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Coherence Theory of Optics
Published in Francis T. S. Yu, Entropy and Information Optics, 2017
It is possible to split a light wave into two paths, to delay one of them, and then to recombine them to form an interference fringe pattern. In this way, we can measure the temporal coherence of the light wave. In other words, the degree of temporal coherence is the measure of the cross-correlation of a wave field at one time with respect to another wave field at a later time. Thus, the definition of temporal coherence can also refer to longitudinal coherence as opposed to transversal (i.e., spatial) coherence. The maximum difference in the optical path lengths of two waves derived from a source is known as the coherent length of that source. Since spatial coherence is determined by the wave field in the transversal direction and temporal coherence is measured along the longitudinal direction, spatial coherence and temporal coherence describe the degree of coherence of a wave field within a spatial volume.
Light Sources
Published in Toru Yoshizawa, Handbook of Optical Metrology, 2015
Coherence is the most prominent characteristic of laser light. The degree of coherence is determined by the degree of correlation between the phases of the electromagnetic field at different locations (spatial coherence) and different times (temporal coherence). Temporal coherence is a measure of the degree of monochromaticity of the light, whereas spatial coherence is a measure of the uniformity of phase across the optical wavefront. An ideal monochromatic point source, illustrated in Figure 1.31, produces perfectly coherent light. As the point source emits an ideal sinusoidal wave, it is easy to predict the phase of the radiation at a given point at a given time t2, if we know what was the phase at the same point at an earlier time t1. This is perfect temporal coherence. The longitudinal spatial coherence requires correlation between the phases in a given moment at two points P1 and P2 located along a radius line and is similar to temporal coherence. Therefore, the temporal coherence is also called longitudinal spatial coherence. Now, let us consider two points P1 and P3 along the same wavefront. Perfect transverse spatial coherence means that if we know the phase of the wave at point P1 at time t1, we can predict the phase of the field at this same moment at point P3 along the same wavefront.
Nanometer-Scale and Low-Density Imaging with Extreme Ultraviolet and Soft X-ray Radiation
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
In the incoherent sources, there is practically no spatial and temporal phase relationship between the two electromagnetic waves, originating from nonoverlapping spatiotem-poral coordinates. Thus, upon their overlap, no interference phenomena will occur. This means that there is no modulation intensity in the region where the waves are superimposed. Of course, if the source is fully coherent, the modulation between those two waves is maximal; however, in case of partial coherence, the modulation will be reduced, accordingly to the degree of coherence. Herein, we will discuss the sources of incoherent EUV and SXR radiation with very low spatial and temporal coherence, which, for all practical reasons, might be considered incoherent.
Wave structure functions of optical waves in weakly compressible turbulence
Published in Waves in Random and Complex Media, 2022
Jinyu Xie, Lu Bai, Yankun Wang, Lixin Guo
A second-order moment at two observation points is given as [16] where is the complex amplitude of the optical field at distance L of wave propagation. and are the positions of two points on the plane of the wave propagation direction. A star denotes the complex conjugate, and angular brackets represent the ensemble of turbulence realizations. Then, the degree of coherence is related to the WSF where is the WSF, which is required when using the extended Huygens–Fresnel method to calculate the diffracted optical field and fourth-order moment of turbulence.
Scintillation experiments with non-uniformly and uniformly correlated spatially partially coherent laser beams propagating underwater
Published in Journal of Modern Optics, 2019
S. Avramov-Zamurovic, C. Nelson, M. Hyde
A brief overview of the theory behind the generation of the non-uniformly correlated (NUC) beams (21,22,33) follows. From (21) the following spectral (scalar) degree of coherence for a NUC is: where the parameters are the same as in Equation (1) and is real vector that represents the location of the defocus point. Lens defocus using Zernike polynomials provides a method (22) to construct the screens for NUCs where the curvature of the lens, , is drawn from the Gaussian distribution and applied as an SLM screen. Reference (22) gives the details of the beam construction, requiring that sufficient number of the screens are necessary in order to approximate the non-uniformly correlated spectral degree of coherence for the generated spatially partial coherent NUC beams (see Figure 1). We used 150 NUC screens for each measurement.
Evolution of linear edge dislocation in atmospheric turbulence and free space
Published in Journal of Modern Optics, 2019
Peng-hui Gao, Lu Bai, Zhen-sen Wu, Li-xin Guo
The spectral degree of coherence is defined as in Equation (17) (30) where I(ρi, z) = W(ρi, ρi , z) (i = 1, 2) denotes the spectral intensity of the point (ρi, z). The position of phase singularities is determined by using Equations (18) and (19) (31) where Re and Im are the real and imaginary parts, respectively. The sign of optical vortices are determined by the vorticity of phase contours around singularities (32), that is, the sign of the topological charge corresponds to ‘+’ and ‘−’ when the varying phases are in counterclockwise and clockwise directions, respectively, and the corresponding topological charge is m when the phase changes to 2mπ.