Heather I. Campbell

Generalized phase diversity for wave-front sensing.

Phase diversity is a phase-retrieval algorithm that uses a pair of intensity images taken symmetrically about the wave front to be determined. If these images are taken about the system input pupil this is equivalent to a curvature-sensing algorithm. Traditionally a defocus aberration kernel is used to produce the phase-diverse data. We present a generalization of this method to allow the use of other functions as the diversity kernel. We discuss the necessary and sufficient conditions that such a function must satisfy for use in a null wave-front sensor. Computer simulations were used to validate these results.

Three-dimensional particle imaging by wavefront sensing

We present two methods for three-dimensional particle metrology from a single two-dimensional view. The techniques are based on wavefront sensing where the three-dimensional location of a particle is encoded into a single image plane. The first technique is based on multiplanar imaging, and the second produces three-dimensional location information via anamorphic distortion of the recorded images. Preliminary results show that an uncertainty of 8 microm in depth can be obtained for low-particle density over a thin plane, and an uncertainty of 30 microm for higher particle density over a 10 mm deep volume.

High-speed, 3-dimensional, telecentric imaging

The design, testing and operation of a system for telecentric 3-dimensional imaging of dynamic objects is presented. The simple system is capable of rapid electronic scanning of a single focal plane within a specimen or of simultaneous focusing on multiple planes whose depth and relative spacing within the specimen can be changed electronically. Application to studies of dynamic processes in microscopy is considered.

Small angle expansion: a solution to the phase-retrieval problem using generalized phase diversity in pupil space

Phase diversity is a phase-retrieval algorithm that uses a pair of defocused intensity images taken symmetrically about the wavefront to be determined. Generalised phase diversity is a phase-retrieval algorithm that uses diversity functions other than defocus. The approach adopted assumes that unknown phase changes satisfy the small-angle approximation over spatial regions that can be selected by choice of the diversity function. For smooth functions, and for discontinuous functions with only small discontinuities, this leads to a very simple analytic solution. Computer simulations were used to validate this method for the retrieved phase.

Extended wavefront sensing with novel diversity functions

Generalized Phase Diversity (GPD) is a phase retrieval algorithm which requires a pair of intensity images. These are created by applying equal and opposite diversity phase to the input wavefront. Unlike traditional phase diversity methods GPD is not limited to the use of defocus as the applied diversity phase. The conditions that a suitable diversity function must satisfy for use in a null sensor were presented at the 4th IWAOIM. Following our recent development of a small angle solution to the inverse problem, in this paper the GPD method will be extended to use as a full wavefront sensor. This method has a wide range of applications, including laser beam shaping, analysis of segmented optics, and metrology. Results will be presented to show the versatility and accuracy of this novel wavefront sensing method.

Wavefront sensing for 3D particle metrology and velocimetry

We present the application of wavefront sensing to 3-dimensional particle metrology for measuring the 3-component velocity vector field in a fluid flow across a volume. The technique is based upon measuring the wavefront scattered by a tracer particle from which the 3-dimensional tracer location can be calculated. Using a temporally resolved sequence of 3-dimensional particle locations the velocity vector field is obtained. In this paper we focus on an anamophic technique to capture the data required to measure the wavefront. Data is presented from a reconstruction of the phase of the wavefront as well as from a more pragmatic approach that examines only the defocus of that wavefront. The methods are optically efficient and robust and can be applied to both coherent and incoherent light in contrast to classical interferometric methods. A focus of this paper has been the filtering techniques in order to reliably extract the particle images from the overall image field. The resolution and repeatability of the depth (or range) measurements have been quantified experimentally using a single mode fiber source representing a tracer particle. A first proof of principle experiment using this technique for 3-dimensional PIV on a sparsely seeded gas phase flow is also presented.

Anisoplanatic atmospheric measurements for terrestrial imaging

Applications of adaptive optics to terrestrial imaging involve anisoplanatic imaging conditions in which the turbulence-distorted wavefront may be highly scintillated and have present phase discontinuities. We will describe experiments designed to assess these properties of the wavefront, and discuss the observational strategy for measurement of atmospheric properties under a range of atmospheric conditions and propagation distances. By reconstructing the wavefront and comparing the calculated and measured images we will also aim to investigate the effect of strong scintillation on phase diversity wavefront reconstruction techniques. Laboratory tests of the equipment and preliminary measurements will be described, as well as some theory and modeling.

Generalised Phase Diversity: Initial Tests

Some early results demonstrating the performance of the Generalised Phase Diversity Wavefront Sensor were presented. In these computer simulations we would seek to validate the theoretical analysis that we have previously published and to explore the optimisation of the sensor for various forms of wavefront error. Consideration would be given to the extent to which optimisation that exploits a priori information about the wavefront decreases the chance to detect other wavefront characteristics.

Generalised Phase Diversity Wavefront Sensor

Phase-Diversity is an algorithm for reconstruction of wavefront phase from data corresponding to images of the input wavefront intensity on two planes normal to the direction of propagation and located at different positions along the axis of propagation. These planes are generally described as symmetrically placed about the image plane, but can equally well be symmetrically placed about the system input pupil. In this case the phase diversity algorithm becomes essentially the same as the wavefront curvature algorithm. For reconstruction of the wavefront phase the inverse problem is presented in terms of the di.erential Intensity Transport Equation and solved either iteratively or through use of Green’s functions. Here we will explore what other aberrations, other than defocus, can be used in a generalised phase diversity wavefront reconstruction. The possible advantages of this approach will be considered.

Compact adaptive optics

In this presentation we will explore the generalisation of the phase diversity approach, and show what properties the aberration function used should have in order to provide a null sensor. We will show that this general approach offers scope for the implementation of adaptive optics systems that can be remarkably compact and in which the corrected image can be stored simultaneously with an estimate of residual wavefront errors averaged over the exposure time. We will consider the issues of data reduction using this generalised approach to reconstruct the input wavefront shape.