Reduced-complexity representation of the coherent point-spread function in the presence of aberrations and arbitrarily large defocus

Saeed Bagheri, Daniela Pucci de Farias, George Barbastathis, Mark A Neifeld

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We introduce a method to analyze the diffraction integral for evaluating the point-spread function. Our method is based on the use of higher-order Airy functions along with Zernike and Taylor expansions. Our approach is applicable when we are considering a finite, arbitrary number of aberrations and arbitrarily large defocus simultaneously. We present an upper bound for the complexity and the convergence rate of this method. We also compare the cost and accuracy of this method with those of traditional ones and show the efficiency of our method through these comparisons. In particular, we rigorously show that this method is constructed in a way that the complexity of the analysis (i.e., the number of terms needed for expressing the light disturbance) does not increase as either defocus or resolution of interest increases. This has applications in several fields such as biological microscopy, lithography, and multidomain optimization in optical systems.

Original languageEnglish (US)
Pages (from-to)2476-2493
Number of pages18
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume23
Issue number10
DOIs
StatePublished - 2006

Fingerprint

Optical transfer function
Aberrations
Optical systems
Lithography
Microscopic examination
Diffraction
Costs
Optical Devices
Systems Analysis
Microscopy
Light
Costs and Cost Analysis

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Computer Vision and Pattern Recognition

Cite this

Reduced-complexity representation of the coherent point-spread function in the presence of aberrations and arbitrarily large defocus. / Bagheri, Saeed; de Farias, Daniela Pucci; Barbastathis, George; Neifeld, Mark A.

In: Journal of the Optical Society of America A: Optics and Image Science, and Vision, Vol. 23, No. 10, 2006, p. 2476-2493.

Research output: Contribution to journalArticle

@article{d393658fe7ee4fbb925879ced6ef331f,
title = "Reduced-complexity representation of the coherent point-spread function in the presence of aberrations and arbitrarily large defocus",
abstract = "We introduce a method to analyze the diffraction integral for evaluating the point-spread function. Our method is based on the use of higher-order Airy functions along with Zernike and Taylor expansions. Our approach is applicable when we are considering a finite, arbitrary number of aberrations and arbitrarily large defocus simultaneously. We present an upper bound for the complexity and the convergence rate of this method. We also compare the cost and accuracy of this method with those of traditional ones and show the efficiency of our method through these comparisons. In particular, we rigorously show that this method is constructed in a way that the complexity of the analysis (i.e., the number of terms needed for expressing the light disturbance) does not increase as either defocus or resolution of interest increases. This has applications in several fields such as biological microscopy, lithography, and multidomain optimization in optical systems.",
author = "Saeed Bagheri and {de Farias}, {Daniela Pucci} and George Barbastathis and Neifeld, {Mark A}",
year = "2006",
doi = "10.1364/JOSAA.23.002476",
language = "English (US)",
volume = "23",
pages = "2476--2493",
journal = "Journal of the Optical Society of America A: Optics and Image Science, and Vision",
issn = "1084-7529",
publisher = "The Optical Society",
number = "10",

}

TY - JOUR

T1 - Reduced-complexity representation of the coherent point-spread function in the presence of aberrations and arbitrarily large defocus

AU - Bagheri, Saeed

AU - de Farias, Daniela Pucci

AU - Barbastathis, George

AU - Neifeld, Mark A

PY - 2006

Y1 - 2006

N2 - We introduce a method to analyze the diffraction integral for evaluating the point-spread function. Our method is based on the use of higher-order Airy functions along with Zernike and Taylor expansions. Our approach is applicable when we are considering a finite, arbitrary number of aberrations and arbitrarily large defocus simultaneously. We present an upper bound for the complexity and the convergence rate of this method. We also compare the cost and accuracy of this method with those of traditional ones and show the efficiency of our method through these comparisons. In particular, we rigorously show that this method is constructed in a way that the complexity of the analysis (i.e., the number of terms needed for expressing the light disturbance) does not increase as either defocus or resolution of interest increases. This has applications in several fields such as biological microscopy, lithography, and multidomain optimization in optical systems.

AB - We introduce a method to analyze the diffraction integral for evaluating the point-spread function. Our method is based on the use of higher-order Airy functions along with Zernike and Taylor expansions. Our approach is applicable when we are considering a finite, arbitrary number of aberrations and arbitrarily large defocus simultaneously. We present an upper bound for the complexity and the convergence rate of this method. We also compare the cost and accuracy of this method with those of traditional ones and show the efficiency of our method through these comparisons. In particular, we rigorously show that this method is constructed in a way that the complexity of the analysis (i.e., the number of terms needed for expressing the light disturbance) does not increase as either defocus or resolution of interest increases. This has applications in several fields such as biological microscopy, lithography, and multidomain optimization in optical systems.

UR - http://www.scopus.com/inward/record.url?scp=33751224746&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751224746&partnerID=8YFLogxK

U2 - 10.1364/JOSAA.23.002476

DO - 10.1364/JOSAA.23.002476

M3 - Article

VL - 23

SP - 2476

EP - 2493

JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision

JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision

SN - 1084-7529

IS - 10

ER -