Far-field Case Research Articles

Detection efficiency of coherent optical radar

Using the Huygens-Fresnel principle, the detection efficiency of a coherent optical radar is formulated. This formulation includes the effect of misalignment between the signal field and the local oscillator field. In the far-field case, the detection efficiency of a diffuse target is approximately half that of a glint target when the transmitter and the receiver are of the same size and the misalignment angle is small. The effect of finite detector size on the detection efficiency is also studied. For a uniform local oscillator field mixed with a signal field at the detector surface, the optimum angular detector size is ~2λ/d2, where d2 is the receiver aperture size. This conclusion is valid for both diffuse and glint targets.

Irradiation of Prolate Spheroidal Models of Humans in the Near Field of a Short Electric Dipole

Analysis of the near-field irradiation of prolate spheroidal models of humans and animals by a short electrical dipole is described. The method of solution involves an integral equation formulation of the problem in terms of the transverse dyadic Green's function and expanding the fields irradiated by a short dipole in terms of the vector spherical harmonics. The extended boundary condition method (EBCM) is employed to solve the integral equations. The power distribution and the average specific absorption rate (SAR) are calculated and plotted as a function of the separation distance. It is shown that for a dipole placed along the major axis of the spheroidal (k-polarization), and for a very short separation distance, d= 0.15 lambda, the relative power values at both ends of the spheroid are about 40 compared with the ratio of 15 in the planewave exposure case. Furthermore, the calculated average SAR values as a function of the separation distance were found to oscillate around the constant value obtained from the planewave irradiation case. Differences between the near-and far-field exposure cases occurred only at separation distances shorter than 0.5 lambda where the magnitudes of the electric and magnetic energy densities are higher than the time-average radiation power density.

Scattering of electromagnetic waves from moving surfaces

Electromagnetic wave scattering from moving objects is considered. Use is made of the reformulated current method in which the object is replaced by a current distribution radiating into an unbounded media. Cylindrical and spherical profiles in nondeterministic motion are considered. Results are obtained for far-field and steady-state cases when the radii of curvature are large compared to the wavelength.

Virtual pulse effect in incoherent scattering

During incoherent scattering of a radar pulse from an extended volume region it is appropriate, because of transit-time considerations, to work with a virtual pulse which differs from the true (transmitted) pulse both in size and shape. We have determined the coordinate transformation leading to the virtual pulse for the general far-field case. The Gaussian spheroidal incident pulse is then considered as a prototype, and implications on measurements are discussed.

Effect of turbulent fluctuations in an optically active fluid medium.

The effect of a beam traversing an optically active medium of turbulent fluctuations of the index of refraction in the medium is investigated theoretically. The general far-field case is solved by integration of the wave equation with both gain and fluctuations of the index refraction, simplified by neglecting the Laplacian of the fluctuating part of the electric field and one of the time derivatives. The far-field diffraction pattern is identical to that for a nonactive medium. For small to moderate extinction there is a loss of power from the coherent beam but only a slight change in the diffraction pattern, accompanied by wide-angle incoherent scattering. For high-gain cases it is possible to have the extinction coefficient less than the gain, but with complete extinction of the coherent beam and a large incoherent scattering pattern. The use of a more realistic turbulence spectrum than previously used has led to the discovery of a second branch in the curve, in which the far exceeds the previously given limiting resolution as the aperture size is increased beyond a certain limit, and approaches the diffraction pattern based on the aperture, although there may be considerable attenuation in the intensity in the diffraction pattern of the coherent beam. These results are applicable, for example, to the use of large aperture optics in turbulene wind tunnels.

Angular Distribution of the Acoustic Radiation from a Tuning Fork

It is shown by elementary arguments that the familiar loudness distribution pattern in the immediate neighborhood of a tuning fork is not, as is often suggested in elementary texts, due to pathlength-dependent phase differences between the waves reaching the ear from the different faces of the prongs, but to pathlength-dependent amplitude differences. At great distances from the fork, however, amplitude variations become negligible and pathlength-dependent phase differences give rise to a quite different loudness distribution pattern. From an idealized model, which represents a tuning fork as four colinear sources of strengths +B, −B, −B, +B, the velocity potential is calculated and the mean-square-pressure and intensity distributions are derived. It is shown that the mean-square-pressure distribution depends on polar angle (θ) and distance (R) as (3 cos2θ − 1)2/R6 close to the fork—the easily audible (amplitude-dependent) nearfield pattern; and as cos4θ/R2 at great distances—the less familiar (phase-dependent) farfield case. The intensity distribution comprises a cos4θ/R2 radial outward flow with, superposed, a circulation of energy from equatorial (θ ≈ 90°) to polar (θ ≈ 0,thinsp;180°) regions, varying with distance as 1/R4. There are two zeroes of intensity: where R = 0.225λ, θ = 0 and 180°. The power radiated is estimated for a typical 520 cps fork, and is found to be 2.5 × 10−15 W when the prongs vibrate with an amplitude of 0.2 mm.

Near-field gain of aperture antennas

Formulas for the ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\eta</tex> of received to transmitted power are examined for microwave aperture antennas at any range. It is shown that with optimum aperture illuminations the farfield range equation continues to hold fairly well in the near field down to a distance at which it implies that nearly all the transmitted power is received! However, the aperture illuminations with maximum <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\eta</tex> (nearly 100 per cent) are different from the uniform, constant phase illumination which is optimum in the far-field case. The optimum near-field illuminations not only have the phase variation associated with elliptic rather than parabolic reflectors but they also have some amplitude variations. Some simple illuminations which can be realized practically by lenses and dishes are shown to be sufficiently close to the optimum cases for most practical purposes. A formula for the power density in the near field of a transmitting aperture is also derived and it is shown how to maximize the power flow through any given area of space by design of the transmitting aperture illumination.