Comparison of simulated quenching algorithms for design of diffractive optical elements

J. S. Liu, A. J. Caley, A. J. Waddie, M. R. Taghizadeh

Research output: Contribution to journalArticle

Abstract

We compare the performance of very fast simulated quenching; generalized simulated quenching, which unifies classical Boltzmann simulated quenching and Cauchy fast simulated quenching; and variable step size simulated quenching. The comparison is carried out by applying these algorithms to the design of diffractive optical elements for beam shaping of monochromatic, spatially incoherent light to a tightly focused image spot, whose central lobe should be smaller than the geometrical-optics limit. For generalized simulated quenching we choose values of visiting and acceptance shape parameters recommended by other investigators and use both a one-dimensional and a multidimensional Tsallis random number generator. We find that, under our test conditions, variable step size simulated quenching, which generates each parameter's new states based on the acceptance ratio instead of a certain theoretical probability distribution, produces the best results. Finally, we demonstrate experimentally a tightly focused image spot, with a central lobe 0.22-0.68 times the geometrical-optics limit and a relative sidelobe intensity 55%-60% that of the central maximum intensity. © 2008 Optical Society of America.

Original languageEnglish
Pages (from-to)807-816
Number of pages10
JournalApplied Optics
Volume47
Issue number6
DOIs
Publication statusPublished - 20 Feb 2008

Fingerprint

quenching
geometrical optics
acceptability
lobes
random numbers
sidelobes
generators

Cite this

Liu, J. S. ; Caley, A. J. ; Waddie, A. J. ; Taghizadeh, M. R. / Comparison of simulated quenching algorithms for design of diffractive optical elements. In: Applied Optics. 2008 ; Vol. 47, No. 6. pp. 807-816.
@article{3c7fe88d0b2b455ca6a9a5c7128f2655,
title = "Comparison of simulated quenching algorithms for design of diffractive optical elements",
abstract = "We compare the performance of very fast simulated quenching; generalized simulated quenching, which unifies classical Boltzmann simulated quenching and Cauchy fast simulated quenching; and variable step size simulated quenching. The comparison is carried out by applying these algorithms to the design of diffractive optical elements for beam shaping of monochromatic, spatially incoherent light to a tightly focused image spot, whose central lobe should be smaller than the geometrical-optics limit. For generalized simulated quenching we choose values of visiting and acceptance shape parameters recommended by other investigators and use both a one-dimensional and a multidimensional Tsallis random number generator. We find that, under our test conditions, variable step size simulated quenching, which generates each parameter's new states based on the acceptance ratio instead of a certain theoretical probability distribution, produces the best results. Finally, we demonstrate experimentally a tightly focused image spot, with a central lobe 0.22-0.68 times the geometrical-optics limit and a relative sidelobe intensity 55{\%}-60{\%} that of the central maximum intensity. {\circledC} 2008 Optical Society of America.",
author = "Liu, {J. S.} and Caley, {A. J.} and Waddie, {A. J.} and Taghizadeh, {M. R.}",
year = "2008",
month = "2",
day = "20",
doi = "10.1364/AO.47.000807",
language = "English",
volume = "47",
pages = "807--816",
journal = "Applied Optics",
issn = "0003-6935",
number = "6",

}

Comparison of simulated quenching algorithms for design of diffractive optical elements. / Liu, J. S.; Caley, A. J.; Waddie, A. J.; Taghizadeh, M. R.

In: Applied Optics, Vol. 47, No. 6, 20.02.2008, p. 807-816.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Comparison of simulated quenching algorithms for design of diffractive optical elements

AU - Liu, J. S.

AU - Caley, A. J.

AU - Waddie, A. J.

AU - Taghizadeh, M. R.

PY - 2008/2/20

Y1 - 2008/2/20

N2 - We compare the performance of very fast simulated quenching; generalized simulated quenching, which unifies classical Boltzmann simulated quenching and Cauchy fast simulated quenching; and variable step size simulated quenching. The comparison is carried out by applying these algorithms to the design of diffractive optical elements for beam shaping of monochromatic, spatially incoherent light to a tightly focused image spot, whose central lobe should be smaller than the geometrical-optics limit. For generalized simulated quenching we choose values of visiting and acceptance shape parameters recommended by other investigators and use both a one-dimensional and a multidimensional Tsallis random number generator. We find that, under our test conditions, variable step size simulated quenching, which generates each parameter's new states based on the acceptance ratio instead of a certain theoretical probability distribution, produces the best results. Finally, we demonstrate experimentally a tightly focused image spot, with a central lobe 0.22-0.68 times the geometrical-optics limit and a relative sidelobe intensity 55%-60% that of the central maximum intensity. © 2008 Optical Society of America.

AB - We compare the performance of very fast simulated quenching; generalized simulated quenching, which unifies classical Boltzmann simulated quenching and Cauchy fast simulated quenching; and variable step size simulated quenching. The comparison is carried out by applying these algorithms to the design of diffractive optical elements for beam shaping of monochromatic, spatially incoherent light to a tightly focused image spot, whose central lobe should be smaller than the geometrical-optics limit. For generalized simulated quenching we choose values of visiting and acceptance shape parameters recommended by other investigators and use both a one-dimensional and a multidimensional Tsallis random number generator. We find that, under our test conditions, variable step size simulated quenching, which generates each parameter's new states based on the acceptance ratio instead of a certain theoretical probability distribution, produces the best results. Finally, we demonstrate experimentally a tightly focused image spot, with a central lobe 0.22-0.68 times the geometrical-optics limit and a relative sidelobe intensity 55%-60% that of the central maximum intensity. © 2008 Optical Society of America.

UR - http://www.scopus.com/inward/record.url?scp=42549129688&partnerID=8YFLogxK

U2 - 10.1364/AO.47.000807

DO - 10.1364/AO.47.000807

M3 - Article

VL - 47

SP - 807

EP - 816

JO - Applied Optics

JF - Applied Optics

SN - 0003-6935

IS - 6

ER -