Performance bounds on wave-front curvature ranging

The spatial coherence function |Γ(s)| of ruby laser pulses has been measured by self-diffraction at a laser-induced grating depending on the distances between two points in the beam profile. The spatial coherence of the laser beam was changed by operating the laser in the fundamental transverse mode, in a transverse multimode and by applying different pump powers. The degree of spatial coherence was experimentally found to be a Gaussian, as described by the Collett-Wolf model. The new method for measuring the spatial coherence function |Γ(s)| is described and possible improvements are discussed.

Abstract. We have examined, for the first time, the spatial coherence of oceanic parameters, namely, the ocean surface wind and significant wave height (SWH), using near-instantaneous along-track sampling over vast oceanic tracks provided by Poseidon-2 Radar Altimeter onboard Jason-1. The spatial coherence length scales over the Arabian Sea and the Bay of Bengal regions, derived using Auto correlation analysis, display interesting characteristics in relation to onset and evolution of SW Monsoon over India. The estimated spatial coherence scales are found to be of the order of 100–500 km. Generally, SWH coherence lengths over Arabian Sea are observed to increase from June to July during good monsoon year (2012). This trend is not followed for the poor monsoon year (2002). Similar trend is observed for spatial coherence scales for wind speed. The temporal evolution of analyzed spatial coherence scales of winds and waves over Arabian Sea clearly brings out the distinction between a "good" (2012) and a "poor" (2002) monsoon year. The spatial coherence lengths of these parameters over the Bay of Bengal are found to be shorter and do not show any systematic relation to onset and evolution of SW monsoon. Anisotropy in coherence lengths is also analyzed by treating ascending and descending tracks separately. Generally, the descending tracks measurements show higher spatial coherence lengths than the ascending ones. Like the spatial coherence scales, the anisotropy of the coherence scales over the Arabian Sea also mimics the behaviour of the strength of SW Monsoon.

Spatial coherence of transient stimulated Raman scattering

In this paper, we proposed a novel optical geometry for direct visualization of spatial coherence function. The full-field distribution of the coherence function from an incoherent circular aperture source is experimentally investigated. Meanwhile, the experiments of non-diffracting coherence function from an incoherent circular slit source have also been done. The experimental results show that the coherence function generated by an incoherent circular aperture source is in the form of Fresnel diffraction integral which diffracting during the propagation and the coherence function generated by an incoherent circular slit source is unaltered by propagating in free space.

An improved illumination system is proposed for creating a temporally coherent and spatially incoherent extended source to be used for spatial coherence control and reconstruction of a coherent hologram. Taking into account the fact that a rotating ground glass does not behave as an ideal Lambertian diffuser, the new illumination system tailors the directivity of the scattered lights to direct the lights efficiently into an interferometer so that a spatial coherence function can be better controlled and detected with higher fidelity. Experimental results are presented that demonstrate improved performance of the proposed system.

Acoustic attenuation in seawater is sufficiently weak that it usually has little effect on the spatial characteristics of ambient noise. However, at frequencies above 10 kHz and depths below 6 km, seawater attenuation may influence the directionality of surface-generated ambient noise. In a semi-infinite, homogeneous ocean, all the noise is downward-traveling, since there are no bottom reflections, and, in the absence of attenuation, the directional density function varies as the cosine of the polar angle measured from the zenith. When attenuation is present, the angular width of this noise lobe becomes narrower, because sound from distant surface sources is attenuated more than acoustic arrivals from overhead. This narrowing effect increases as frequency rises, since the attenuation is a rapidly increasing function of frequency. The spatial coherence of the noise is also modified by the attenuation. For a pair of horizontally (vertically) aligned sensors, the zeroes in the spatial coherence function are shifted to higher (lower) frequencies. These effects of attenuation on the noise field are sufficiently large to be detectable using the recently developed, deep diving instrument platform Deep Sound, which is capable of measuring broadband ambient noise on multiple hydrophones to depths of 11 km. [Research supported by ONR.]

Multireference partial field decomposition (PFD) can be used to generate coherent holograms for scan-based near-field acoustical holography measurements. PFD is successful when the reference array completely senses all independent subsources, but meeting this requirement is not straightforward when the number of subsources and their locations are ambiguous (such as in aeroacoustic sources). A figure of merit based on spatial coherence lengths, called references per coherence length (RPLc), is a useful metric to guide inter-reference spacing in the array design so that the source is spanned. Coherence length is defined as the axial distance over which the ordinary coherence drops from unity to some desired value. Numerical experiments involving an extended, partially correlated source show that sufficiency of the reference array for different source conditions may be simply expressed in terms of RPLc. For sources of varying spatial coherence and over a large range of frequencies, one reference per coherence length is equivalent to sensing all independent subsources.

The notion spatial coherence is used by sonar systems such as Correlation Velocity Logs (CVL) and Synthetic Aperture Sonars (SAS). It exploits correlation between acoustic signals sensed in space and time to estimate for example platform displacement. The Van Cittert Zernike (VCZ) theorem, is a classical statistical optics theorem that predicts the spatial coherence of a pressure field backscattered by a random medium. However it appears that intrinsic characteristics of Low Frequency Synthetic Aperture Sonar (LFSAS) can breach VCZ asumptions.In this paper, the notion of spatial coherence applied to a Low Frequency SAS system (LFSAS) is investigated. In a first part, the notion of spatial coherence and the VCZ therorem is presented. Then the High Resolution LFSAS (HRLFSAS) developed by NATO CMRE and used in this work is introduced. In the same time, a simulation tool is presented. In this paper, typical coherence functions obtained on simulation are presented. That allows to point out the link between the shape of the coherence function and the length of the transmit antenna. These functions are compared to the coherence observed on LFSAS data. Differences are investigated in terms of signal to noise ratio.

We report on the experimental determination of the complete two coordinate spatial coherence function of light emitted by a quasi-random laser, implemented on recently introduced dye-doped transparent wood. The spatial coherence was measured by means of a double grating interferometer, which has some advantages over the standard Young's interferometer. Analysis of the spatial coherence reveals that emission from such a material can be considered as a superposition of several spatial modes produced by individual emitters within semi-ordered scattering medium. The overall degree of coherence, γ¯, for this quasi-random laser was found to be 0.16 ± 0.01, having possible applications in speckle free laser imaging and illumination.

Spatial coherence measurement of X-ray undulator radiation

Long-range spatial coherence can be induced in incoherent thermal emitters by embedding a periodic grating within a material supporting propagating polaritons or dielectric modes. However, only a single spatially coherent mode is supported by purely periodic thermal emitters. While various designs have been proposed for the purpose of allowing arbitrary emission profiles, the limitations associated with the partial spatial coherence of thermal emitters are not known. Here, we explore superstructure gratings (SSGs) to control the spatial and spectral properties of thermal emitters. SSGs have long-range periodicity but employ a unit cell that provides multiple Bragg vectors to interact with light. These Bragg vectors allow simultaneous launching of polaritons with different frequencies/wavevectors in a single grating, manifesting as additional spatial and spectral modes in the thermal emission profile. However, SSGs still have a well-defined period, which allows us to assess the role that finite spatial coherence plays in thermal emitters. We find that the spatial coherence length defines the maximum possible SSG period that can be used. This provides a fundamental limit on the degree of spatial coherence that can be induced in a thermal emitter and has broader implications for the use of techniques such as inverse design for structure optimization.

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.

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.

We study, experimentally as well as theoretically, the spatial coherence function and the Wigner distribution function for one-dimensional projections of optical vortices of different orders. The information entropy derived from the spatial coherence functions has been used to quantify the information content of the vortices and compared with those obtained for the Gaussian beam. The experimental results verify the theoretical findings of Agarwal and Banerji [Opt. Lett. 27, 800 (2002)].

We present a model based on the Fresnel diffraction scheme for the spatial coherence function of random fields created by scattering optical vortex and perfect vortex beams. By using the spatial coherence function we showed analytically, numerically, and experimentally the dependence and independence of the speckle size of an optical vortex and perfect optical vortex (POV) with a topological charge, respectively. We also showed in both cases the linear dependence of speckle size on the distance of propagation. Furthermore, we describe a regime in which the spatial coherence function is nonevolving for the optical vortex beam and the POV beam with the propagation distance.