Coastal Errors in Radio Direction-Finding

Behavior of Plated Microbumps during Ultrasonic Flip-Chip Bonding Determined from Dynamic Strain Measurement

“…It is of interest in connection with errors in direction-finding by wireless waves as observed at a station near the sea coast. (25) Conditions corresponding to any change of velocity of waves on crossing the boundary were attained by providing one-half of the tank with a false bottom only slightly submerged. In the photographs the boundary is clearly apparent.…”

The concept of an angular spectrum of plane waves, and its relation to that of polar diagram and aperture distribution

“…so that the aperture distribution in the plane x = 0 is by the second shift rule in Section 2, using the replacements given by (22) and (23), that the angular spectrum corresponding to the aperture distribution of eqn. (49) is…”

A relation between the Sommerfeld theory of radio propagation over a flat earth and the theory of diffraction at a straight edge

“…With r/ small compared with rf, as it usually is in practice, the Brewster angle of elevation is small. Strictly, the Brewster angle of elevation is the angle whose tangent [not sine as given by (23)] is 77/7/; but for small angles the difference is unimportant. We shall begin by considering an earth whose reflection coefficient is any function of the sine S of angle of elevation, and subsequently pay special attention to the reflection coefficient (22), which covers most practical requirements in connection with the earth.…”

“…Great care is therefore necessary in interpreting the angular spectrum as a polar diagram, 8 and it is precisely this approximation that is made in the ray theory. No difficulty occurs for a perfectly conducting earth, because then the characteristic admittance of the earth is infinite, making the sine of the Brewster angle, S o , zero by (23), and this makes the amplitude of the Zenneck wave (34) and (35) zero. For an imperfectly reflecting earth, however, the amplitude of the Zenneck wave to be diffracted under the image line is not zero, and the image involves an aperture distribution, infinitely wide, extending indefinitely downwards from the image line.…”

“…By an application of the method of steepest descent 9 ' 10 we may extend the validity of (45) to almost any practical transmitter close to the earth's surface. This means that, if we substitute for cf^ in (45) the field at range r (appreciably greater than A) near a perfectly reflecting earth for the transmitter in which we are interested, then % will be the field for the same transmitter at the same range near the surface of an imperfectly reflecting earth, the sine of whose (small) Brewster angle of elevation is S Q> given by (23).…”