Table of contents

The use of complementary semicircular or half-plane apertures in the objective lens back focal plane of an optical system to determine from image intensity measurements the complex image wavefunction is discussed. This method for the solution of the phase problem in optics is restricted to bright-field optics, where the primary wave is allowed to interfere with the scattered wave. It is shown that in this modified bright-field situation, using semicircular (half-plane) apertures rather than the normal circular objective aperture, it is possible to determine for complementary positions of the apertures a Hilbert relation between the real and imaginary parts of the image wavefunction. The initial estimate for the complex wavefunction may be systematically corrected for nonlinear effects occurring in the equations for the image intensity.

A recently proposed method of data analysis applicable to the study of polydisperse systems by photon correlation spectroscopy has been experimentally tested for random-coil polystyrene in cyclohexane. Using this method a useful average diffusion coefficient can be obtained. This allows, for the first time, a determination of the weight-average molecular weight of a polydisperse solute to be made using the Svedberg equation. Another parameter determined by this method provides a useful index of polydispersity.

It is shown how a simple sawtooth phase modulator can be used to shift the frequency of a laser Doppler signal. Such a device permits the determination of velocity sense and aids interpretation of turbulent distributions. These applications are demonstrated, and a null method of velocity determination which can form the basis of a feedback tracking loop is suggested.

A method for simultaneous determination of the optical gain, saturation intensity and internal losses of a 6328 Å He-Ne laser is reported. It involves measurements of laser power deflected off an intra-cavity plate which rotates away from its Brewster angle. From these experimental data the laser parameters are graphically deduced.

A general solution is given to the uncoupled one-dimensional equations for the stress wave in a semi-infinite body due to an absorbed heat flux that is spatially uniform but varies in an arbitrary manner with time. The solution is in the form of a convolution integral that is applicable when both the thermal conductivity and the exponential absorption depth of the material are nonzero. Analytical results in terms of real and complex error functions are given for the cases where the flux is steady or varies in an impulsive, linear or exponential manner with time.

Analysis of the phase shift of ultrasonic waves on reflection at a bonded transducer is extended to the case of thin-film piezoelectric transducers and is complemented by measurements. The certainty of determination of ultrasonic velocities by use of thin-film transducers is shown to be much greater than that attained by bonded-transducer techniques.

A direct comparison is drawn between sampled-continuous-wave resonances and pulse-superposition pseudoresonances in ultrasonic samples. To justify this comparison, measurements of ultrasonic transit times in GaAs single crystals have been made by both techniques, using thin-film CdS transducers. The validity of use of the pulse-superposition technique to make accurate measurements of ultrasonic velocities is demonstrated.

Direct Ultrasonic Visualisation of Defects (DUVD) is a new method for forming and displaying images of acoustic discontinuities in an otherwise homogeneous medium. The principle is novel, since it combines known techniques in a new way to achieve a result which has no direct analogy to previous methods for manipulating wave motions in order to provide images.

The focusing constraints required to render the system operable are derived analytically, and simplified graphical methods are presented for facilitating actual design. Demonstrations are presented showing that the new system works when inspecting either solid or liquid media. Medical applications are therefore possible.

Unlike other pictorial methods of ultrasonic inspection, DUVD operates without the need for mechanical or electronic scanning, does not need coherent light, and operates in real time.

Under certain narrow limits of initial pressure conditions, self-sustaining detonation waves in gaseous mixtures exhibit large periodic variations of velocity with distance, although the mean value is close to the calculated Chapman-Jouguet value; these waves are known as `galloping' waves.

A microwave interferometer, employing the fundamental TE₀₁ mode at a frequency of 9000 MHz, is used to study the propagation of these waves in a rectangular tube of 23×10 mm² section and 30 m in length. A continuous monitor is obtained of the combustion zone velocity trajectory, with a spatial resolution of about 2 cm, over the whole length of the tube. The technique also enables changes to be detected in the frontal configuration of the wave through the accentuated reflection of microwave energy from the transverse shocks; in this way, modal changes preceding the deceleration phase are clearly depicted. During the low-velocity régime, in which the causal shock and combustion fronts are dissociated, new and more detailed information is obtained on the unsteady behaviour of the latter.

The state-space method for scattering from dielectric bodies is extended to scattering from conducting bodies of revolution. Using spherical wave expansions and Waterman's extended boundary condition the scattering problem is reduced to the solution of first-order linear differential equations in state-space form with known initial conditions. The vanishing of the multipole coefficients for the ingoing scattered radiation at the outer boundary of the body is suggested as a check for the accuracy of the solution. Applications to certain class of surfaces are discussed and a general comparison is made with methods using only linear algebraic equations.

Intensity distributions of Fresnel fringes are calculated from a consideration of various specimen edge cross sections, where the penetration power and the phase shift of the electron beam are continuously varied with distance from the specimen edge.

The variation of the calculated distributions shows a good accordance with the experiments in the following features: (i) the intensity distributions of overfocused and underfocused Fresnel fringes show a remarkable difference from each other in the region of relatively small defocusing value; (ii) the distribution is varied with the defocusing value and the specimen tilting angle, and the variation can be explained by the effective change of specimen edge form.

Field emission in a plane-parallel electrode geometry at energies up to the relativistic regime is considered with the inclusion of finite velocity of electron emission from the cathode surface. The effect of this velocity is subsequently shown to be negligible. A technique is developed for evaluating the anode current/voltage/electrode-spacing characteristics for any cathode material, from which the electrical impedance of the diode can be calculated. The completely space-charge-limited case is of particular interest, and a criterion is established that imposes an upper limit on the cathode workfunction in order that a particular diode should be at least 90% space-charge-limited. Fulfilment of this criterion implies that the diode current and impedance are determined, to 5% accuracy, solely by the anode voltage, electrode spacing and cathode area. Consideration is also given to the transition from the field-emission discharge to the vacuum arc and another criterion imposed on the cathode material in order that this transition should not occur. Finally the bearing of this analysis on field emission in nonplanar geometries is considered.

Analytical expressions are derived for the power spectral density of the current in optical heterodyning when phase front curvature mismatch, tilt or axis displacement occurs between the beating light beams. The signal beam is the far field of an incoherent source of circular shape, and the local oscillator is the fundamental mode of a stabilized laser. The cases in which the signal beam either illuminates the detector coherently or has a coherence area small compared with the detector area are shown to have simple solutions. An analogous analysis is carried out for homodyning (self-beating). The dependence of the signal-to-noise ratio on the detector aperture and optimum and tolerance values for the latter are obtained for a given misalignment.

A CO₂ laser has been used to observe photoconductivity in p-type germanium due to electronic transitions between the light- and heavy-hole bands. The magnitude of this effect, which contributes to nonlinear behaviour in germanium devices, has been measured as a function of crystal impurity concentration. An approximate phenomenological theory of the effect is fitted to the data. It is pointed out that the effect may have device applications and an example - optical pulse length measurement - is described.

A pulse of radiation from a circularly polarized 3 cm maser can be reflected with dramatic changes in intensity and frequency by electrons in a magnetostatic field of the order of 0·4 T.

An effective relaxation constant for the CO₂ (00v) and CO(v) vibrational levels has been experimentally obtained from measurements in the discharge. Using this relaxation constant and known excitation cross sections, a comprehensive picture of the kinetics of the CO₂-He laser has been obtained. This approach does not require knowledge of the electron energy distribution function. Populations and temperatures of different vibrational levels have been calculated, as well as energy transfer rates to these levels. Quantitative results are presented and compared with otherwise known data on small-signal gain and energy transfer rates.

The dissociation of carbon dioxide in the positive column of a glow discharge has been measured in CO₂ and in CO₂-N₂ and CO₂-N₂-He mixtures as used in low-pressure (1-20 Torr) gas lasers. Both for continuous and pulsed discharges the measured dissociation rate is proportional to the electron density. The dissociation coefficient increases with the reduced field strength E/p, but for a given E/p it is very much greater for CO₂-N₂-He than for CO₂-N₂, and is greater for CO₂-N₂ than for CO₂. This variation is consistent with the variation of the electron energy distribution and drift velocity with the different gases, and it is not necessary to postulate more than one dissociation mechanism.

Continuous-wave laser oscillation on transitions of singly ionized iodine has been obtained at increased laser efficiency in helium-iodine gas mixtures using a narrow-bore (3 mm), multiple-anode/hollow-cathode laser tube. The sixteen CW laser lines observed include among their number six which have not formerly been reported as oscillating on a CW basis. Output characteristics of the laser as a function of helium pressure, iodine partial pressure and discharge current have been studied. The output intensity for all lines rises linearly for increasing discharge current beyond threshold to the limit of currents investigated.

The Sparrow criterion of resolution is used to obtain an expression for the limit of resolution of a circular aperture, with non-uniform illumination by partially coherent light. Also the image intensity distributions for the two partially coherent points with different separations are obtained.

An accurate alternative method to energy-multigroup theory for slowing-down problems is considered in which a particular energy range is represented by discrete energy points while the larger part of the energy range is treated by groups. Applications of the technique are made for homogeneous iron-sodium and uranium-graphite mixtures, and for two-region cells composed of these materials. It is demonstrated that by suitable distribution of the energy points within the selected energy range, reaction rates and their temperature coefficients can be predicted with better accuracy than the conventional multigroup method of treating the energy range as a single group.

The redistribution of electronic concentration due to heating of a plasma by a gaussian electromagnetic beam has been studied. The Boltzmann equation has been solved for the electron distribution function in the steady state, with proper account being taken of space-charge field effects. The redistribution of the carriers has been shown to be very sensitive to the velocity dependence of the collision frequency; carriers are not redistributed in a diatomic plasma, while their redistribution is a maximum for electron-ion collision-dominated plasmas. The dielectric constant shows a saturation behaviour with respect to the field. The absorption tends to zero for a Coulomb collision-dominated plasma; while in a plasma having constant collision cross section, absorption tends to a constant value. The self-focusing of waves in such media resembles that observed in similar studies in dielectrics.

A multi-grid orifice probe and analysis technique are presented which permit the measurement of the following plasma parameters: the electron number density n_e, the electron temperature T_e, the space potential V_s, and an estimate of the metastable number density n_m. Simultaneously, the analysis allows the quantitative determination of instrumental parameters such as the reflection coefficient for slow (<30 eV) electrons from the grids R_e(G) and roughened (gold-black) collector R_e(C), the secondary electron emission coefficient for fast (> 30 eV) electrons γ_e(G) from the grids, and the effective transparencies of the grids for electrons τ_e(G), and for metastables τ_m(G). Experimental ion, electron and total current characteristics are presented for a low-pressure (1·8×10⁻² Torr) RF discharge in argon. The major part of the analysis method involves the use of ten `plateau values' obtained from the characteristics to determine values for most of these parameters. T_e and V_s are determined separately. The values obtained are: n_e=2·74×10⁹ cm⁻³±18%, kT_e=1·92 eV±5%, V_s=11·7±0·1 V, n_m similar, equals 3·3×10⁹ cm⁻³±50%, R_e(G)=0·65±0·10, R_e(C)=0·22±0·10, γ_e(G)=0·935±0·010, τ_e(G)=0·830±0·002, and τ_m(G)=0·850±0·002. The transparencies τ_e(G) and τ_m(G) are within 4% of the geometrical transparency τ(G)=0·860. Approximately equal numbers of atoms (1 in 2×10⁵) are in metastable and ionized states.

Measurements were carried out on a slow linear pinch in argon using rates of current rise between 10⁸ and 10¹⁰ A s⁻¹. Determination of the wall hang-up time t_w by comparison of the measured time to pinch with theoretical collapse models gave values that strongly disagreed with estimates obtained from image converter observation. However, the duration of the initial plateau in the tube voltage waveform yielded values of t_w that were in excellent agreement with values obtained from magnetic probe data. These measurements gave the dependence , which was weaker than the dependences predicted by theories based on neutral depletion , pressure balance , magnetically reduced conductivity and wall evaporation . Moreover, all of these theories gave numerical values of t_w that were very different from the measured times.

A microwave radiometric technique has been used to study the positive column instability in pulsed nitrogen discharges. The technique involves monitoring the effective temperature of microwave radiation as a function of the longitudinal magnetic field. The critical magnetic field B_c for the onset of the instability is found to be dependent on both the discharge current and the duration of the excitation pulse. The experimental results are consistent with an explanation based on significant cumulative ionization.

The plasma became turbulent at progressively lower values of magnetic field above B_c as the discharge current was increased. Further increase in current led to the unstable regime beyond B_c reverting back to stability on progressively increasing the magnetic field.

The minimum value of the peak RMS electric field for the TE₁₁ mode resulting in the breakdown of pure nitric oxide has been measured in the pressure range 0·5-10 Torr. The microwave frequency was 9·361 GHz. For each pressure selected, the breakdown formation time τ was found as a function of the electric field. For all breakdown formation times, the minimum breakdown field occured at a pressure of 3-4 Torr, the pulse repetition frequency and pulse length being 100 pps and 4·7 ms respectively.

The theory predicting the limiting E/p (electric field strength/gas pressure), below which uniform-field breakdown is not possible, is extended to cover those electronegative gases where unstable negative ions are effective. The result is consistent with the experimental results of other authors in oxygen. It is shown that in general at the limiting E/p the growth of current with distance is not linear, in contrast to the case where only stable negative ions are formed.

Experiments are reported which demonstrate that the imminent electrical breakdown of a long, point-plane gap can be predicted at a sufficiently early point in time for the surge to be diverted through a bypass sphere gap. With a positive voltage surge of risetime 150 μs, imminent breakdown can be detected some 7 μs before it actually occurs, by measuring the quantity of charge injected into the gap during the breakdown corona. As a result it is possible to arrest the developing spark by triggering a bypass gap only 3 μs before breakdown would normally occur.

The experiments show that the critical charge criterion is a very reliable indicator of the impending breakdown of a point-plane gap. It is possible in a series of identical surges to switch out only those which would cause breakdown of the gap if preventive action were not taken.

Measurements of Brillouin scattering in ethyl ether and ethyl alcohol were made for scattering angles of 42-150°. The spectra were excited by 4416 Å radiation from an He-Cd laser and analysed with a pressure-scanned Fabry-Perot spectrometer. The measured frequency shifts and linewidths of the Brillouin components were used to determine the velocities and the lifetimes of thermal waves. The frequency range of the hypersonic waves was 2·6-5·9 GHz for ethyl ether and 2·6-6·8 GHz for ethyl alcohol. The measurements do not indicate any dispersion of the sonic velocity within the investigated frequency range and good agreement is obtained with earlier ultrasonic measurements.

The theory given by Gavis and Koszman for the electrification of hydrocarbon liquids during pipeline flow is examined. It is shown experimentally that a process of charge relaxation can occur at the pipe outlet. This process markedly reduces the streaming current predicted by the Gavis and Koszman theory when Vτ, the product of flow velocity and dielectric relaxation time of the liquid, is comparable to or less than the distance from the pipe outlet to the collecting vessel. To account for this process a theory is developed which can be used to extend the applicability of the Gavis and Koszman theory to higher conductivities and lower velocities.