Alan H. Greenaway

The Phase Problem

The paper discusses the use of the theory of entire functions for solving the phase problem. In all practical cases only three forms of logarithmic Hilbert transform could possibly be required. The paper defines them and analyses their applicability. A generating form is also put forward for cases of possible theoretical interest. The uniqueness of the phase obtained from a logarithmic Hilbert transform is investigated and the difficulties due to the presence of zeros in the complex plane are discussed. Methods are put forward for both the removal of the zeros and, when this is not possible, for locating them in order to include their effect. The paper analyses known experimental methods for phase determination from the point of view of the theory presented and highlights their unique character.

Simultaneous multiplane imaging with a distorted diffraction grating

We describe a simple technique for simultaneously imaging multiple layers within an object field onto a single camera. The approach uses a binary diffraction grating in which the lines are distorted such that a different level of defocus is associated with each diffraction order. The design of the gratings is discussed, and their ability to image multiple object planes is validated experimentally. Extension of the technique for spherical-aberration correction is described, and it is shown how the gratings can be used as part of a wave-front-sensing system.

Remotely addressed optical fibre curvature sensor using multicore photonic crystal fibre

We demonstrate an all-fibre curvature sensor that uses two-core photonic crystal fibre (PCF) as the sensing element. The PCF acts as a two-beam interferometer in which phase difference is a function of curvature in the plane containing the cores. A broadband source illuminates both cores, and the spectrum at a single point in the far-field interferogram is recorded. Applying a three-wavelength phase recovery algorithm to the data provides an unambiguous measurement of the interferometer phase, and hence curvature.

Estimation of spatial power spectra in speckle interferometry

Calculations of the signal-to-noise ratio (SNR) of estimates of the power spectra of spatially varying random processes, such as stellar speckle patterns, usually include realizations that contain less than two detected photons. It is shown in this paper that if these cases are excluded from the analysis procedure either implicitly or explicitly, then under the usual definition of SNR, the overall SNR of an estimate can increase by up to a factor of N¯−1/2, where N¯≪1 is the average number of detected photons per realization.

Two-dimensional bend sensing with a single, multi-core optical fibre

Measurement of two-dimensional bending in a structural element using intrinsic optical fibre strain gauges would normally require three sensors to be attached to, or embedded within, the structure. The same measurement can now be made using a single multi-core optical fibre, reducing deployment cost and increasing practicality. Fabrication of a novel three-core photonic crystal fibre is described. The ability of the fibre sensor to measure bend in two dimensions is demonstrated in the laboratory using interferometric interrogation at a single wavelength. Deployment of the sensor to measure the deformation of a bridge undergoing loading trials is described.

Multiplane imaging and three dimensional nanoscale particle tracking in biological microscopy

A conventional microscope produces a sharp image from just a single object-plane. This is often a limitation, notably in cell biology. We present a microscope attachment which records sharp images from several object-planes simultaneously. The key concept is to introduce a distorted diffraction grating into the optical system, establishing an order-dependent focussing power in order to generate several images, each arising from a different object-plane. We exploit this multiplane imaging not just for bio-imaging but also for nano-particle tracking, achieving approximately 10 nm z position resolution by parameterising the images with an image sharpness metric.

Adaptive beam profile control using a simulated annealing algorithm

We present a programmable beam-shaping method based on the combination of a deformable mirror membrane mirror and a simulated annealing algorithm. The algorithm iteratively adjusts the control voltages of 37 independent electrodes to reduce the variance between the chosen shape and the actual beam shape. The experimental results show that the system is capable of adaptively creating, on demand, Gaussian and super-Gaussian beam profiles that closely match the desired target parameters.

Phase-diversity wave-front sensing with a distorted diffraction grating

We describe a novel wave-front sensor comprising a distorted diffraction grating, simple optics, and a single camera. A noniterative phase-diversity algorithm is used for wave-front reconstruction. The sensor concept and practical implementation are described in detail, and performance is validated against different Zernike modes and a representative atmospheric phase map.

The Doppler Imaging System: Initial observations of the auroral thermosphere

Abstract During December 1982, a novel Fabry-Perot interferometer—a Doppler Imaging System (DIS)— was used at Kiruna Geophysical Institute (KGI), Sweden (67.8°N, 21.2°E) to complement a series of coordinated observations of global thermospheric dynamics utilizing a number of conventional ground-based Fabry-Perot interferometers and the NASA Dynamics Explorer satellite. The DIS is an interferometer with two unique attributes : it has a luminosity or etendue more than one hundred times that of the conventional Fabry-Perot interferometer, and it is also capable of deducing a two-dimensional velocity field of a suitable line-emitting areal source by independently measuring the Doppler shift at a large number of points within the field of view. On 17 December 1982, a very large geomagnetic Storm Sudden Commencement (08.05 U.T.) preceded a major geomagnetic disturbance. During this disturbance, Northern Scandinavia was influenced by a strong eastward auroral electrojet for an extended period (10–19 U.T.). The DIS was able to observe the dynamical response of the upper thermosphere to this event in conjunction with a second Fabry-Perot interferometer (FPI) at KGI. Westward thermospheric winds of about 900 m s −1 occurred during the disturbance and, at the peak of the disturbance, the combined DIS and FPI observations indicate that the thermospheric flow was quite chaotic. Fluctuations of the order of ± 150 m s −1 , associated with spatial scales of the order of 100 or 200 km occurred within the mean westward flow inside the 800 km diameter region observed from Kiruna.

OPTICAL APERTURE SYNTHESIS

The principles of aperture synthesis are outlined and the implementation of these principles in some algorithms is examined with reference to radio astronomy. Progress made in applying these techniques at optical frequencies in terrestrial and spacecraft instruments is briefly reviewed.