R. P. Millane

University of Canterbury, Christchurch, Canterbury, New Zealand

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Publications (195)282.33 Total impact

  • Rick P. Millane · Romain D. Arnal
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    ABSTRACT: Uniqueness of the phase problem in macromolecular crystallography, and its relationship to the case of single particle imaging, is considered. The crystallographic problem is characterized by a constraint ratio that depends only on the size and symmetry of the molecule and the unit cell. The results are used to evaluate the effect of various real-space constraints. The case of an unknown molecular envelope is considered in detail. The results indicate the quite wide circumstances under which ab initio phasing should be possible.
    No preview · Article · Nov 2015 · Acta Crystallographica Section A: Foundations and Advances
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    Preview · Article · Aug 2015 · Acta Crystallographica Section A: Foundations and Advances
  • Rick P. Millane · Joe P. J. Chen
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    ABSTRACT: The problem of reconstructing multiple objects from the average of their diffracted intensities is investigated. Reconstruction feasibility (uniqueness) depends on the number of objects, their support shapes and dimensionality, and an appropriately calculated constraint ratio. For objects with sufficiently different supports, and a favorable constraint ratio, the reconstruction problem has a unique solution. For objects with identical supports, there can be multiple solutions, even with a favorable constraint ratio. However, positivity of the objects and noncentrosymmetry of the support reduce the number of multiple solutions, and a unique solution may exist with a favorable constraint ratio. An iterative projection based algorithm to reconstruct the individual objects is described. The efficacy of the reconstruction algorithm and the uniqueness results are demonstrated by simulation.
    No preview · Article · Jul 2015 · Journal of the Optical Society of America A
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    Rick P Millane · Joe P J Chen
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    ABSTRACT: X-ray free-electron laser diffraction patterns from protein nanocrystals provide information on the diffracted amplitudes between the Bragg reflections, offering the possibility of direct phase retrieval without the use of ancillary experimental data. Proposals for implementing direct phase retrieval are reviewed. These approaches are limited by the signal-to-noise levels in the data and the presence of different and incomplete unit cells in the nanocrystals. The effects of low signal to noise can be ameliorated by appropriate selection of the intensity data samples that are used. The effects of incomplete unit cells may be small in some cases, and a unique solution is likely if there are four or fewer molecular orientations in the unit cell.
    Preview · Article · Jul 2014 · Philosophical Transactions of The Royal Society B Biological Sciences
  • Chunhong Yoon · Rick P. Millane
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    ABSTRACT: Expressions are derived for diffraction by the triangular Ising antiferromagnet, a disordered lattice system consisting of two kinds of scatterer and exhibiting geometric frustration. Analysis of the expressions shows characteristics of the diffraction patterns, including the presence of Bragg and diffuse diffraction, superlattice reflections, and their behavior with temperature. These characteristics are illustrated by numerical simulations. The results have application to diffraction imaging of disordered systems.
    No preview · Article · Jul 2014 · Journal of the Optical Society of America A
  • Joe P J Chen · John C H Spence · Rick P Millane
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    ABSTRACT: X-ray free-electron lasers solve a number of difficulties in protein crystallography by providing intense but ultra-short pulses of X-rays, allowing collection of useful diffraction data from nanocrystals. Whereas the diffraction from large crystals corresponds only to samples of the Fourier amplitude of the molecular transform at the Bragg peaks, diffraction from very small crystals allows measurement of the diffraction amplitudes between the Bragg samples. Although highly attenuated, these additional samples offer the possibility of iterative phase retrieval without the use of ancillary experimental data [Spence et al. (2011). Opt. Express, 19, 2866-2873]. This first of a series of two papers examines in detail the characteristics of diffraction patterns from collections of nanocrystals, estimation of the molecular transform and the noise characteristics of the measurements. The second paper [Chen et al. (2014). Acta Cryst. A70, 154-161] examines iterative phase-retrieval methods for reconstructing molecular structures in the presence of the variable noise levels in such data.
    No preview · Article · Mar 2014 · Acta Crystallographica Section A: Foundations and Advances
  • Joe P J Chen · John C H Spence · Rick P Millane
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    ABSTRACT: X-ray free-electron laser diffraction patterns from protein nanocrystals provide information on the diffracted amplitudes between the Bragg reflections, offering the possibility of direct phase retrieval without the use of ancillary experimental diffraction data [Spence et al. (2011). Opt. Express, 19, 2866-2873]. The estimated continuous transform is highly noisy however [Chen et al. (2014). Acta Cryst. A70, 143-153]. This second of a series of two papers describes a data-selection strategy to ameliorate the effects of the high noise levels and the subsequent use of iterative phase-retrieval algorithms to reconstruct the electron density. Simulation results show that employing such a strategy increases the noise levels that can be tolerated.
    No preview · Article · Mar 2014 · Acta Crystallographica Section A: Foundations and Advances
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    Joe P J Chen · Rick P Millane
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    ABSTRACT: X-ray femtosecond nanocrystallography is a new, potentially powerful technique for imaging biological macromolecules that uses ensemble-averaged measurements of diffraction of x-ray free-electron laser pulses from nanocrytalline specimens. Nanocrystals have some diffraction characteristics that are distinct from those of macroscopic crystals, due to the presence of different kinds of unit cell in the crystal and of truncated unit cells on the crystal surface. Expressions are derived for diffraction by nanocrystals with variable and incomplete unit cells, averaged over a distribution of crystal sizes and shapes. The diffraction contains differently modulated Bragg components that are due to interference effects within and between the full and incomplete unit cells. Estimates are obtained for the relative magnitudes of the components. The nature of the diffraction is illustrated by two-dimensional simulations. Implications for molecular imaging are discussed.
    Preview · Article · Dec 2013 · Journal of the Optical Society of America A
  • Joe Chen · Rick Millane
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    ABSTRACT: X-ray crystallography is a method for determining three-dimensional images of materials arranged in regular arrays through the phenomenon of diffraction. These periodic arrays exist within structures of crystals and each period of this array is termed the unit cell. The recent invention of a new x-ray source offer novel ways of doing x-ray crystallography where very small crystals, only a few unit cells across, can be used. As a result of their larger surface-to-volume ratio, disorder on the surface of small crystals will have a larger impact on their diffraction than for large crystals. This edge-effect of crystals being terminated with partial segments of the whole unit cell, which we refer to as “partial unit cells,” are investigated via simulation and we propose a simple way to “grow” crystals in the computer based on a random-walk type construction. Diffraction patterns from an ensemble of crystals grown in this way with different unit cell contents and different partial unit cells on their surface is studied and the characteristics of the diffraction is discussed.
    No preview · Conference Paper · Nov 2013
  • Rick P. Millane · Victor L. Lo
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    ABSTRACT: A general class of iterative projection algorithms is described and proposed as a tool for phasing in protein crystallography in order to improve the radius of convergence over that of conventional density‐modification algorithms. Their relationship to conventional density modification is described. The common iterative projection algorithms, their convergence properties and their application to protein crystallography are described. These algorithms offer the possibility of protein structure determination starting with only information on the molecular envelope and low‐order non‐crystallographic symmetry.
    No preview · Article · Sep 2013 · Acta Crystallographica Section A Foundations of Crystallography
  • Joe P. J. Chen · John C. H. Spence · Rick P. Millane
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    ABSTRACT: Protein X-ray crystallography is a method for determining the 3-dimensional structures of large biological molecules arranged in regular arrays inside a crystal. Samples of the Fourier magnitude of the molecular charge density can be measured from the amplitudes of the scattered X-rays but the determination of the Fourier phases requires chemical modification to the sample and collection of additional data. There is thus a need for a direct digital phasing method that does not require modified specimens. The diffraction from very small crystals allows for a finer sampling of the diffraction amplitude and although highly attenuated, these additional samples offer the possibility of iterative phase retrieval without the use of ancillary experimental data. Following on from a previous study [6], we examine in detail the noise characteristics of finite crystal diffraction and propose a data selection strategy to improve 3-dimensional reconstructions of the molecular charge density using iterative phase retrieval algorithms. Simulation results verify that higher noise levels can indeed be tolerated by employing such a strategy to precondition the data.
    No preview · Conference Paper · Nov 2012
  • Ni Zhang · Rick P. Millane · Einar Enevoldson · James E. Murray
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    ABSTRACT: The problem of estimating wind velocities from limited flight data recordings is considered, with application to sailplane flights in high-altitude atmospheric mountain waves. Sailplane flight recorders routinely measure only GPS position and the problem is highly underdetermined. The nature of this problem is studied and a maximum a posteriori estimator is developed using prior information on the wind velocity and the sailplane airspeed and heading. The method is tested by simulation and by application to sailplane flight data.
    No preview · Article · Oct 2012 · Proceedings of SPIE - The International Society for Optical Engineering
  • Victor Lo · Rick P. Millane
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    ABSTRACT: A brief description of various iterative projection algorithms and the relationships between them is given, along with some possible reasons for their ability to solve non-convex problems. An empirical model of their behaviour when applied to non-convex problems is also described.
    No preview · Article · Oct 2012 · Proceedings of SPIE - The International Society for Optical Engineering
  • Joe P. J. Chen · John C. H. Spence · Rick P. Millane
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    ABSTRACT: Protein X-ray crystallography is a method for determining the three-dimensional structures of large biological molecules by analysing the amplitudes of X-rays scattered from a crystalline specimen of the molecule under study. Conventional structure determination in protein crystallography requires chemical modification to the sample and collection of additional data in order to solve the corresponding phase problem. There is an urgent need for a direct (digital) low-resolution phasing method that does not require modified specimens. Whereas diffraction from large crystals corresponds to samples (so-called Bragg samples) of the amplitude of the Fourier transform of the scattering density, the diffraction from very small crystals allows measurement of the diffraction amplitude between the Bragg samples. Although highly attenuated, these additional measurements offer the possibility of iterative phase retrieval without the use of ancillary experimental data. In this study we examine the noise characteristics of small-crystal diffraction and propose a data selection strategy to improve the quality of reconstructions using iterative phase retrieval algorithms. Simulation results verify that a higher noise level can be tolerated by using such a data selection strategy.
    No preview · Article · Oct 2012 · Proceedings of SPIE - The International Society for Optical Engineering
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    G. D. Stirling · R. P. Millane · E. Enevoldson · J. E. Murray
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    ABSTRACT: Mountainous terrain can, under certain conditions, induce stationary atmospheric waves in the lee of the mountains, with large vertical air velocities. These waves are used as a source of strong lift by sailplane pilots. Methods are developed for inverting data of airspeed and GPS-derived position taken from sailplane data logs, to obtain estimates of the airmass vertical velocity in mountain waves. The method accounts for the static and dynamic aerodynamics of the sailplane and the eects of altitude. The airmass vertical velocity estimates are combined with estimates of the horizontal wind velocity to estimate the mountain wave structure and its relationship to the upwind topography. The methods are applied to data from a Perlan Project flight in the lee waves of the Sierra Nevada Mountain range in California.
    Preview · Article · Apr 2012
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    ABSTRACT: Plasma-assisted molecular beam epitaxy was employed to create porous nanonetworks of ZnO directly on GaN epilayers without the use of catalysts or templates. Detailed analysis of scanning electron microscopy (SEM) images of both as-grown and etched samples reveals that the typical porous nanonetwork structure is multilayered, and suggests that dislocations originating at the GaN/sapphire heterointerface and/or defects characterizing an unusually rough GaN surface are responsible. The pore size distribution of the nanonetwork was measured using nuclear magnetic resonance (NMR) cryoporometry. A bimodal pore size distribution centred at 4 nm and 70 nm, respectively, was observed, consistent with the existence of small nanoscale pores in the bulk of the sample, and large open pores on the surface of the porous nanonetwork as observed by SEM.
    No preview · Article · Apr 2012 · Journal of Physics D Applied Physics
  • Ni Zhang · Rick P. Millane · Alan J. Hunter
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    ABSTRACT: The problem of estimating wind velocities from limited flight data recordings is considered, with application to sailplane flights in high-altitude mountain waves. Sailplane flight recorders routinely measure only GPS position and, infrequently, also airspeed and the problem is underdeter- mined. Maximum likelihood and maximum a posteriori estimators are developed for these kinds of data and tested by simulation and by application to sailplane flight data.
    No preview · Article · Dec 2011
  • Bing Wu · Rick P Millane · Richard Watts · Philip J Bones
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    ABSTRACT: Two improved compressed sensing (CS)-based image reconstruction methods for MRI are proposed: prior estimate-based compressed sensing (PECS) and sensitivity encoding-based compressed sensing (SENSECS). PECS allows prior knowledge of the underlying image to be intrinsically incorporated in the image recovery process, extending the use of data sorting as first proposed by Adluru and DiBella (Int J Biomed Imaging 2008: 341648). It does so by rearranging the elements in the underlying image based on the magnitude information gathered from a prior image estimate, so that the underlying image can be recovered in a new form that exhibits a higher level of sparsity. SENSECS is an application of PECS in parallel imaging. In SENSECS, image reconstruction is carried out in two stages: SENSE and PECS, with the SENSE reconstruction being used as a image prior estimate in the following PECS reconstruction. SENSECS bypasses the conflict of sampling pattern design in directly applying CS recovery in multicoil data sets and exploits the complementary characteristics of SENSE-type and CS-type reconstructions, hence achieving better image reconstructions than using SENSE or CS alone. The characteristics of PECS and SENSECS are investigated using experimental data.
    No preview · Article · Jan 2011 · Magnetic Resonance in Medicine
  • Joe Chen · Veit Elser · R. P. Millane
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    ABSTRACT: The problem of optimizing antenna locations in a radio telescope with a large number of antennas is addressed. An algorithm is developed that first optimizes the probability density function of the antenna positions and this distribution is subsequently sampled. This approach avoids the large number of variables with many antennas. The density function is optimized subject to terrain constraints and the distribution of visibility samples. The optimization is solved by mapping the problem to a phase retrieval problem which is solved using an iterative projection algorithm.
    No preview · Article · Nov 2010
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    Philip J. Bones · Michael A. Fiddy · Rick P. Millane

    Full-text · Article · Aug 2010 · Proceedings of SPIE - The International Society for Optical Engineering

Publication Stats

2k Citations
282.33 Total Impact Points

Institutions

  • 1980-2015
    • University of Canterbury
      • Department of Electrical and Computer Engineering
      Christchurch, Canterbury, New Zealand
  • 1983-2006
    • Purdue University
      • • Whistler Center for Carbohydrate Research
      • • Department of Biological Sciences
      ウェストラファイエット, Indiana, United States
  • 2005
    • Girne American University Canterbury
      Cantorbery, England, United Kingdom
    • Canterbury Christ Church University
      Cantorbery, England, United Kingdom