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This study sought to improve general understanding on rainfall timing in Nigeria. Observed monthly rainfall data for 38 meteorological stations, spanning 30 years was utilized, and the dates of onset and cessation of rainfall were estimated using Walter’s method. The interrelationships among the variables and the dependency of the amount of rainfall were calculated using Pearson’s moment correlation coefficient and multiple regression, respectively. The variance of the Standardized Anomaly Index (SAI) was used as a measure of spatial coherence. The study revealed divergent characteristics between the onset and the cessation of rainfall; progressing in opposite direction, with a very high latitudinal variation in each. Rainfall onset has a relatively high interannual variability, with an average CV of 21%, compared to 3.9% for cessation. Onset also has a larger spatial range of 137 days, compared to 82 days for cessation. Additionally, rainfall cessation was found to be more spatially coherent than the onset, but both revealed a weak spatial coherence. The relative spatial incoherence and high interannual variability of onset contrive to make it much less predictable than cessation. Interestingly, rainfall amount shows greater association with, and dependency on, onset, cessation, and rainy season length in stations of the extreme north, than in southern stations.

We use seasonal forecasts from the Climate Historical Forecast Project (CHFP) to study the skill of multiple climate models in predicting Indian summer monsoon precipitation. The multi-model average of seasonal forecasts from eight prediction systems shows statistically significant skill for predicting Indian monsoon precipitation at seasonal lead times. Rapid convergence of tropical rainfall skill with ensemble size suggests that the skill of seasonal monsoon rainfall forecasts improves only marginally when using multi-model ensemble (MME) means as compared to the single most skillful system. There is also a large range in the skill of individual models. Some individual models show correlation skill as high as 0.6, which is similar to the MME mean, while others show low skill. We also investigate the effect of spatial averaging on the skill of predicting monsoon rainfall and show that the predictions averaged over a larger area than the verifying observations can yield higher skill due to the extended spatial coherence of monsoon rainfall variability. We also document current errors in seasonal prediction systems and show that these are more strongly related to the errors in El-Nino Southern Oscillation (ENSO) teleconnections than they are to mean rainfall biases. Finally, we examine the ENSO-monsoon relationship and confirm that this relationship is likely to be stationary, despite fluctuations in the observed relationship, which can simply be explained as sampling variability on an underlying stationary teleconnection between ENSO and the Indian monsoon.

Optical phase microscopy is an indispensable tool to quantify various biophysical parameters of cells and tissues with high accuracy. Quantitative information about cell or tissue morphology, dynamic membrane fluctuations, refractive index, dry mass, haemoglobin concentration etc. are essential for early stage diagnosis of various diseases. During the last three decades various quantitative phase microscopic techniques have been developed world wide and utilized for various applications. In this paper we provide an overview of the field with emphasis on the work carried out in India. The most widely used techniques such as, digital holographic microscopy, white light interference microscopy and low spatial coherence optical tomographic techniques are described and reviewed. Experimental results of quantitative imaging of red blood cells, oral cancer cells and tomographic sectioning of multilayer structure are presented.

Reliable saliency detection can be used to quickly and effectively locate objects in images. In this paper, a novel algorithm for saliency detection based on superpixels clustering and stereo disparity (SDC) is proposed. Firstly, we use an improved superpixels clustering method to decompose the given image. Then, the disparity of each superpixel is computed by a modified stereo correspondence algorithm. Finally, a new measure which combines stereo disparity with color contrast and spatial coherence is defined to evaluate the saliency of each superpixel. From the experiments we can see that regions with high disparity can get higher saliency value, and the saliency maps have the same resolution with the source images, objects in the map have clear boundaries. Due to the use of superpixel and stereo disparity information, the proposed method is computationally efficient and outperforms some state-of-the-art colorbased saliency detection methods.

A set of principal modes that maintain pulse properties and spatial coherence despite propagation in 100 metres of multimode fibre are observed.

We present a thermal imaging field design for climatological studies with an application to microscale cold-air flow analysis. Measurements of microclimatic processes are often limited by a lack of spatial coherence and consequently incomplete information on spatial and temporal patterns in the airflow. We introduce and evaluate an approach for investigating cold-air flow using an infrared camera pointed at a custom-built projection screen. A statistical analysis of a cold-air-flow case study is presented that explores the potential and limitations of the proposed technique. Results indicate good compatibility with traditional methods, while spatial coherence in measurements is achieved. A few examples of additional information obtained from the thermal camera analysis are presented, including analyses of cold-air-flow characteristics.

Knowledge-intensive industries have attracted a great attention nowadays in researches because of its contribution to the development of knowledge-driven economy. They generate positive effects on the regional economy and have increasingly high importance in less developed regions, like Hungary. The identification of spatial distribution, the geographical co-location of knowledge-intensive economic activities is substantial to define potential leading industrial branches in regions. This paper aims to identify the spatial coherence and concentration of knowledge-intensive industries nationwide in Hungary at subregional level, and presents results using Ellison-Glaeser geographic concentration index and the measure of spatial autocorrelation with Moran index.

The Goos-Hänchen (GH) shifts in the reflected light are investigated both for p and s polarized partial coherent light beams incident on epsilon-near-zero (ENZ) metamaterials. In contrary to the coherent counterparts, the magnitude of GH shift becomes non-zero for p polarized partial coherent light beam; while GH shift can be relatively large with a small degree of spatial coherence for s polarized partial coherent beam. Dependence on the beam width and the permittivity of ENZ metamaterials is also revealed for partial coherent light fields. Our results on the GH shifts provide a direction on the applications for partial coherent light sources in ENZ metamaterials.

Noise in sensory signals can vary over both space and time. Moving random dot stimuli are commonly used to quantify how the visual system accounts for spatial noise. In these stimuli, a fixed proportion of “signal” dots move in the same direction and the remaining “noise” dots are randomly replotted. The spatial coherence, or proportion of signal versus noise dots, is fixed across time; however, this means that little is known about how temporally-noisy signals are integrated. Here we use a stimulus with low temporal coherence; the signal direction is only presented on a fraction of frames. Human observers are able to reliably detect and discriminate the direction of a 200 ms motion pulse, even when just 25% of frames within the pulse move in the signal direction. Using psychophysical reverse-correlation analyses, we show that observers are strongly influenced by the number of near-target directions spread throughout the pulse and that consecutive signal frames have only a small additional influence on perception. Finally, we develop a model inspired by the leaky integration of the responses of direction-selective neurons, which reliably represents motion direction and which can account for observers’ sub-optimal detection of motion pulses by incorporating a noisy decision threshold.

Summary form only given. Phase-space optics allows simultaneous visualization of both space (x) and spatial frequency (k) information. This is in distinct contrast with normal measurements, such as normal images and Fourier transforms, which record intensities in x-space or k-space only. For coherent beams, which are fully described by a 2D complex function (e.g. amplitude and phase), a phase-space description is useful but redundant. For partially coherent beams, on the other hand, each position x in the beam can have its own local power spectrum, so that a 4D description is often necessary. This is particularly true for propagation, as the beam coherence determines the evolution of its intensity. While a variety of theories has been developed to describe phase-space properties [1], there has been very little progress on the experimental front. Pinhole (Hartmann) or lenslet (Shack-Hartmann) arrays are most commonly used, but the arrays force a trade-off between spatial and angular sampling, usually resulting in poor resolution [2] (and often reduced dynamic range [3]) in both domains. Here, we demonstrate an alternative method for obtaining 4D phase-space distributions quickly, without sacrificing resolution in either dimension [4].The experimental setup is shown in Fig. 1. For measurement, we record a spatial spectrogram (windowed Wigner distribution function) by using a Spatial Light Modulator (SLM) to scan an aperture across the transverse field of the beam. The method is simple, fast, and free of mechanical scanning errors and artifacts [5]. For coherence control, we use a second SLM as a dynamically changing local diffuser with spatially varying statistics, allowing design and creation of arbitrary phase-space distributions. An example is shown Fig. 2, in which each small region in {x} has a variable Gaussian distribution in {k}. Traditional measurements along the marginals of the 4D distribution, i.e. the intensity and power spectrum projections 1(x) = f f(x, k)dk and S(k) = f f(x, k)dx, miss the coherence properties within the volume of phase space. Measurement and control of such higher-dimensional beams will have applications in coherence holography, encoding, illumination, and display.

A complete picture of changes in climate extremes has been presented for Shanxi Province, China using data from all 61 available stations. The results reveal large spatial coherence of trends for the majority of extremes, especially for temperature extremes. Significant and symmetric increasing trends of the annual mean maximum and mean minimum temperatures (TXam, TNam) are detected over the past 50 years. Significant positive trends are detected for warm days and nights (TX90p, TN90p), the highest and lowest maximum and minimum temperatures (TXx, TXn, TNx, TNn), and the growing season length (GSL). Significant negative trends are revealed for cold days and nights (TX10p, TN10p) and frost days (FD). Significant decreases are found in the number of heavy precipitation days (R10mm) and wet day precipitation (PRCPTOT). Although Shanxi and the northern half of North China Plain (NNCP) have been grouped into the North China region and assessed together in previous studies for China, the changes in climate extremes in the NNCP have some pronounced differences in comparison with Shanxi. Noticeably, the increase of the TNam is at a rate nearly three times that of the TXam during 1959–2008 over the NNCP. The warming for the nighttime indices TN90p, TN10p, TNx, and TNn is stronger, but the warming for the daytime indices TX10p, TX90p, and TXx is weaker in the NNCP. There is no significant decrease for R10mm and PRCPTOT in the NNCP.

As irrigation demands usually take the largest share of water supply, paddy fallow is considered as a drought relieving measure in some Asian paddy growing countries by transferring the water saved to the municipal and industrial sectors. But the relationship between fallow area and irrigation demand reduction is not necessarily linear, there may be more than dozens combinations of fallow farm that can meet the same amount of irrigation demand reduction requirement. The Joint Count Statistics (JCS), an index commonly used in spatial analysis to measure the spatial coherence among cells was modified as a spatial aggregation index for evaluating the irrigation demand reduction effectiveness from a spatial perspective. This Modified JCS is supposed to identify the degree of spatial aggregation by taking underlying irrigation network into considerations. The modified JCS was proved to be effective to identify better fallow pattern through a case study in Taiwan.

The theory of coupled mode is used for modeling the long-range bottom reverberation in shallow water caused by bottom roughness. The distant bottom reverberation level and spatial coherence of impulsive source are both derived. The results agree with those from the classical reverberation model, and are compared with the experimental data. The influence of source bandwidth and the distance between sources and receivers on the intensity of bottom reverberation are particularly discussed. The method is shown to be available for both the mono- and the bi-static cases.

Local field potential (LFP) multielectrode recordings of spontaneous rhythms in an isolated whole hippocampal preparation are characterized with respect to their spatial variability within the hippocampus, and their frequency properties. Using simulated data, we categorize potential relationships between frequency variation over time in LFP recordings and spatial variability between electrodes. We then use data recorded from the intact preparation to distinguish between our theoretical categories. We find that the LFP recordings have a close to spatially invariant frequency distribution (not phase) across the hippocampus, and differ in frequency only in a component that may be seen as physiological noise. From these facts, we conclude that the isolated hippocampal LFP recordings represent a single signal and may be regarded as a unitary circuitry. We additionally examine phase differences across our recording sites. We use our characterization of the hippocampal isolate's properties to predict its spatial coherence in response to high frequency stimulation. We find that there is a finely tuned inverse relationship between temporal variability in the hippocampal isolate's LFP recordings and their spatial coherence.

Interactive selection of desired textures and textured objects from a video is a challenging problem in video editing. In this paper, we present a scalable framework that accurately selects textured objects with only moderate user interaction. Our method applies the active learning methodology, and the user only needs to label minimal initial training data and subsequent query data. An active learning algorithm uses these labeled data to obtain an initial classifier and iteratively improves it until its performance becomes satisfactory. A revised graph-cut algorithm based on the trained classifier has also been developed to improve the spatial coherence of selected texture regions. We show that our system is responsive even with videos of a large number of frames, and it frees the user from extensive labeling work. A variety of operations, such as color editing, compositing, and texture cloning, can be then applied to the selected textures to achieve interesting editing effects.

It has been demonstrated recently that surface plasmons can change the state of coherence of light emanating from a Young’s double-slit interferometer. This suggests the possibility of developing a “coherence-converting” device with a large array of subwavelength holes in a metal plate. We have taken an intermediate approach by considering a three-slit geometry, in which we investigated the effects on the modulation of the spatial coherence when an additional slit is placed between the pair of Young’s slits. Our results show that the amount of modulation (enhancement or suppression) can be increased or decreased in the three-slit geometry, compared to the double-slit configuration. This is promising for achieving coherence converting optical devices with suitable arrays of subwavelength holes.

The analysis of weak variations in the energetic particle flux, as detected by neutron or muon monitors, can often be considerably improved by analysing data from monitor networks and thereby exploiting the spatial coherence of the flux. We present a statistical framework for carrying out such an analysis and discuss its physical interpretation. Two other applications are also presented: filling data gaps and removing trends. This study focuses on the method and its various uses.

In this paper, a new spatial coherence model of seismic ground motions is proposed by a fitting procedure. The analytical expressions of modal combination (correlation) coefficients of structural response are developed for multi-support seismic excitations. The coefficients from both the numerical integration and analytical solutions are compared to verify the accuracy of the solutions. It is shown that the analytical expressions of numerical modal combination coefficients are of high accuracy. The results of random responses of an example bridge show that the analytical modal combination coefficients developed in this paper are accurate enough to meet the requirements needed in practice. In addition, the computational efficiency of the analytical solutions of the modal combination coefficients is demonstrated by the response computation of the example bridge. It is found that the time required for the structural response analysis by using the analytical modal combination coefficients is less than 1/20 of that using numerical integral methods.

A general algorithm is proposed for constructing coherent boundaries. This algorithm is based on the interrelation between the spatial coherence of structural fragments in nanoparticles and the geometric connection in the corresponding associated bundle. A local approach is used to describe the structure of coherent boundaries in zirconia nanoparticles. The inference is made that the models of structures thus obtained should be preferred over the models constructed in terms of the theory of coincident site lattice.

We present theoretical and experimental investigations of factors that may influence the surface quality of insulators patterned by 157 nm F2 laser ablation. Aspects covered include modelling of beam spatial coherence and diffraction effects for proximity mask exposure, and the role of melt relaxation on surface microstructures. Experimental results for micron-scale patterning of N-BK7 glass and NaCl crystals using proximity masks are presented and discussed within the framework of the modelling.

We report on imaging through solid scattering media with photorefractive holography using sources of low temporal and spatial coherence. Holograms were recorded through samples of moderate thickness by using low-cost light-emitting diodes. The reduction of speckle noise is demonstrated.

The limit properties of spatial coherence of seismic ground motion are studied based on the differential relation between rotation and translation in elastic theory, the results show that the empirical mathematical model of spatial coherence must satisfy some functional characteristics. It is also indicated that the key problem to estimate rotational power spectrum densities is to obtain precisely the two order derivative of spatial coherence.

The technique of principal component analysis and of cluster analysis has been applied to two sets of precipitation data in Switzerland, one containing 47 stations (1961-80), and the other 101 stations (1981-1993), with the aim of understanding more fully the spatial distribution of precipitation regimes. Seven regions were highlighted in the first case and 13 in the second. The high spatial coherence which appeared is quite remarkable and confirms the usefulness of these techniques for the analysis of the spatial distribution of meteorological variables, even in a topographically complex area such as Switzerland. The two regional distributions obtained not only correspond fairly well to the large, well-known physical regions of Switzerland, but also go much further, separating the Swiss Plateau into 3 clearly differentiated regions, for example. Regional distributions such as those discussed here can have value for climate change issues, and in particular numerical modeling of climate or climate change impacts on forests.

The loss of coherence of seismic waves, even over small distances, can become significant and consequently important for engineering applications. This coherence loss depends on several parameters (frequency, inter-station distance), but their dependencies are not well understood yet. We show the results of a detailed analysis of the spatial variability of the coherence between two signals. This analysis is based on a simple model which is an exponential function of inter-station distance and frequency. Data from a temporary network of 36 weak-motion instruments installed at the EURO-SEISTEST site, north-east of Thessaloniki (Greece), is used in this work. The data offers the unique possibility to study the loss of coherence over a wide range of distances, as the inter-station distances are between 8 m and 5488 m. We test the influence on the coherence of the length of the time-window of the signals, of the type of the waves present in the time-window and of the common energy of the signals. We also show that, at least at this particular site, the loss of coherence with distance is probably marked by a "cross over" distance, distinguishing two different ranges: one for inter-station distances up to 100 m and the other above 100 m. Finally, we find that the coherence determined from noise recordings behaves in a rather similar way to the one determined from coda-waves and more stationary (longer) signals. Therefore, noise can be useful for a rough, but quick estimation of the loss of coherence, at least for inter-station distances larger than 100 m.

Experimentally obtained time coherence has traditionally been interpreted as streamwise one-dimensional spatial coherence through Taylor’s hypothesis. We calculate corrections to the highwavenumber part of the coherence to account for the errors caused by the deviation from Taylor’s hypothesis in high-intensity turbulent flows. The small-scale turbulence is assumed to be frozen and convected by a fluctuating convection velocity. Both Lumley’s two-term approximation and the Gaussian approximation are used in the calculations. In general, we find that the coherence for crossstream separations is significantly overestimated by the direct use of Taylor’s hypothesis, the error increasing with wavenumber; that for streamwise separations is underestimated. The analyses are compared with cross-stream coherence measurements in the atmospheric surface layer. Our results indicate that predictions from Lumley’s approximation yield better agreement with experimental data for cross-stream separations than those from the Gaussian model. Our study suggests that reliable measurement of two-point spatial coherence can be achieved only for scales not too small compared to the sensor separation.

This paper describes a change in optical spectrum on propagation in free space for a particular class of spatially partially coherent fields emanating from a polychromatic secondary source. A rectangular opening aperture in an opaque screen, illuminated with an extended incoherent polychromatic primary source, works as the secondary source. The spectral change is explored in detail theoretically and experimentally in association with spatial coherence in the secondary source as well as dispersive diffraction by the secondary source. The peak shift of the spectrum is associated with the coherence area for characterizing the secondary source. The peak shift becomes maximum if the secondary source is spatially coherent, but no shift occurs if the secondary source is spatially incoherent.

In the case of high angular resolution techniques (speckle interferometry, long baseline Michelson interferometry), one has studied how varies the signal-to-noise ratio (SNR) in terms of the spectral bandwidth Δλ. For values of Δλ varying from 0 up to 100 nanometers, it is shown that the SNR, contrary to the predictions, has no maximum value. In addition, in the case of the high frequency approximation, the effects of a finite spatial-coherence outer scale, the influence of the turbulence model used and of the “optical energy” of the turbulence on the optimal spectral bandwidth have been analyzed and discussed.

In the past decade spectral changes depending on the spatial coherence of the source have been described by a cross-spectral density method. It is shown that for Gaussian-Schell model sources a quasi-optical approach is valid which uses Gaussian beams and ABCD matrices to describe the optical system.

This paper shows how spatial coherence can be exploited to accelerate form-factor calculation for the radiosity method. A certain number of form factors are calculated by a new technique combining hemisphere and ray tracing, while the other form factors are estimated. This estimation method has reduced form-factor calculation by a factor greate than three, for some test scenes.

The mutual intensity of the optical field in the Fraunhofer diffraction region produced from the end of an optical fibre under illumination of a coherent beam, is theoretically analysed by using an optical fibre-end source model. In this source model, the optical field at the end of the fibre is expressed as an aggregation of independent plane waves with random directions and phases, because the guided modes propagating through the fibre may be regarded as a stochastic process. It is found that the optical field in the diffraction region from the multimode optical fibre is not homogeneous butquasi homogeneous in a statistical sense. The spatial coherence properties in the field are discussed in connection with theV number (the normalized frequency) of the fibre and in comparison with those in the field produced from an incoherent source obeying the van Cittert-Zernike theorem.

Relationships between the duration of antennular attachment of cyprids ofBalanus amphitrite and forces associated with detachment were assessed in a small flume. For six of twelve sets of measurements obtained on separate dates between 27 January and 2 June 1989, drag forces associated with detachment were significantly and positively correlated with duration of attachment within the range 100 to 103 s. In general, the instantaneous drag force exerted on cyprids at detachment was more strongly correlated with duration of attachment than was either the maximum or mean force exerted prior to detachment. Our indirect method of estimating drag forces from shear velocities measured ≤0.5 cm from cyprids (i.e., ≤10 body lengths) probably underestimated the true association between detachment force and attachment time since the spatial coherence of shear velocities characterizing turbulent flows in the flume was not strong at these scales. The relationship between attachment time and drag force at detachment suggests that spatial and temporal variability in fluid forces in situ may contribute to stochastic variations in intensities of settlement ofB. amphitrite. Stresses sustained by the antennular adhesive of cyprids ofB. amphitrite were calculated to standardize forces to the area of antennular contact and permit comparisons with similar measurements made onSemibalanus balanoides by other investigators. Stresses sustained by the adhesive ofB. amphitrite were an order of magnitude lower than those reported for the adhesive of the larger cyprids ofS. balanoides. This difference may reflect differences in the stress sustainable by the adhesive secreted onto antennular pads when loaded purely in tension (measured previously) rather than in a combination of shear and tension (calculated here). Alternatively, there may be interspecific differences in the adhesive used for reversible attachment or in behavioral responses of exploring cyprids to strong flow.

This paper focuses on some experiments done using field emitter arrays (FEAs) produced at CEA-LETI, experiments which are outside of the display or microwave amplifier contexts. Among various studies done at CEA-LETI with FEAs we have selected:- the search towards a spin polarized electron source,- a study on the spatial coherence of the electron beam emitted by a single emitter,- the incorporation of an optical command in a FEA and finally,- the application of a FEA to electron injection into rare gas liquids.

This paper describes the peak shift in a Gaussian-like spectrum caused by the effects of spatial coherence and dispersive diffraction. The peak shift depends greatly on the ratio of the coherence areaAc produced by a primary incoherent source to the area лр2 of a circular aperture in the secondary source plane. The measured results are in reasonably good agreement with the numerical computational results. The peak shift is caused by a mixture of spatial coherence and dispersive diffraction in the region 0

A review is presented of various recent investigations on the classical optical radiation laws in the light of the modern concepts of coherence and statistical optics. Temporal coherence of black-body radiation, spatial coherence of Lambertian and non-Lambertian sources, and the interaction of matter with radiation of any state of coherence are emphasized.

The intensity distribution in the interference pattern of a multiple-slit aperture illuminated with the partially coherent light is examined experimentally. The experimental results showing excellent agreement with the theoretical predictions indicate both a gradual loss in the contrast of interference fringes and a broadening of the principal maximum fringes with decreasing spatial coherence of the illumination.

A relation between spatial coherence function and source encoding intensity transmittance function is presented. Since the spatial coherence is depending upon the information processing operation, a strictly broad spatial coherence function may not be required for the processing. The advantage of the source encoding is to relax the constraints of strict coherence requirement, so that the processing operation can be carried out with an extended incoherent source. Emphasis of the source encodings and experimental demonstrations are given. The constraint of temperal coherence requirement is also discussed.

Vertical coherence and phase delay between wind components in strong winds in the lowest 20 m over uniform terrain in New Zealand have been analysed. The vertical decay constants and slopes for the horizontal wind components could be described as linear functions of the ratio of vertical spacing to mean height (δz/z), with relatively little scatter. The decay constants for the lateral were smaller than for the longitudinal components, the slopes larger for the lateral components, as found previously. The coherence of vertical velocity is best described by exponential decay functions multiplied by a parameter which decreases linearly from 1 (for δz/z=0) to 0.5 (for δz/z=1). The decay constants increased linearly with δz/z, as in the case of the horizontal components. There were no significant phase differences for the vertical components. Lateral and vertical decay constants for the longitudinal wind component could be fitted to identical functions of δy/z and δz/z, respectively.

Simultaneous temperature fluctuations have been measured along directions both parallel and orthogonal to the wind direction in the atmospheric surface layer. Ensemble-averaged temperature distributions associated with the ramp-like feature observed in instantaneous temperature traces indicate that the average duration of the ramp is approximately independent of height. Application of Davenport's geometric similarity of coherence of temperature fluctuations yields approximate estimates for the spatial extent of the structure characterized by the ramp. The longitudinal extent is approximately 12 times the vertical extent and 17 times the lateral extent.

Thus, in this paper the results of experimental and theoretical investigations of thermal self-stressing of laser beams in turbulent media were discussed. The following problems were considered: 1) The effect of turbulent agitation on thermal defocusing; 2) reduction of intensity fluctuations of wide and narrow, in comparison with the dimensions of turbulent inhomogeneities, laser beams due to defocusing by a thick thermal lens; 3) reduction of fluctuations due to defocusing by random temperature inhomogeneities induced by intensity fluctuations; 4) fluctuations in the presence of thermal self-stressing of pulsed radiation, the effect on it of spatial coherence of the field; 5) fluctuations in the presence of selfstressing in a moving medium.

Correlations of monthly totals from different stations were used to identify coherent regions in terms of parallel fluctuations of rainfall amounts from year to year. One coherent region was found during the fall, three during the winter and two during the spring. An attempt to explain the existence of those coherent regions with different known features of the rainfall regime and to relate them to different synoptic systems, was done.

Generalizing our results, one can identify the basic mechanism responsible for the mutual influence of temporal and spatial fluctuations in the amplitude of a light field in a moving medium with thermal nonlinearity.

The ensemble-averaged spatial coherence of quasi-thermal light, produced by passing a focused laser beam through a rotating ground glass plate, is studied as a function of the illuminated area, the fineness of the glass used, the speed of rotation of the glass, and the laser mode selected as a primary source. It becomes clear that the ensemble-averaged spatial coherence depends strongly upon the illuminated area and on the fineness of the rotating ground glass, and also on the laser mode chosen but not on the speed of rotation of the glass.

The van Cittert-Zernike theorem states that the spatial coherence over a space illuminated by an incoherent extended source is described by the Fourier transform of the intensity distribution over the source. The theorem is usually used in a restricted case of the spatial coherence in a plane parallel to the source plane and illuminated by an incoherent extended source of uniform intensity distribution. In this paper we re-examine the van Cittert-Zernike theorem by reviewing it in an original formulation and extend the theorem to the spatial coherence at any two points of a light field illuminated by an incoherent extended source having a non-uniform intensity distribution.

Experiments were carried out to measure the optical coherence of an argon laser beam in tap water, distilled water, ocean coastal water and in processed water with 3% sodium chloride added. Measurements were made for water path lengths up to 2.9 m using two different procedures. The first was Young's experiment and the second involved an optical geometry common to the Laser Doppler Velocimeter. Results showed no degradation in the normalized degree of coherence over the measured distances. However, local changes in the index of refraction did cause the interference fringes to have some motion (approximately one-fourth of a fringe width). Tests were also carried out using the Laser Doppler Velocimeter in the back-scatter mode to measure the centre line velocity of a submerged jet. Results agreed very well with independent measurements.

A simple Young-type two-point correlation experiment with photographic detection is described. Comparisons are made for the various factors contributing to the spatial coherence. The determining role of the number of superimposed transverse modes is confirmed. The importance of the back mirror, the active medium and the short build-up time is found, experimentally.

An experimental apparatus is described which makes possible to measure quantitatively the spatial coherence of various kinds of sources. The numerical values obtained for the spatial coherence of a helium-neon laser are reported.