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An accurate numerical method has been devised to solve half-range problems for the scattering of azimuth-independent polarized radiation in stellar atmospheres. The use of the method is illustrated by solving the Milne problem for the radiation intensity at any optical depth, for the extrapolation distance, and for the law of darkening.

A theory suitable for the interpretation of measurements of light scattering from cladded multimode optical fibres is presented. The model used is based on geometrical optics and enables the effects of depolarization, the angular distribution of the propagating beam, as well as refraction and reflection at the core-cladding interface to be taken into account. Good agreement is obtained between the theory and experiment.

The theory of scattering of electromagnetic plane waves of arbitrary incidence and polarization from an infinite rectangular-mesh ground screen is treated. The screen is composed of thin wires of circular cross section, and is parallel to the interface between two homogeneous media. The theoretical results for parallel-wire screens are obtained in the limit of large wire spacing for one dimension of the mesh screen. Results presented for incident parallel polarized plane waves indicate that both the parallel-wire and mesh screens may exhibit a change in reflecting properties as the plane of incidence is varied from the wire axis direction. In addition, it is shown that the parallel-wire screen can produce appreciably higher cross-polarized fields than a square-mesh screen of the same wire spacing.

The statistical properties of the amplitude and phase-fading of pulsed radio signals reflected off the ionosphere at vertical incidence are examined and compared with the results of modern random-screen diffraction theory. Normalized second and third moments of the intensity and the observed r.m.s. phase deviation, are calculated from an extensive data sample obtained by the Kinesonde at various radio frequencies and heights (89–120 km); a consistent behavior of these parameters is found which can only occur, according to the theory, through a focusing mechanism. The geometry and available statistics of a simple rippled-reflector model are examined and judged inadequate to explain the focusing properties of the data. A model is discussed in which the scattering from weak density fluctuations is amplified very near the level of total internal reflection in the ionosphere, through an angle-of-incidence-dependent mechanism, thus tending to place the observer near the ‘focus’ of this scattering process for all distances and frequencies of observation. The resulting scattered field may bear a close resemblance to the ‘speckle pattern’ observed in the scattering of laser light from a matte surface.

The relation between the form of the scattering particles and the outer part of the small-angle X-ray scattering curve has been studied. The particles are assumed to be independent, identical, and randomly oriented and to have a uniform electron density and a smooth, strictly convex boundary surface. The electron density of the solvent is also assumed to be uniform. As earlier calculations by the authors and others have shown, the effects of the particle shape on the scattered intensity can often be conveniently described by a function called the chord, or intersect, distribution G(M). A chord, or intersect, is a straight line that has both ends on the particle boundary surface, and G(M) is defined to have the property that G(M)dM is the probability that the chord length will lie between M and M+ dM. The outer part of the scattering curve is shown to depend on the form of G(M) only in the neighborhoods of M = 0 and of any M values at which G(M) or G'(M) are discontinuous. Methods are developed for finding where these discontinuities occur and for calculating the form of G(M) in the neighborhood of these M values. In the outer part of the scattering curve, the intensity I(h) is shown to have the limiting form where h = 4 -1 sin (/2), 2 is the X-ray wavelength, is the scattering angle, Ie is the intensity scattered by a single electron, A is the particle surface area, the Di are the values of M at which G(M) or G'(M) is discontinuous, and j-2 and the ji, i, and i are quantities which can be calculated from the principal curvatures and other properties of the surface at the two points where it contacts the chord with length Di. The values of the i are shown to lie in the interval 0 i 1. In this equation the assumption is made that only the term or terms which vanish least rapidly as h increases are to be retained. In addition to the assumptions which conventionally are made in the analysis of the small-angle X-ray scattering from dilute suspensions, the limiting expression for the intensity for large h requires only that the particle boundary be smooth and strictly convex. This approximation is useful for determining the effect of the particle shape on the outer part of the scattering curve. In addition, the equation can be employed for numerical calculations for large h, where other methods of computation often are unwieldy or inapplicable.

Some experiences of multiple diffraction of neutrons by an aluminum crystal are described in this paper. The experimental conditions needed to assure that the results are treatable by the analytical methods developed earlier,1,2) are discussed. It was found that the Soller collimators are not adequate in this technique, as they do not limit the vertical divergence of the incident beam; a new type of collimator, described in the text, had a notable result in the peak resolution. It is seen that the simultaneous differential equations2) cease to be valid, as expected, when the crystal approaches perfection, that is, in this context, when the mosaic angular spread η is lower than about 0.01°; then, the problem has to be treated dynamically.

The characteristics of electromagnetic radiations scattered in a narrow forward direction ϑ = 1°(1°) 10° by a homogeneous absorbing and non-absorbing spheres [x=2πr/gl1(1)100] with refractive indices 1.47, and 1.47— 0.5i are studied. The computations are carried out using the logarithmic derivative of one of the complex function of Mie scattering theory. The functions are computed by downward recurrence formula, as upward recurrence method is found to be unstable for large particle size parameter. The efficiency factors for extinction (Qext) scattering (Qsca), absorption (Qabs) and radiation pressure (Qpr) have been obtained. Albedo sca ext Q Q for single scattering has also been obtained for all particle size parameters. The plot of (Qext) vs x indicates oscillatory behaviour for non-absorbing sphere, while the oscillations are damped for absorbing spheres. In both the cases, the limiting value tends towards that given by geometrical optics. Qpr have been obtained from assymetry factor Cos ϑ. The nature of the curves of Qpr vs x, appears to be similar for absorbing and non-absorbing spheres, except small oscillation in case of dielectric spheres. Degree of polarization P is obtained for ϑ=1°(1°) 10°. The curves of P vs x show sharp maxima corresponding to definate particle size parameter. This particular feature is interesting and provides a clue to determine particle size in the disperesed phase.

Inelastic neutron scattering measurements on single-domain orthorhombic KNbO3 at room temperature show no evidence of overdamped scattering, in contrast with previous neutron results in the cubic phase. As in the case of KTaO3, the observed diffuse x-ray planes are shown to correspond to a highly anisotropic transverse acoustic branch with an unusually flat dispersion in the 'soft' plane. In addition, a well defined optic branch with a polarization related to the orthorhombic-rhombohedral phase transition is seen to become soft as q to 0 in the soft plane. A mode-eigenvector determination confirms the x-ray result that essentially only one atom (niobium) moves in the flat transverse acoustic mode. The connection with other experimental results and with the independent chain model is discussed.

A time-of-flight spectrometer utilizing a magnetically pulsed beam has been placed in operation at the High Flux Isotope Reactor at the Oak Ridge National Laboratory. The pulsing is accomplished by rapidly changing the magnetic moment direction in a ferrite crystal that serves to both monochromate and pulse the beam. Good neutron reflectivity is obtained from the ferrite crystal and pulse risetimes of the order of 1 μs are available. The spectrometer is interfaced to a Digital Equipment Corporation PDP-15-30 computer which drives pulsed motors to set up the desired scattering geometry and collects and analyzes the time-of-flight data. The magnetically pulsed beam is ideal for use with the cross-correlation technique and spectra are presented which show the accuracy of the pulsing technique and the power of the cross correlation methods in obtaining neutron scattering data.

Previous work (see ibid., vol.16, 577) has been continued to determine the practical capabilities of the system. A higher resolution Ge(Li) detector has been used to portray the scattering along the lines of passage of a 137Cs gamma -ray beam, and from these results it is possible to construct density cross-sections of the body. The limitations are shown to be due to (a) signal/noise arising from multiple scattering in the body and (b) resolution, which is governed by the finite beam width and finite aperture needed in front of the crystal. A suggested design of a twin-headed machine for clinical use is given.

Two heterodyne laser anemometers incorporating frequency pre-shifting are described. A thin scattering disc provides scattered light from a focused laser beam to form a reference beam whose frequency can be shifted by rotating the disc. The method is both simple and inexpensive. It extends the range of laser velocity measurements, removes directional ambiguity, and facilitates estimations of instrumental broadening. The instruments are analysed, compared with conventional anemometers, and their range and capability demonstrated.

The exact solutions are obtained for a one dimensional model of a scattering and absorbing medium. The results are given for both the reflected and transmitted radiance for any arbitrary surface albedo as well as for the interior radiance. These same quantities are calculated by the matrix operator method. The relative error of the solutions is obtained by comparison with the exact solutions as well as by an error analysis of the equations. The importance of an accurate starting value for the reflection and transmission operators is shown. A fourth order Runge-Kutta method can be used to solve the differential equations satisfied by these operators in order to obtain such accurate starting values.

Simultaneous matrix equations are first given for solving the problems of scattering by many homogeneous gyrotropic cylinders of different kinds. The numerical results are illustrated for two circular ferrite cylinders, elliptic and circular ferrite cylinders, two parallel linear arrays of circular ferrite cylinders, and a circular array of twelve circular plasma cylinders around a magnetic current source. It is indicated that a sharp main lobe of the linear arrays illuminated by an E -plane wave can be veered by a reversal of the applied static magnetic field, and that with a cyclic change of the dc magnetic fields applied to the circular array one can rotate the radiation pattern having a single big lobe with suppressed side lobes. Some discussions for electronic lobe switching and electronic scanning by gyrotropic cylinders are given. The effects of interactions among the cylinders are also discussed.

It is shown that it is always possible to expand the scattering matrix for an isotropic medium in generalized spherical functions. Additional physical symmetry properties of the scattering process, e.g., time-reversal invariance or reflection invariance, give rise to simple symmetry relations for the expansion coefficents. The expansion in generalized spherical functions naturally leads to decomposition of variables and appears to be the simplest way to include the various symmetry relations for the scattering matrix discussed in the literature.

A closed‐form solution is presented describing the performance of a parametric receiver using a pump wave which is spherically spreading in the interaction region. The development of this solution is simplified by restricting the width of the pump beam to a value not greater than the beamwidth of the parametric receiver. The results are shown to be in good agreement with those obtained by the numerical evaluation of the scattering integral using the method discussed in the paper of G. R. Barnard et el. [J. Acoust. Soc. Am. 52, 1437 (1972)]. The same approach is used to develop a closed‐form solution for the nearfield performance of a parametric receiver. Experimental results are presented and compared with computed results, showing good agreement.

A theoretical analysis is given of single and dual beam scattering flowmeters. All propagating beams are treated rigorously, taking their Gaussian characteristics into account. An exact derivation of the Doppler frequency shows how it depends on the position of the scattering particle within the scattering volume. The spatial and spectral resolutions of both Doppler systems are given. It is shown in what way these depend on the geometry of the optical arrangement. The average power spectrum of the detector signal is derived as a function of the particle concentration. The signal-to-noise ratios of both systems are calculated and compared. Some inherent differences between the two systems will be pointed out.

The ultrasonic echo back-scattered by blood fluctuates as a function of time delay and lateral displacement of the source-receiver. This granular echo is not due to any special structure in the blood on the scale observed, but probably arises from fluctuation scattering by the random distribution of red cells; the dimensions of the ultrasonic pulse determine the scale of fluctuation detected. A statistical diffraction theory is developed, and formulae derived for the mean relative echo envelope Pi , and the mean rates of fluctuation Ni and NR of the envelope about its mean as the time delay and lateral displacement are varied. Ni and NR agree reasonably with experiment, but Pi is in error by a factor of thirteen; this discrepancy is discussed, and possible explanations suggested.

The optical properties of a snowpack are calculated, giving relations between the asymptotic flux extinction coefficient and albedo under diffuse illumination on the one hand and the density, grain size, and wavelength, on the other. A geometrical optics calculation of the properties of a single grain is used with approximate solutions of the radiative transfer problem. Most of the scattering is the result of change in direction of the light beam upon transmission through the grain, rather than reflection. The asymptotic flux extinction coefficient is directly proportional to the snowpack density and inversely proportional to the square root of the grain size. The albedo under diffuse illumination is independent of density and proportional to the square root of the grain size. The derived relations agree with experimental data to within 20% for the flux extinction coefficient and to better than 2% for the albedo without using adjustable parameters. Higher values of the flux extinction coefficient will be measured if the snow is confined within a finite cylinder with absorbing sides. An analysis of this effect is given.

The imaging photopolarimeter aboard Pioneer 10 produced hundreds of red and blue images of Jupiter covering a wide range of phase angles and having good linearity and signal-to-noise characteristics. In this preliminary analysis the limb darkening across two of the red images (at phase angles of about 34 and 109 deg) in both a prominent dark belt and a bright zone are compared with multiple-scattering models. Of the simple models tried, the smallest deviations from the observations result for ones consisting of a thin absorbing layer above a semiinfinite atmosphere of particles scattering according to the Henyey-Greenstein phase function. The asymmetry parameter for the best fits to both the belt and the zone data is in the range g = 0 to 0.25, corresponding to particles small in comparison with the wavelength of red light. The phase integral derived from the models lies in the range of about 1.5 to 1.6, implying a substantial internal heat source for Jupiter.

A method is given for synthesizing a desired scattering pattern by reactively loading an N -port scatterer. The procedure involves specifying the pattern in magnitude only, without restriction of its phase. The real port current (or voltage) which gives a least-squares approximation to a desired radiation field magnitude is found and then resonated by reactive loads at the ports. If a sufficient number of ports is chosen, and if the body is of electrically small or of intermediate size, then the scattered field pattern is approximately the same as the synthesized radiation pattern. Numerical examples of the method are given for a body consisting of a wire triangle with two cross wires, on which four ports are defined.

This paper reviews scattering theory required for analysis of light reflected by planetary atmospheres. Section 1 defines the radiative quantities which are observed. Section 2 demonstrates the dependence of single-scattered radiation on the physical properties of the scatterers. Section 3 describes several methods to compute the effects of multiple scattering on the reflected light.

Interband light absorption in a disordered semiconductor is considered with due allowance for exciton effects. Allowance is made for the scattering of the electron and hole in a weak static random field and also for collisions of the second kind experienced by the exciton on interaction with a random field. It is shown that the contribution of these latter to the half width of the absorption line of the exciton spectrum (even at temperatures of the order of the exciton ionization energy) is considerably smaller than the contribution arising from the scattering of the particles forming the exciton.

The slowly varying component of solar centimeter wavelength radiation can often be attributed to thermal emission from density enhancements above an active region. This assertion is justified by the success in reproducing the observations by ray tracing calculations in appropriate coronal models. Similar components have been observed at meter wavelengths and thermal radiation from density enhancements has again been suggested as the emission mechanism. However ray tracing calculations at meter wavelengths, unlike those at centimeter wavelengths, must include both refraction and scattering effects for realistic modelling. In this study, in which scattering is included for the first time, it is shown that scattering may lead to lower emission from density enhancements rather than higher emission as predicted by models in which refraction alone is considered. This strongly suggests that the emission observed at meter wavelengths is of non-thermal origin.

In calculations of the thermal utilization factor for heterogeneous reactors the anisotropic scattering is taken into account usually in the transport and sometimes in the linear-anisotropic approximations. The work of Eccleston and McCormick make doubtful the generally accepted opinion that the second angular moment of the scattering kernel has little effect on the disadvantage factor in slab cells in nuclear reactors. In the present work we have investigated the effect of the second and higher angular moments of the scattering kernel on the thermal utilization factor. The formulas appropriate for the qualitative analysis of the question under consideration are given and a set of cells was calculated by various methods. A disagreement between the data obtained and those reported by Eccleston and McCormick is shown.

Characteristic features of the TOF (time of flight) neutron diffraction are summarized. In this method, i) all the reciproal points on the rod passing through the origin in the reciprocal space can be scanned by each burst of white neutrons, ii) it is easy to measure high index reflections at the large scattering angle, iii) each reflection is not affected by the higher-order harmonics, and iv) it is easy to measure the physical properties depending on the neutron wavelength.The pulse neutron generator as well as the data acquisition system in the Laboratory of Naclear Science of Tohoku University is described.The TOF method seems to be very powerful if it is applied to the accurate structure analysis. The data correction methods are discussed. The TOF method is prospective to the study of transient phenomena. In this method one can apply to the crystalline sample an external field pulsed with the same frequency as the neutrons. By using this method, the transient state of the polarization reversal of the ferroelectric NaNO2 has been observed.The magnetically pulsed neutron TOF spectrometer is briefly introduced after a review of the choper history.

Small-angle multiple scattering of high energy protons has recently been shown to give rise to an edge pattern which can be used for radiography. The authors derive the intensity pattern involved and discuss its implications for radiography. They also derive the degradation of the intensity pattern by obscuring matter and various instrumental effects and use it in design of arrangements for taking scattering radiographs with protons of 160 MeV and 7 100 MeV. Sample radiographs illustrate the main differences from, and advantages of the technique over, x-radiography recorded on film. The resemblance to xero-radiography is pointed out.

Computations of the equivalent widths of absorption lines as a function of planetary phase angle are made for a homogeneous cloud with particles having the properties (shape, refractive index, and size distribution) deduced from polarimetry of Venus. The computed equivalent widths show an 'inverse phase effect' comparable to that which is observed for CO2 lines on Venus. This result verifies a recent suggestion of Regas et al. that the existence of an inverse phase effect does not by itself imply the presence of multiple layers of scattering particles in the atmosphere of Venus.

Radio scattering measurements have been made of a region of the ionosphere above the Institute for Telecommunication Sciences' ionospheric heating facility at Platteville, Colorado. Strong scattering was observed at frequencies in the HF and VHF bands. The scattering has been shown to originate from electron density fluctuations that are highly elongated in the direction of the geomagnetic field. Radar scattering cross sections of 70 to 80 dbsm are measured in the HF and low VHF bands. The scattering cross section decreases at a rate of 20 to 30 db per octave at the high end of the VHF band. The scattering irregularities are produced by operation of the heating facility with o-mode polarization at frequencies that reflect within the ionosphere. The strength of the scattered energy decreases at a rate of at least 10 db per degree for observation geometries that do not match the geometry for specular reflections from long cylinders aligned with the geomagnetic field. The spatial distribution of irregularities has been estimated for both E- and F-region heating. The temporal properties of the scattering have also been determined including the frequency spectrum of the scattered signals. The processes by which ionospheric heating produces these irregularities are not yet fully explained. Several potentially useful applications of radio scattering from such irregularities are discussed.

The paper presents a model for radio wave scattering from the ionospheric irregularities generated by the intense radio wave transmissions from the Platteville heater. The model is based upon the HF-UHF radar backscatter observations for a physical description of the scattering medium and upon the theory of weak scattering (Born approximation) from anisotropic irregularities for mathematical development. According to the model, the electron density fluctuations responsible for radio wave scattering having an rms value of 1 to 1.5% are aligned along the earth's magnetic field and are distributed in a diffuse pancake-shaped volume of 15 km gaussian thickness vertically and of the size of the heater beam which is 100 km in gaussian diameter horizontally. At radio frequencies the irregularities within the disturbed volume are highly aspect sensitive and consequently only those scatterers which lie on the surface of specularity where a radar views transverse to the magnetic field count in contributing to the received signal. Model computations have been made of the scattering cross sections for monostatic as well as bistatic radar configurations and they are found to be in good agreement with the observations. The radar cross section at a given frequency for bistatic geometry is substantially greater than that for monostatic geometry, all else being equal. Finally, it is shown that the width of the scatter-illuminated bands on the ground is set primarily by the finite dimensions of the scattering volume rather than by the finite aspect sensitivity of the individual scatterers.

A theory of X-ray diffraction from polymer crystals accompanying with thermal disorders is developed under harmonic approximation. Temperature factor based on the displacement in the radial direction (in cylindrical coordinates) is given in terms of modified Bessel functions. A new selection rule which depends on thermal vibrational mode is derived, so that it is shown that the strong diffuse streak scattering appears on N 0 -th layer line ( N 0 is the number of turns of the helix in its repeat unit), when interaction energies between polymer chains are weak enough.

The measured filling-in of Fraunhofer lines in the sky spectrum 3850–4450 Å is compared with synthetic filling-in computed for three different incoherent scattering processes, i.e. rotational Raman scattering by O2 and N2, Rayleigh wing scattering from the Earth's surface, and atmospheric aerosol fluorescence. It is concluded that rotational Raman scattering is the most likely contributor to the observed filling-in.

The first measurements have been made of the linear polarization of sunlight scattered by the Jupiter atmosphere at phase angles greater than 12 deg, using the imaging photopolarimeter on Pioneer 10. The data are of high accuracy, in spite of several problems in the instrument. The polarization is positive at 440 nm. There is no direct evidence for spherical particles in the Jupiter clouds. Using a simple model of Rayleigh scattering above a Lambertian cloud layer, a unique fit is found to the observed intensity and polarization at each point on the planet. The resulting Rayleigh optical depths, if they are attributed to molecular scattering alone (i.e., no aerosols above the cloud tops), can be converted into physical altitudes of the cloud tops. The first results suggest that the north tropical zone, parts of the equatorial zone, and the red spot are all elevated regions.

The interior radiances are calculated within an optically deep absorbing medium scattering according to the Rayleigh phase function. The accuracy of the matrix operator method is improved by many orders of magnitude through the use of accurate starting values obtained by the Runge-Kutta method rather than from the single scattering approximation. The radiance and flux are given for a range of solar zenith angles and for single scattering albedos of 1, 0.99, 0.9, 0.5 and 0.1. The development of the asymptotic angular distribution of the radiance is illustrated. It is shown that this asymptotic distribution is probably physically unobservable when ω0 < 0.8, since the flux is less than 10-8 of its original value at the beginning of the asymptotic region. The ratio of the upward to downward flux is calculated and is shown to be remarkably constant within the medium except very close to the boundaries. The heating rate within the medium is found to be very nearly proportional to the downward flux, except near the boundaries. When the single scattering albedo is small, a number of examples illustrate the significant contribution of the direct solar flux to the total flux even at great optical depths within the medium. The total downward flux decreases exponentially with optical depth away from boundaries when the single scattering albedo is greater than or equal to 0.9; when it is less than or equal to 0.5 only an approximate exponential fit can be obtained within the region accessible to experimental observation.

It is shown that a lower limit exists on the microwave brightness of the rings of Saturn, if they are assumed to be composed of Mie scatterers of geological composition. The lower limit (about 15°K) is due to scattering of planetary microwave emission. Significant variation of brightness with azimuth along the rings is expected if the particles are typically of 2–3cm radius. Implications for the multiple-scattering hypothesis of the radar cross section of the rings are noted.

The physical properties of the concepts frequently used in radiationdosimetry to compute dose are studied for high‐energy x‐ray beams. The dose in tissue is divided into total incident and phantom‐scatter components. The incident beam includes the primary photons as well as the collimatorscattering contribution. The phantom scattering is composed of back‐ and front‐scatter functions. The former function is shown to have essentially zero effect on dose at 33‐ and 45‐MV energy x rays.Characteristics of tissue‐maximum‐ratio (TMR) at high energies are investigated and TMR tables are provided. Contrary to the definition of TMR, this function is observed to depend on SSD. TMR curves are fitted with a semi‐empirical function with a maximum deviation of 1%. Mathematical equations are derived for the computation of dose from TMR. The applicability of the equivalent square technique to high energy photons is examined and found to be adequate. Properties of percent depth dose are studied and a number of related phenomena are discussed.

Extensive Mie computations have revealed that it is possible to determine the diameter of a sphere from knowledge of the extrema of the scattering intensities by a simple method requiring no computational aids. The present work treats the case of dielectric sphere with: (a) refractive index N in the range 2.1 ≤ N ≤ 3.1 and size parameter α less than 24, (b) N ≤ 2.0 and size parameter in the range 24 ≤ α ≤ 54, and (c) N ≤ 1.75 and α ≥ 24 with the extrema counted from the backward direction. In cases (a), (b) only the perpendicular scattering intensity avails itself to the method. In case (c) both the perpendicular and the parallel scattering intensities avail themselves to the method, and more so the average of these corresponding to a completely unpolarized incident beam.

A new light scattering instrument is described for measuring, as a function of scattering angle, the elements of the matrix describing light scattered from small particle systems. The instrument uses a piezo‐optical birefringence modulator to modulate the polarization state of the incident light beam, and uses lock‐in amplifier detection of the scattered light. The first and second harmonics of the modulation frequency are used with various combinations of filters and orientations to give the separate matrix elements. A treatment of a simple scattering experiment by means of Mueller calculus is carried through to illustrate the interactions of the light with the scattering system and with the various components of the measuring instrument. Evaluation of the instrumental performance is shown through measurements on two systems of monodisperse polystyrene spheres of average radius 550 and 3940 A, compared with Mie calculations. Further measurements on sulfur colloids are presented, and suggestions of the va...

Antisymmetric charge distortions form the basic deformation of the shell lattice dynamics models. The effect of these deformations on the scattering factors of atoms in a solid is investigated through the Born beta coupling coefficients. Particular reference is made to the alkali halides. The Fourier transform coefficients which directly affect the X-ray scattering intensities are calculated for fitted shell models of NaF and NaCl. The theory is extended to define deformation matrices useful for antisymmetric distortions. These matrices are related to the shell-core displacements. Real space coupling parameters are found and values for a microcrystal of atoms surrounding the origin have been calculated. These give some insight into the relative effect of different polarization mechanisms. They also show that second- and third-neighbour coupling parameters are comparable in magnitude to the nearest-neighbour parameter.

In a manner similar to that given in a preceding paper (cf. Castiet al., 1970), in this paper we show how to get a Cauchy system for the scattering and transmission matrices of the azimuth-independent term of partially polarized light in accordance with Rayleigh scattering in a homogeneous atmosphere bounded by a specular reflector. This set of integro-differential equations for the scattering and transmission matrices is suitable for numerical computation by high-speed digital computer.

The random grid search method and the minimization search method recently developed by Fymat (1972) for solving inverse multiple-scattering problems of planetary atmospheres are employed for a study of the extent and nature of true information yielded by theoretical partial fits of observed planetary curves. The study is conducted with the Venusian visual phase curve as a background example. It is shown that such fits cannot be used toinfer the model scattering parameters of the planet's atmosphere. They cannot provide any indication of the shape of the scattering diagram, even in the region of the fit. It is also shown that the measured Bond albedo can provide neither a criterion for sorting out different possible scattering model candidates nor a means for accurately determining the single scattering albedo. A high value of the latter albedo for Venus' atmosphere at visible wavelengths(ωo ≈ 0·99) is also found, and Euler's scattering model is definitely discarded for this planet.

The deflection of light by acoustic surface waves in multimode waveguides is studied in the present work. Conditions on deflection of single‐mode and multimode optical power are derived, and expressions are presented for the number of resolvable spots and the efficiency that may be obtained with these scattering processes. A description of the waveguide analog to anisotropic Bragg scattering is given, and the advantages and disadvantages of this approach are discussed in detail.

1. Spike responses of single optic tectal units to plane polarized light have been recorded with extracellular electrodes in the goldfish. Responses to a series of eight 500 msec flashes were summed and the quantitative effects ofe-vector direction studied over 4–5 log units of intensity with white light and narrow spectral bands of equal quantal content at 460, 540 and 620 nm. 2. As previously reported all or nearly all tectal cells tested (115) were sensitive to the direction of the stimulus' polarization plane. Control experiments with a thin high order birefringent retarder next to the cornea and acting as a pseudo depolarizer provided further proof that thee-vector discrimination found in the optic tectum (as well as the previously reported oriented behavior to polarized light in fish) depends on an intraocular analyzer. 3. Systematic study of tectal cells has been made at various depths and in all directly accessible areas. No localized or differential effects of recording depth one-vector discrimination have been found. However, both directions of maximum response and degree of polarized light sensitivity (PLS) show distinctive patterns over the tectal area. 4. On the basis of established tectal projection maps these data show that preferred retinale-vector directions are tangentially arranged around the eye axis when the stimulus is axial. Distribution of this angular sensitivity seems continuous without discrete channels favoring particular polarization planes. 5. Sensitivity (determined from intensity response curves) is minimal in the center of the retina for an axial stimulus and increases peripherally out to 50–60° or more off axis. Sensitivity ratios of 4–6 are common and much larger ones have been occasionally recorded. 6. Shifting the direction of stimulus from axial to 45° and 60° upward from the axis proved that retinal patterns of preferrede-vector directions and sensitivities are symmetrical relative to the beam axis rather than the anatomical eye axis. Therefore individual tectal cells and before them their retinal receptor elements show different directions ofe-vector preference and different PLS ratios depending on the stimulus configuration. 7. Intensity response curves determined with the red, green and blue narrow spectral bands were essentially superimposable. Therefore, we have no evidence that there is any special interaction of λ and PLS. 8. The effects of stimulus intensity and retinal adaptation on the IR curves do not indicate any particular selective effects. Substantial polarized light sensitivity was present in both the light adapted and dark adapted state. PLS ratios in various cases were (1) about the same at different intensity levels or (2) greater at low than high intensities or (3) greater at high than low intensities. 9. We conclude that linearly polarized light evokes a large entoptic image in the goldfish eye. Two opposite light sectors perpendicular to thee-vector alternate with two dark sectors parallel to thee-vector. Both Haidinger's brushes and Boehm's brushes in human vision show some similarities but also some important differences. The goldfish PL image is achromatic, weak or absent axially and strong peripherally. Also the contrast between the sectors does not depend on movement of the stimulus on the retina to prevent fading as it does in both of the other phenomena. 10. The most likely mechanism for the observed PLS in the goldfish eye is either differential scattering intraocularly or oblique entry of light into the receptor outer segments. Yet present data prevent a firm choice between them.

The calculated integral scatter characteristics for monodisperse scattering media serve as the basis for determining the ranges of relative sizes of scattering particles within which the shape of the optical scatter characteristics depends uniquely on the refractive index and the absorptivity of these particles. As a result, the ranges of particle sizes where the integral indicatrix becomes most sensitive to variations in absorptivity are found to coincide with the minima of the corresponding scatter coefficient as a function of the diffraction parameter.

Two‐dimensional series expansions of cylindrical harmonics are used to study the diffraction of a wave radiated by a pulsating cylindrical transducer at a cage grating that surrounds the transducer. Farfield radiation patterns and radiation impedances, as distorted by the cage grating, are presented as a function of cage radius and number of rods. Decreasing the distance between the cylindrical scatterers and thereby increasing the scattering interaction is shown to increase the frequency range of nearly uniform cylindrical waves emitted from the grating. The shape of the radiation reactance in the frequency intervals where resonant peaks occur in the radiation resistance is explained in terms of Kramers‐Kronig relations. Good agreement is shown between the predictions of the two‐dimensional analysis and experimental measurements of farfield radiation patterns of a finite‐length transducer and cage.