Selected Publications of Kieran Larkin

Alliteration and latterday literary lunacy ?
"Only the anacrusis, the main event remains..."

Year
Demonemonic
Title and links
Descriptors

2001
Logarithmic Radial Harmonic Function
              with 7th order spiral 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
Logarithmic Radial Harmonic Function
              with 7th order spiral A Triplet inspired by Spiral Phase
Optics Express freely available text



Chronological and illogical
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
phase correlation plot

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
PSA flowchart
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
matched Fourier gradient
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
3 demodulation alorithms:one so much
              smoother
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
Hilbert symmetrizes DIC image
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
Quantization Errors
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
...a
                vortex of dazzling thought?
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
temporary image 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
Coordinate mapping for phase space
              representation
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
temporary image 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
Logarithmic Radial Harmonic Function with 7th order
              spiral
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
temporary image 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
Different tiling of the Wigner space
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
temporary image Information capacity and resolution in three-dimensional imaging
PDF
C. J. R. Sheppard, and K. G. Larkin
Optik  113, (12), 548-550, (2003)

2004
Logarithmic Radial Harmonic Function with 7th order
              spiral 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
temporary image Uniform estimation of orientation using local and nonlocal 2-D energy operators
PDF
K. G. Larkin
Optics Express  13, (20), 8097 - 8121, (2005)

2006
Fingerprint compressed by 240 times
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
temporary image 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
temporary image 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
Multiplicate decomposition is
              the trick
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
quasipolarFourier transform of hyperbolic chirps
              array
Affine-invariant image watermarking using the hyperbolic chirp
PDF
P. A. Fletcher, K. G. Larkin, and S. Hardy,
DICTA 2009, (Melbourne: 2009)


2010

Demodulate before locating zeros

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 MTF anywhere
                in image (space variant PSFs)


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

Tartan test
              pattern with selected Fourier components
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 real part of high
              order Riesz kernels
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
one
                frame of animation sequence
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
Riesz phase versus quantitative phase
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
Isn't
                the inverse Riesz just a Riesz transform?

Image visualisation using Riesz transforms

Slides (2.7MB PDF)
Australian Mathematical Sciences Institute  Workshop in Harmonic Analysis and its Applications, 2014

October
2014
dainty projection
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
region of positivity

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
demodulation spectra
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
Mouse x-rays

Phase contrast image guidance for synchrotron microbeam radiotherapy

2016 Institute of Physics and Engineering in Medicine


, and    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

Delentropy, enter stage left

Backwards in coming forward

Reflections on Shannon
Information:


the search for a natural two-dimensional information-entropy



arXiv
6 Sept 2016

Symmetry
Simplicity
Parsimony
...Propinquity...

Published January 2017
Inverse Riesz image of surf clam Spisula solidissima oocyte

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

Scheduled 2017
Where black is the color, and none is the number...


On the Dainty Conjecture:
Nature's forbidden zeros




...where black is the
color and none is the number...


Later in 2017

Perfection mediated through the  Fourier transform


Warping of Bandlimited Images:
The Search for Perfection

[ = lossless + reversible]


Kieran G. Larkin

This page is in a state of flux...and
still needs more work


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