divergence angle and spatial coherence degree were gauged using the second-moment method and spatial coherence degree integral average value method for the devices of980 nm wavelength VCSEL arrays. The influence of array-units distance on far-field characteristics and coherent characteristics was also discussed. With the increasing of array element spacing from200 μm to 300 μm,the far-field divergence angle of VCSEL arrays device increases from 9. 5° to12. 5°,and the spatial coherence degree decreases from 0. 719 to 0. 526,while the unit aperture of triangle array is 150 μm. Under the same injection current condition,the optical powers of three VCSEL array devices are almost equal.

Effect of the temporal coherence of radiation fields of X-ray sources on the spatial coherence of beams and pulses

The behavior of a spatial coherence function is considered, depending on time, the coherence of the source radiation, and the distance to a source and its size. It is shown that as the distance grows, the source’s partial temporal coherence reduces the degree of spatial coherence and there is a change in the form of the function of spatial coherence, which also begins to depend on the choice of a point in the cross section of an X-ray beam or a pulse.

Inter-annual variability and spatial coherence of net primary productivity across a western Oregon Cascades landscape

Inter-annual variability (IAV) of forest Net Primary Productivity (NPP) is a function of both extrinsic (e.g., climate) and intrinsic (e.g., stand dynamics) drivers. As estimates of NPP in forests are scaled from trees to stands to the landscape, an understanding of the relative effects of these factors on spatial and temporal behavior of NPP is important. Although a high degree of spatial coherence (i.e., the degree of spatial synchrony over time) is often assumed, this inherent behavior is rarely examined. Quantifying this term may improve future predictions as site-level estimates are scaled up spatially. We quantified the spatial coherence of bole biomass production (BBP) within and between trees, and bole-related NPP (NPPB) between sites of varying age, elevation, moisture, and species composition across a forested landscape in the western Cascade Range of Oregon. Within sites, individual trees with lower than average BBP were the most coherent. IAV of BBP increased as average tree BBP increased and spatial coherence was reduced. Among sites, NPPB was the most spatially coherent (r=0.92) between young sites, while older sites and comparisons between age classes revealed a much larger range in spatial coherence (r=−0.18 to 0.85). Our findings indicate climate variability may be of greater importance for spatial coherence between young sites, and that intrinsic factors could be decreasing spatial coherence between older sites or sites not in close proximity. The wide range in spatial coherence between sites found in this study, coupled with the complex land use history patterns across forested landscapes, has significant implications for modeling and scaling of NPP.

Quantitative phase imaging with partially coherent illumination.

In this Letter, we formulate a mathematical model for predicting experimental outcomes in quantitative phase imaging (QPI) when the illumination field is partially spatially coherent. We derive formulae that apply to QPI and discuss expected results for two classes of QPI experiments: common path and traditional interferometry, under varying degrees of spatial coherence. In particular, our results describe the physical relationship between the spatial coherence of the illuminating field and the halo effect, which is well known in phase-contrast microscopy. We performed experiments relevant to this common situation and found that our theory is in excellent agreement with the data. With this new understanding of the effects of spatial coherence, our formulae offer an avenue for removing halo artifacts from phase images.

Ronchi test for characterization of X-ray nanofocusing optics and beamlines

A Ronchi interferometer for hard X-rays is reported in order to characterize the performance of the nanofocusing optics as well as the beamline stability. Characteristic interference fringes yield qualitative data on present aberrations in the optics. Moreover, the visibility of the fringes on the detector gives information on the degree of spatial coherence in the beamline. This enables the possibility to detect sources of instabilities in the beamline like vibrations of components or temperature drift. Examples are shown for two different nanofocusing hard X-ray optics: a compound refractive lens and a zone plate.

Multiple interfacing between classical ray-tracing and wave-optical simulation approaches: a study on applicability and accuracy.

In this study the applicability of an interface procedure for combined ray-tracing and finite difference time domain (FDTD) simulations of optical systems which contain two diffractive gratings is discussed. The simulation of suchlike systems requires multiple FDTD↔RT steps. In order to minimize the error due to the loss of the phase information in an FDTD→RT step, we derive an equation for a maximal coherence correlation function (MCCF) which describes the maximum degree of impact of phase effects between these two different diffraction gratings and which depends on: the spatial distance between the gratings, the degree of spatial coherence of the light source and the diffraction angle of the first grating for the wavelength of light used. This MCCF builds an envelope of the oscillations caused by the distance dependent coupling effects between the two diffractive optical elements. Furthermore, by comparing the far field projections of pure FDTD simulations with the results of an RT→FDTD→RT→FDTD→RT interface procedure simulation we show that this function strongly correlates with the error caused by the interface procedure.

Characterization of spatial coherence of synchrotron radiation with non-redundant arrays of apertures.

A method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern is presented. The technique is based on scattering from non-redundant arrays (NRAs) of slits and records the degree of spatial coherence at several relative separations from 1 to 15 µm, simultaneously. Using NRAs the spatial coherence of the X-ray beam at the XUV X-ray beamline P04 of the PETRA III synchrotron storage ring was measured as a function of different beam parameters. To verify the results obtained with the NRAs, additional Young's double-pinhole experiments were conducted and showed good agreement.

Modal representation of spatial coherence in dissipative and resonant photonic systems

We provide a self-consistent electromagnetic theory of the link between spatial coherence and optical resonances in three-dimensional open and dissipative photonic systems. The theory that relies on the concept of quasinormal modes with complex frequencies provides an accurate modal expansion of the imaginary part of the Green tensor that correctly treats the effects of radiative leakage, absorption, and dispersion. It represents a powerful tool for calculating and understanding the degree of spatial coherence in complex photonic or plasmonic systems that are governed by a small number of resonances. Comparisons with fully vectorial calculations evidence the high accuracy of the predictions achieved by our semianalytical treatment in the case of coupled photonic-crystal microcavities and plasmonic nanoantennas made of metallic nanorods.

Spatial coherence properties of organic molecules coupled to plasmonic surface lattice resonances in the weak and strong coupling regimes.

We study spatial coherence properties of a system composed of periodic silver nanoparticle arrays covered with a fluorescent organic molecule (DiD) film. The evolution of spatial coherence of this composite structure from the weak to the strong coupling regime is investigated by systematically varying the coupling strength between the localized DiD excitons and the collective, delocalized modes of the nanoparticle array known as surface lattice resonances. A gradual evolution of coherence from the weak to the strong coupling regime is observed, with the strong coupling features clearly visible in interference fringes. A high degree of spatial coherence is demonstrated in the strong coupling regime, even when the mode is very excitonlike (80%), in contrast to the purely localized nature of molecular excitons. We show that coherence appears in proportion to the weight of the plasmonic component of the mode throughout the weak-to-strong coupling crossover, providing evidence for the hybrid nature of the normal modes.

大功率VCSEL器件的空间相干性的研究

The spatial coherence properties of high power vertical cavity surface emitting lasers (VCSELs) are studied based on the theorem of partially coherent light proposed by Van Cittert-Zernike. The interference stripe patterns are gauged using the Young's double-slit experiment for the devices of 980 nm wavelength VCSEL single emitters. Then interference patterns are switched to grayscale by intensity distribution patterns for data collection. In this paper, the integral average value method is proposed to calculate the degree of spatial coherence. The proposed integral average value method and traditional average method are used respectively to calculate the light intensity of the pattern. The results are compared with those calculated by the theoretical value of Van Cittert-Zernike theorem. The VCSEL optical apertures' influence on coherent characteristics are also discussed. The experimental results show that, a relative error within 2.5%~9.4% is reached by our integral average value method. On the contrary, a relative error of 7.5%~67.4% are got from the traditional average method. Apparently, traditional average value method causes the error generally 1.5~27 times worse than our integral average value method. Moreover, for single emitter VCSELs with optical aperture from 200 m to 500 m, the smaller the optical aperture are, the larger the coherent degrees (between 0.731~0.426) are. The conclusion can be wildly used on theoretical and experimental design for VCSEL coherent arrays.

Lateral-shearing, delay-dithering Mach–Zehnder interferometer for spatial coherence measurement

An image-shearing interferometer of Mach-Zehnder type with corner cubes is introduced for the purpose of measuring spatial coherence at the output of inhomogeneous optical sources, such as multimode fibers (MMFs). One arm of the interferometer is modulated in optical delay to produce dynamic interference fringes. Fringe visibility and the two individual intensities are measured nearly simultaneously to allow direct calculation of the modulus of the complex degree of coherence as a function of the lateral shear between the two interferometer arms. Spatial degree of coherence is measured for a step-index MMF pumped with monochromatic and broadband optical sources.

Two-point resolution of asymmetrically apodized optical systems

Effect of asymmetric apodization applied to two dimensional complex pupil filters on resolution of object points in the image plane of apodized optical systems has been investigated. The required pupil function and its transmittance is formulated and studied. These sparrow limits have been discussed as functions of the degree of spatial coherence of the illumination, intensity ratio of two object points and asymmetric apodization parameter (b). The sparrow resolution limit increases as the degree of coherence increases, irrespective of the intensity ratio of two point objects. With respect to intensity ratio of two points it is clearly found that for all cases of illumination, employing complex pupil filters in the presence of asymmetric apodization leads to an improvement in resolution of two object points.

Numerical modeling of spatial coherence using the elementary function method

The elementary function method is an approximate method for propagation calculations in spatially, partially coherent light in two dimensions. In this paper, we present the numerical application of this method to a 248 nm UV excimer laser source. We present experimental results of the measurement of the degree of spatial coherence and the beam profile of this source. The elementary function method is then applied to the real beam data and used to simulate the effects of imaging an opaque edge with a source of varying degrees of spatial coherence. The effect of spatial coherence on beam homogenization is also presented.

Experimental comparison of full and partial coherent illumination in coherent diffraction imaging reconstructions

In this paper, we will present coherent diffraction imaging reconstruction of a well-known object by use of a Hybrid Input-Output algorithm. The sample was imaged at 400 nm wavelength with a fully coherent laser source and at 0.41 nm wavelength in partially coherent illumination. The comparison of the two experiments, completed with theoretical simulations, will highlight the influence of the degree of spatial coherence in the reconstruction process.

Examining the validity of using a Gaussian Schell-model source to model the scattering of a fully coherent Gaussian beam from a rough impedance surface

Military applications that use adaptive optics (AO) often require a point source beacon at the target to measure and correct for wavefront aberrations introduced by atmospheric turbulence. However, turbulence prevents the formation of such a point beacon. The extended beacons that are created instead have finite spatial extents and exhibit varying degrees of spatial coherence. Modeling these extended beacons using a Gaussian Schell-model (GSM) form for the autocorrelation function would be a convenient approach due to the analytical tractability of Gaussian functions. We examine the validity of using such a model by evaluating the field scattered from a rough impedance surface using a full-wave computational technique called the method of moments (MoM). The MoM improves the fidelity of the analysis since it captures all the physics of the laser-target interaction, such as masking, shadowing, multiple reflections, etc. Two rough-surface targets with different roughness statistics are analyzed. The simulation results are verified with experimental bidirectional reflectance distribution function measurements. It is seen that for rough surfaces, in general, the scattered-field autocorrelation function is not of a GSM form. However, under certain conditions, modeling an extended beacon as a GSM source is legitimate. This analysis will aid in understanding the behavior of extended beacons and how they affect the overall performance of an AO system.

Spatial coherence measurement of polychromatic light with modified Young’s interferometer

Partial spatial coherence is a fundamental concept in optical systems. Theoretically, the normalized mutual coherence function gives a quantitative measure for partial spatial coherence regardless of the spectral nature of the radiation. For narrowband light the degree of spatial coherence can be measured in terms of the fringe modulation in the classic Young's two-pinhole interferometer. Though not commonly appreciated, with polychromatic radiation this is not the case owing to the wavelength dependence of diffraction. In this work we show that with a modified two-beam interferometer containing an achromatic Fresnel transformer the degree of spatial coherence is again related to the visibility of intensity fringes in Young's experiment for any polychromatic light. This result, which is demonstrated both theoretically and experimentally, thus restores the usefulness of the two-pinhole interferometer in the measurement of the spatial coherence of light beams of arbitrary spectral widths.

Measurement of the spatial coherence of extended light source by twin beams-interference method

The coherence of light source have been employed in many aspects, such as optical processing and optical coherence holography. For this reason it has attracted vast interest in developing quantitative methods for measuring the spatial coherence characteristics of an optical field. We propose a novel method for measuring the spatial coherence degree of optical fields based on the triangular interferometer. Spatially separated twin beams are formed by an interferometer, and the interferogram formed by the twin beams is captured by an image detector. Because the separation of the twin beams is related to the coordinate position of the input beam, a series of positions are sampled by moving a pinhole and corresponding interference patterns are recorded. Then the visibilities of the interference patterns are calculated for measuring the spatial coherence degree. Experimentally measured and theoretically calculated values of spatial coherence degree fit well. The measurement error is 3.8%. Experimental results show the method proposed here is effective, simple, and robust without any special optical elements.

Spatial Coherence and Optical Beam Shifts

A beam of light, reflected at a planar interface, does not follow perfectly the ray optics prediction. Diffractive corrections lead to beam shifts; the reflected beam is displaced (spatial Goos-Hänchen type shifts) and/or travels in a different direction (angular Imbert-Fedorov type shifts), as compared to geometric optics. How does the degree of spatial coherence of light influence these shifts? We investigate this issue first experimentally and find that the degree of spatial coherence influences the angular beam shifts, while the spatial beam shifts are unaffected.