Publications of Kieran G. Larkin

Selected Publications of Kieran Larkin Alliteration and latterday literary lunacy ? "Only the anacrusis, the main event remains..."

Year	Demonemonic	Title and links	Descriptors
2001		My PhD thesis Topics in Multi dimensional Signal Demodulation http://hdl.handle.net/2123/367	Problems in the demodulation of one, two, and three-dimensional signals are investigated... Full PDF directly
2001- 2007		A Triplet inspired by Spiral Phase Optics Express freely available text
Chronological and illogical
1981		Computer aided design of a large field spectrograph. Fortran based design took place at night after the PDP11 had finished its other daily tasks. Brochure	Kieran G. Larkin for Applied Photophysics at the Royal Institution, Albemarle St, London
1990		Development of a prototype instrument for non-contact shape measurement of master tooling at the Royal Australian Mint PDF not available	B. F. Oreb, K. G. Larkin, P. S. Fairman, Y. Gilliand, et al., CSIRO Technical Memorandum, (DAP-C0029), (1990).
1990- 1992		Optical Surface Profiler (Precision 3-D Measurement) Brochure 1 Brochure (info sheet) 2 Brochure (specs) 3	CSIRO Division of Applied Physics in collaboration with The Royal Australian Mint
1991		Restoration of shadow details in projected fringe profilometer images PDF	K. G. Larkin, P. S. Fairman, D. I. Farrant, and B. F. Oreb, DICTA-91 Digital Image Computing: Techniques and Applications, B. M. J. A.J.Maeder, ed., Melbourne, 1991, pp. 237-243.
1992		Propagation of errors in different phase-shifting algorithms: a special property of the arctangent function PDF	K. G. Larkin, and B. F. Oreb SPIE International Symposium on Optical Applied Science and Engineering, San Diego, California, (1992), 219-227.
1992		A new seven sample phase-shifting algorithm PDF	K. G. Larkin, and B. F. Oreb, SPIE International Symposium on Optical Applied Science and Engineering, San Diego, California, 1992
1992		Design and assessment of Symmetrical Phase-Shifting Algorithms PDF	K. G. Larkin, and B. F. Oreb, Journal of the Optical Society of America, A 9, (10), 1740-1748, (1992)
1992		Moire based Optical Surface Profiler for the Minting Industry PDF	B. F. Oreb, K. G. Larkin, P. S. Fairman, and M. Ghaffari, “SPIE International Symposium on Optical Applied Science and Engineering, San Diego, California, (1992), p48-57
1994		The specimen illumination path and its effect on image quality book chapter PDF	C. J. Cogswell, and K. G. Larkin, Handbook of Biological Confocal Microscopy, ed. Pawley, J. B. Second ed. (New York: Plenum, 1994)
1994		High-resolution, multiple optical mode confocal microscope: I.System design, image acquisition an 3D visualization PDF	C. J. Cogswell, K. G. Larkin, J. W. O'Byrne, and M. R. Arnison, Three-Dimensional Microscopy:Image Acquisition and Processing, IS&T/SPIE Symposium on Electronic Imaging Science and Technology, San Jose, California, (1994)
1994		The geometric phase: interferometric observations with white light PDF	P. Hariharan, K. G. Larkin, and M. Roy, Journal of Modern Optics 41, (4), 663-667, (1994)
1994		High-resolution, multiple optical mode confocal microscope: II. Theoretical aspects of confocal transmission microscopy PDF	K. G. Larkin, C. J. Cogswell, J. W. O'Byrne, and M. R. Arnison, Three-Dimensional Microscopy:Image Acquisition and Processing, IS&T/SPIE Electronic Imaging, San Jose, California, (1994)
1994		Optimal concentration of electromagnetic radiation PDF	C. J. R. Sheppard, and K. G. Larkin Journal of Modern Optics 41, (7), 1495-1505, (1994)
1995		3D Fourier analysis methods for digital processing and 3D visualization of confocal transmission images PDF	C. J. Cogswell, K. G. Larkin, M. R. Arnison, and J. W. O'Byrne, Three-Dimensional Microscopy:Image Acquisition and Processing, IS&T/SPIE Symposium on Electronic Imaging, San Jose, California, (1995)
1995		Phase-shifting interferometry for non-sinusoidal waveforms with phase-shift errors PDF	K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin JOSA,A 12, (4), 761-768, (1995)
1995		Simple Formulae for Confocal Resolution Parameters: the Full Width Half Maximum (FWHM), the Ellipsoidal Observation Volume (OBSVOL) and the Root Mean Square Spatial Frequency (RMSF) PDF	K. G. Larkin Focus on Microscopy '95, Taipei, Taiwan. Published in Zoological Studies 34, (Supplement 1), 81-83, (1995)
1995		The Beginner's Guide to the Fractional Fourier Transform, Part 1 PDF	K. G. Larkin, The Australian Optical Society News, June 1995
1995		The Beginner's Guide to the Fractional Fourier Transform, Part 2 PDF	K. G. Larkin, The Australian Optical Society News, December 1995
1995		Effect of numerical aperture on interference fringe spacing PDF	C. J. R. Sheppard, and K. G. Larkin, Applied Optics 34, (22), 4731-4734, (1995)
1996		Fluorescence microtomography: multi-angle image acquisition and 3D digital reconstruction PDF	C. J. Cogswell, K. G. Larkin, and H. U. Klemm, Three-Dimensional Microscopy:Image Acquisition and Processing III, IS&T/SPIE Symposium on Electronic Imaging San Jose, California, (1996), 109-115
1996		Efficient nonlinear algorithm for envelope detection in white light interferometry PDF	K. G. Larkin Journal of the Optical Society of America, A 13, (4), 832-843, (1996)
1996		Efficient Demodulator for Bandpass Sampled AM Signals PDF	K. G. Larkin, Electronics Letters 32, (2), 101-102, (1996)
1997		Quantitative DIC Microscopy Using a Geometric Phase Shifter PDF	C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, Three-Dimensional Microscopy: Image Acquisition and Processing IV, IST/SPIE Electronic Imaging, San Jose, California, (1997), 7281-
1997		Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts PDF	K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, Journal of the Optical Society of America, A 14, (4), 918-930, (1997)
1997		Fast Fourier method for the accurate rotation of sampled images PDF	K. G. Larkin, M. A. Oldfield, and H. U. Klemm, Optics Communications 139, 99-106, (1997)
1997		Vectorial pupil functions and vectorial transfer functions PDF	C. J. R. Sheppard, and K. G. Larkin, Optik 107, (2), 79-87, (1997)
1998		Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts: reply to comment PDF	K. Hibino, K. G. Larkin, B. F. Oreb, and D. I. Farrant, Journal of the Optical Society of America, A 15, 1234-1235, (1998)
1998		Similarity theorems for fractional Fourier transforms and fractional Hankel transforms PDF	C. J. R. Sheppard, and K. G. Larkin, Optics Communications 154, 173-178, (1998)
1999		Direct method for the phase retrieval from the intensity of cylindrical wavefronts PDF	K. G. Larkin, and C. J. R. Sheppard, Journal of the Optical Society of America, A 16, (7), 1838-1844, (1999)
1999		Invariant Large Scale Structure of Axial Diffraction Patterns PDF	K. G. Larkin, and C. Sheppard, Australian Optical SocietyConference, The University of Sydney, 1999. Poster
2000		Using the Hilbert transform for 3D visualization of differential interference contrast microscope images PDF on Maffew's page Direct link to PDF	M. R. ARNISON, C. J. COGSWELL, N. I. SMITH, P. W. FEKETE & K. G. LARKIN Journal of Microscopy, Vol. 199, Pt 1, July 2000, pp. 79-84. Nice way to play with the Fourier symmetry of images and their gradients.
2000		Finite, Tractable Formulae for Correlated Quantisation Errors in Phase Measuring Interferometry PDF	K. G. Larkin, Applied Optics and Opto-electronic Conference, Loughborough, UK, (2000)
2000		Focal Shift, Optical Transfer Function, and Phase-Space Representations Citeseerx PDF Direct	Colin J. R. Sheppard , Kieran G. Larkin Journal of the Optical Society of America, A 17, (4), 772-779, (2000) Lots of interconnections investigated.
2001		Natural demodulation of two-dimensional fringe patterns: I. General background to the spiral phase quadrature transform PDF	K. G. Larkin, D. Bone, and M. A. Oldfield, Journal of the Optical Society of America, A 18, (8), 1862-1870, (2001).
2001		Natural demodulation of two-dimensional fringe patterns: II. Stationary phase analysis of the spiral phase quadrature transform PDF	K. G. Larkin, Journal of the Optical Society of America, A 18, (8), 1871-1881, (2001).
2001		Topics in Multi-dimensional Signal Demodulation PDF	K. G. Larkin, PhD. University of Sydney, 2001 http://hdl.handle.net/2123/367
2001		Natural demodulation of 2D fringe patterns PDF Nice example of unravelling overalapping Fourier lobes via spatial domain orientation unwrapping (to direction)	K. G. Larkin, Fringe'01 - The Fourth International Workshop on Automatic Processing of Fringe Patterns, Bremen, Germany, (2001)
2001		A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns PDF	K. G. Larkin, Optics Express 9, (5), 236-253, (2001) First example of an algorithm that works with arbitrary phase steps and less than 5 frames
2001		An isotropic Hilbert transform in two dimensions: fearful symmetry? PDF	K. G. Larkin, and M. A. Oldfield, Optics and Photonics News 12, (12), 20, (2001)
2001		Wigner function for non-paraxial wavefields PDF	C. J. R. Sheppard, and K. G. Larkin, Journal of the Optical Society of America, A 18, (10), 2486-2490, (2001).
2001		The three-dimensional transfer function and phase space mappings PDF	C. J. R. Sheppard, and K. G. Larkin, Optik 112, (5), 189-192, (2001)
2001		Wigner function for highly convergent three-dimensional wave fields PDF	C. J. R. Sheppard, and K. G. Larkin, Optics Letters 26, (13), 968-970, (2001)
2002		Direct embedding and detection of RST invariant Watermarks PDF	P. A. Fletcher, and K. G. Larkin IH2002, Fifth International Workshop on Information Hiding, F. A. P. Petitcolas, ed. (Springer Verlag, Noordwijkerhout, The Netherlands, 2002), pp. 129-144. Google books has most of it
2001		Wigner Function and Ambiguity Function for Nonparaxial Wavefields PDF	C.J.R. Sheppard, and K. G.Larkin, Optical Processing and Computing: A Tribute to Adolf Lohmann, H. J. C. David P. Casasent, ed. (SPIE Vol, 2001), pp. 99-103.
2002		Wigner Function and Ambiguity Function for Nonparaxial Wavefields PDF	C. J. R. Sheppard, and K. G. Larkin, Chapter 3,Optical Information Processing: A Tribute to Adolf Lohmann, ed. Caulfield, H. J. (Bellingham: SPIE, 2002) PM117: 37-55
2003		Information capacity and resolution in three-dimensional imaging PDF	C. J. R. Sheppard, and K. G. Larkin Optik 113, (12), 548-550, (2003)
2004		Linear phase imaging using differential interference contrast microscopy PDF	M. R. ARNISON, K. G. LARKIN†, C . J. R. SHEPPARD,N. I. SMITH‡ & C . J. COGSWELL Journal of Microscopy, Vol. 214, Pt 1 April 2004, pp. 7–12 The inverse of a gradient can be seen as a Fourier spiral operator.
2005		Uniform estimation of orientation using local and nonlocal 2-D energy operators PDF	K. G. Larkin Optics Express 13, (20), 8097 - 8121, (2005)
2006		Extreme compression of fingerprint images: squeezing patterns until the spirals pop out PDF	K. G. Larkin, and P. A. Fletcher Fifth International Workshop on Information Optics, Toledo, Spain, (2006)
2006		Joint Distribution Functions and the Generalized Optical transfer Function PDF	C. J. R. Sheppard, and K. G. Larkin, Fifth International Workshop on Information Optics, Toledo, Spain, (2006)
2007		A coherent framework for fingerprint analysis: are fingerprints Holograms? PDF	K. G. Larkin, and P. A. Fletcher Optics Express 15, (14), 8667-8677, (2007)
2008		Invited talk Which function spaces do fingerprints inhabit? And why should we care? PDF	K. G. Larkin Function Spaces and Applications, UNSW Research Workshop, (University of NSW: 2008) Abstracts Organisation
2009		Affine-invariant image watermarking using the hyperbolic chirp PDF	P. A. Fletcher, K. G. Larkin, and S. Hardy, DICTA 2009, (Melbourne: 2009)
2010		Invited talk Multiplicative Decomposition in 2-D as a Prototype for Irregular Sampling: Application to the Extreme Compression of Fingerprints PDF	K. G. Larkin in Sampling and Reconstruction: Applications and Advances Banff International Research Station (BIRS) for Mathematical Innovation and Discovery, Banff, Alberta, Canada, 2010
2011		Two-dimensional measurement of the lens optical transfer function from a digital image. Link to SPIE	David P. Morgan-Mar ; Matthew R. Arnison ; Chris A. Deller ; Peter A. Fletcher ; Kieran G. Larkin; Proc. SPIE 7876, Digital Photography VII (January 24, 2011)
2011		Measurement of the lens optical transfer function using a tartan pattern Free PDF available from: http://www.opticsinfobase.org/abstract.cfm?URI=ao-50-15-2158	Matthew R. Arnison, David P. Morgan-Mar, Chris A. Deller, Peter A. Fletcher, and Kieran G. Larkin, "Measurement of the lens optical transfer function using a tartan pattern," Appl. Opt. 50, 2158-2169 (2011)
2011		Invited talk Applications and Extensions of the Riesz transform in image processing PDF	AMSI International Conference on Harmonic Analysis and Applications, Macquarie University, Sydney, 7 – 11 February 2011
2001- - 2014 RIP	27 MB animation	Tenacious tagging of images via Mellin monomials Five Arxiv versions to choose from, but the last is definitive. Which is it: image processing, optics, or information security?	K. G. Larkin, P. A. Fletcher, and S.J. Hardy
March 2014		Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform Free PDF available from OSA	K. G. Larkin and P. A. Fletcher Biomedical Optics Express How to do it yourself (inverse Riesz visualization)
July 2014		Image visualisation using Riesz transforms Slides (2.7MB PDF)	Australian Mathematical Sciences Institute Workshop in Harmonic Analysis and its Applications, 2014
October 2014		On the Dainty Conjecture: Nature's forbidden zeros Abstract: In a 1969 paper Christopher Dainty conjectured that the three dimensional diffraction pattern from a perfect lens with circular aperture has no zeros, except the trivial point zeros on axis and the Airy disk null rings in the image plane. Using Radon projection methods we show that the conjecture can be framed as a continuous sequence of one dimensional problems. The Helmholtz wave equation for such scalar fields has a 3-D Fourier transform that exists only on the cap of an sphere. The projection slice theorem then implies a simple 1-D Fourier relation. We show that within the geometric light cone any zeros are forbidden by a strong symmetry inequality. Outside the light cone – that is to say in the shadow region– the conjecture remains unresolved.	Seminar at Macquarie University, (Rigorous proof finalised. MS still in preparation...)
October 2014		On the positivity of an energy operator and the interplay of amplitude and phase modulation.	Seminar at Mathematical Sciences Institute, ANU, Canberra. Here it is, the PDF
November 2014		Book Chapter The Spiral Phase Transform Phase Estimation in Optical Interferometry	Google books already has it...
January 2015	Unorthodox Contentious Fervent Unfashionable Presumptuous	Structural Similarity Index SSIMplified: Is there really a simpler concept at the heart of image quality measurement?	Arxived, Moderated, Tolerated
Published on 20 July 2016		Phase contrast image guidance for synchrotron microbeam radiotherapy 2016 Institute of Physics and Engineering in Medicine	Daniele Pelliccia, Jeffrey C Crosbie and Kieran G Larkin, Physics in Medicine and Biology, Volume 61, Number 16
Accepted CVEE, August 2016	...In particular, we describe the relationship between the growth conditions of monogenic extensions of square-integrable function f in terms of pointwise bounds or bounds on integral averages on the one hand, and the support of the Fourier transform ^ f or its annihilation by certain higher-dimensional analogues of the signum function on the other.	Hardy, Paley-Wiener and Bernstein Spaces in Clifford Analysis Paley-Wiener underpins phase-retrieval in 1D. In higher dimensions P-W can be defined to have various symmetries...	D.J. Franklin, J.A. Hogan, and K.G. Larkin Complex Variables and Elliptic Equations
First Draft completed August 2016. Preprint Sept 2016		Reflections on Shannon Information: the search for a natural two-dimensional information-entropy	arXiv 6 Sept 2016 Symmetry Simplicity Parsimony ...Propinquity...
Published January 2017		Mapping optical path length and image enhancement using quantitative orientation-independent differential interference contrast microscopy	Michael Shribak, Kieran G. Larkin, David Biggs Journal of Biomedical Optics
Work in progress... generalising conjecture		On the Dainty Conjecture: Nature's forbidden zeros Breaking news December 2017: The conjecture is true in the shadow zone & hence all space...but the proof must be split into 3 zones...	...where black is the color and none is the number...
Sometime...		Pre-history of the Chirp-Z Transform All that stuff you thought you knew, but were afraid to ask... ...pulse compression in 1940s...	Kieran G. Larkin
June 2018		The TOLIMAN space telescope SPIE Conference on Optical and Infrared Interferometry and Imaging VI	Peter Tuthill, Eduardo Bendek, Olivier Guyon, Anthony Horton, Bryn Jeffries, Nemanja Jovanovic, Pete Klupar, Kieran Larkin, Barnaby Norris, Benjamin Pope, Michael Shao.
2018		Precision astrometry mission for exoplanet detection around binary stars SPIE, Space Telescopes and Instrumentation 2018 A neat Fourier trick with negated phase grating regions and pi phase steps allows blurred zero order and focused first orders...	E Bendek, P Tuthill, O Guyon, G Vasisht, R Belikov, K Larkin, C Beichman, ...
2022		On the positivity of Teager-Kaiser’s energy operator Signal Processing 201, 108702 2022 Link	Y Préaux, AO Boudraa, KG Larkin
2024		Getting to know the neighbours: Earth analogues in Alpha Centauri with the TOLIMAN space telescope SPIE, Space Telescopes and Instrumentation 2024…	P Tuthill, C Betters, M Charles, F Crous, C Deagan, L Desdoigts, K Larkin....
April 2026		Warping of Bandlimited Images: The Search for Perfection* [ * lossless + reversible] Bracewell @70 Meeting, 8-9 April 2026 Macquarie University, Sydney, Australia Prelim Presentation	Kieran G. Larkin
March 2026		The TOLIMAN mission: A low-cost space telescope for high precision narrow-angle astrometry JATIS, Journal of Astronomical Telescopes, Instruments, and Systems arXiv preprint arXiv:2603.14683	P Tuthill, C Betters, M Charles, F Crous, DG Dansereau, C Deagan, K Larkin...
Sometime, somewhere in 2026		Everything you always wanted to know about Cardinal B-Splines but were too afraid to ask... Surprising proof : All cardinal B-splines h_n ARE windowed sincs, via Aldroubi's Fourier formula H_n. New function arises sinch(x)=n.sin(x)/sinh(n.x)	Kieran G. Larkin
Sometime Somewhere in Summertime...		Extended Duchon Lanczos windowed sincs: More perfect bandlimited interpolations	Kieran G. Larkin

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