Showing papers on "Coherence (physics) published in 1971"

Internal Wave Spectra in the Presence of Fine-Structure

Abstract: Phillips has shown that an undulating motion of a layered medium relative to a measuring instrument will result in a σ−2 spectrum (frequency or wavenumber) over a bandwidth determined by the thickness of the layers and of the sheets separating them. We show, for any (temperature) fine-structure statisteally stationary in depth with covariance rθ(y1−y2)= , that the covariance of the observed time ceries can be expressed in terms of rθ and the covariance in the vertical displacement ζ, assuming ζ to he josintly normal. An explicit expression for the spectrum is given for the case that the rms value of ζ is large compared to the vertical coherence scale of the fine-structure. We tentatively conclude that the fine-structure dominates in the upper few octaves of the internal wave spectra, and then extends the spectra beyond the cutoff frequency (wavenumber). The loss of vertical coherence due to fine-structure occurs over a distance inversely proportional to frequency, in general agreement ...

Second Moment of a Wave Propagating in a Random Medium

Abstract: The Bethe–Salpeter equation for the second moment of a wave propagating in a random media is solved in the ladder approximation. The solution obtained applies to propagation problems in which the wavelength is much smaller than the scale of the inhomogeneities, and the product of the rms index fluctuation, the wavenumber, and a characteristic scale length of the inhomogeneities is also much smaller than unity. The field is assumed given on an initial plane and to have appreciable amplitude over a domain many wavelengths in extent in this plane. It is not required, however, that this domain be larger than the scale of the inhomogeneities. Quantitative results are given for a gaussian beam. We show that the ensemble-averaged distribution of irradiance remains gaussian and give the e-folding radius of this distribution. The two-point correlation function of the field in such a beam is shown to depend only on the distance between the points, not on their relative position within the beam. The coherence properties of the beam are expressed in terms of a coherence length. We also consider the ensemble-averaged interference pattern of the field from multiple apertures and verify that well-defined interference fringes occur only when the apertures are separated by a distance smaller than the coherence length of the individual beams. The solution of the Bethe–Salpeter equation obtained here satisfies an equation derived by Beran. We show that the local-independence assumption used by Beran is valid for sufficiently weak inhomogeneities.

Transverse Horizontal Coherence of Explosive Signals in Shallow Water

Abstract: Transverse horizontal cross‐coherence lengths as a function of signal frequency were measured by a hydrophone array 80 m long under homogeneous winter conditions with heavy sea state. The decrease of the normalized coherence length with the acoustic wavenumber is shown as an example of sound propagation parallel to the wave crests and is compared with published reverberation measurements. The cross‐coherence length is interpreted in a simple model computation as the reciprocal of a medium‐dependent angular uncertainty.

Coherent light source detector

Abstract: An unequal path interferometer, in which the two optical paths travelled by the radiation beam components before recombination differ by an amount much longer than the coherence lengths of non-coherent radiation, but much shorter than coherence length of radiation from a coherent source (eg, a laser) Scanning of the interferometer so as to cause a change in the difference in the two optical paths will modulate the intensity of the recombined coherence radiation by varying interference effects, while the recombined non-coherent radiation can thus be detected in the presence of non-coherent radiation When a Fabry-Perot etalon, for example, is gradually tilted to cause such changing of the optical path length difference, the resulting coherent radiation intensity modulation pattern also yields information as to the direction and wavelength of the coherent radiation source

Effects of Coherence on the Degrees of Freedom of an Image

Abstract: Starting from the Culgoora paradox, the number of degrees of freedom of an image from a pupil of point-like elements has been determined. The influence of the pupil geometry and of the coherence characteristics has been examined. The results show that striking differences can exist between coherent and incoherent illumination.

Determination of coherence length from speckle contrast on a rough surface

Abstract: The speckle pattern in the image of a diffusely scattering plane surface illuminated by two mutually inclined quasi plane waves split from a common laser source gives a direct display of the coherence properties of that light source. This can be used as a simple device to check the coherence of a laser source for holographic or interferometric work. The speckle contrast is a linear function of the square modulus of the degree of coherence. This relation has been proved experimentally for coherent and for incoherent laser radiation. The main difference of the intensity distributions for coherent and incoherent illumination occurs at low intensities, which have maximum probability in the coherent and minimum probability in the incoherent case. The intensity probability distributions have been determined experimentally for two limiting cases. Within the experimental limitations they show very good agreement with the theoretical predictions.

Measurement of the second-order degree of coherence by means of a wavefront shearing interferometer.

Abstract: A method of measuring the second-order degree of coherence in an arbitrary plane by means of a compact wavefront shearing interferometer is described. The prism interferometer previously described by Saunders produces two sheared images that interfere, allowing measurement of the degree of spatial coherence. If the degree of coherence is a function of coordinate differences only, the visibility is constant; otherwise it varies over the field. Experimental results are given.

Some Consequences of Pump Coherence on Energy Exchange in Nonlinear Optical Processes

Abstract: The finite coherence time of the driving field plays an important role in the rates of energy exchange taking place in nonlinear processes. As a typical example, the problems of the quantum parametric amplifier and frequency converter driven by a fluctuating pump are considered. A closed hierarchy of equations for the moments of the fields is given, which in turn is used for evaluating the average number of photons per mode and the relative variance as functions of time. Significant deviations from the case where the pump field is coherent are found.

Imaging of Tri-Bar Targets and the Theoretical Resolution Limit in Partially Coherent Illumination*

Abstract: In viewing systems that employ critical, Kohler, or collimated illumination, the illumination may frequently be characterized by the complex degree of coherence in the form of a first-order Bessel function divided by its argument. The anomalies that occur in the image of a tri-bar target viewed in partially coherent illumination of this form are discussed for a two-dimensional circular diffraction-limited imaging system. The Sparrow criterion, which in this case correlates with experimental measurements of resolving power, is applied to determine the resolution limit. The computed resolution-limit curve for a tri-bar target is shown and compared to the previously published two-point resolution-limit curve for a one-dimensional system and to the limiting values obtained in a two-dimensional system for coherent and incoherent illumination. In the latter case, the full curve is shown as a special case of the application of the Sparrow criterion to the partially coherent imaging equations for a circular two-dimensional system. Experimental confirmation of the calculations is given.

Propagation of Random Electromagnetic Fields

Abstract: The propagation of a random electromagnetic field in a uniform medium is investigated. It is assumed that the two‐point mutual coherence γ is stationary over an initial plane. It is shown that the mean intensity will be conserved if and only if γ(kx, ky), the spectrum of γ, is zero for kx2+ky2>k2, where k is the wavenumber in the medium, meaning that evanescent waves are not considered; and it is proved that, under this condition, the transverse coherence is unchanged from plane to plane.

A Survey of HF Interferometry for Ionospheric Propagation Research

Abstract: The transform relation between the field distribution and the angular spectrum forms the basis for the application of interferometry to propagation research. It is convenient to divide interferometry into instrumental combination and transform techniques which measure these Fourier relations to provide propagation mode resolution in terms of direction and angular width. Conventional direction-finder instrumentation represents the limiting case of single plane wave solution to the interference field. Computer instrumented interferometers and sampling arrays provide the capability for more general wave field analysis based on non plane wave models. This paper is a summary of interferometry techniques for direction finding, angular spectrum, angular width, and coherence ratio measurements and reviews the evolution of interferometers for propagation research. The reference list includes works from the radio astronomy and propagation literature relevant to fundamental interference analysis and interferometer instrumentation.

Continuous Second Harmonic Generation in Single-Crystal Cadmium Telluride

Abstract: The achievement of second harmonic generation in cadmium telluride at optical frequencies was first observed by C. K. N. Patel. Patel generated the second harmonic at 5.3 μ wavelength using an unfocused carbon dioxide laser operating in the Q-switched mode. Preliminary experiments confirmed that single-crystal high re­ sistivity cadmium telluride could withstand, with no physical degradation, the power densities necessary to generate observable second harmonics on a continuous basis. Figure 1 shows the experimental arrangement. The CO2 gas laser was capable of producing 30 W continuously in the 10.6-μ wavelength region. By means of focusing mirrors the spot size, or radius, of the laser beam could be reduced to a minimum of 0.08 mm. This gave an available power density of up to approxi­ mately 10 W/cm. A cadmium telluride sample 1.275 mm thick was mounted in a Lansing Research mirror mount which in turn was mounted on an Oriel translational mount. This mounting system permitted the crystal to be rotated in the beam for proper crystal orientation and also permitted the crystal to be translated along the beam axis. The translation along the beam axis to and from the focal point allowed variation of spot size and thus varia­ tion of input power density on the cadmium telluride crystal. The second harmonics were detected by a Philco ISC-301 in­ dium antimonide detector cooled to 77 K. The 10.6-μ wave­ length was separated from the 5.3-μ wavelength by means of two sapphire (A12O3) windows mounted in front of the detector which is 85% transmitting at 5.3 μ but opaque at 10.6 μ. The de­ tector signal was visually monitored on an oscilloscope and de­ tector output data was taken with a PAR-HR8 lock-in amplifier using a reference signal from the beam chopper. The input power was measured with a Coherent Radiation Laboratory power meter. The theoretical second harmonic power generated is given by

Coherence in the Image Plane of an Incoherent System

Abstract: Coherence in the image plane of an optical system depends on the conditions of illumination and the impulse response of the optical components. The propagation of the mutual intensity function from object to image plane is evaluated for various conditions. Experimental measurements verify an increase of coherence under conditions where the mutual intensity function in the object plane is not resolved. These considerations demonstrate the requirement for quality in condenser optical components and care when imaging components are cascaded.

Applications of Classical Theory of Interferometry to Holography

Abstract: The elaborate theory and practice of interferometry have been established principally to meet the situation that the available light sources have finite size (finite spatial coherence) and finite coherence length (finite temporal coherence). The theory of localization of fringes provides means to reduce the effect of the source size in a. plane to be considered and give rise to a system of bright and well-defined fringes exclusively in this plane. The symmetric arrangement of two arms of the interferometer is convenient to match the path lengths to a desired accuracy. The advent of lasers seriously changed the situation. If a single mode emission from a He-Ne laser is used in the laboratory experiment, an arrangement of two arms is sufficient to produce clear fringes and no considerations are necessary to compensate both the source size and the coherence length. Once two waves originating from a laser intersect together, there appears a system of non-localized fringes, however complex in shape the waves may be. This ensures the astonishingly well-defined reconstruction of a three-dimensional and diffuse object from a hologram which is nothing but a record of interference fringes between a simple plane or spherical wave (reference wave) and a rather complex wave issuing from the object.

High-coherence ruby laser with slow Q switching

Abstract: Mode selection in a laser with slow Q switching is analyzed. The results of an experimental investigation of a ruby laser are reported.

Time and Space Correlation and Coherence in the Surface Boundary Layer.

Abstract: : Wind component correlation and coherence at 1.5, 4.0, and 16.0 meters are presented as a function of horizontal distance, vertical separation of the sensors, lag time, and sensor line orientation with respect to mean wind, under stable and unstable atmospheric conditions. The results indicate that vertical correlation is dependent not only on the vertical distance between sensors but also on the absolute height of the instruments above ground. (Author)

Distribution de la Somme des Photoélectrons Détectés en L Points sous Eclairement Gaussien Partiellement Cohérent

Abstract: The analysis of the photocount distribution in incoherent Gaussian light detected in L space points of a photodetector is extended to the case of partially coherent light. The second moment of the derived distribution is exact. A function η is introduced which accounts for the spatial coherence aspect of light as does the function ξ, (Mandel) for the temporal coherence aspect. A more general function ζ, which for cross-spectrally pure light reduces to the product ζ = ηξ, depends on both spatial and temporal characteristics of coherence. It is shown both theoretically and experimentally that many different geometrical configurations yield the same normalized second moment. A pseudo-thermal source where T is the detection time and Tc the coherence time) is used for the experimental verification.

Influence of Partially Spatially Coherent Illumination on the Measurement of Two-dimensional Correlation Function†

Abstract: A coherent optical filtering is often applied to the measurement of correlation function of two-dimensional patterns. The present report treats the influence of spatial coherence on such an optical filtering. A general formula for optical filtering with partially spatially coherent illumination is obtained. The intensity distribution of correlation in the output image plane for several special cases is calculated, where different kinds of coherence conditions of illumination in the process of holographic recording of a filter, or of filtering are assumed. An experiment is performed to verify the theory.

Theory for a Unidirectional Interferometric Test of Special Relativity

Abstract: An early criticism of the experimental background of special relativity theory was that the Michelson-Morley experiment was bidirectional in the moving frame. This experiment did not require that the velocity of light is constant in all Galilean frames, but only that the average to-and-fro velocities are constant. These objections were removed with the experimental verification of the time dilation effect predicted by relativity theory. It is coneptually simple to devise a unidirectional ether drift experiment based on a measure of fringe shifts. The experiment could not be performed in Michelson's time because of the large coherence lengths required for the observation of the fringe shifts. For an interference arrangement similar to that used to produce Young's fringes, a coherence length greater than a meter is required in order to observe a displacement of 0.01 fringes. Such coherence lengths are available today from continuous wave lasers.

Zur Störung der Kohärenz zweiter Ordnung durch Wechselwirkung

Abstract: A definition of the disturbance of the second order coherence of a photon field, scattered by an electron, is formulated within the framework of quantum electrodynamical coherence theory. As a special case forward scattering is considered, thus yielding a simple relation with the matrix element for one-photon-scattering. The scattering on a free polarized electron is treated as an example.