Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems

Psang Dain Lin

doi:doi:10.11648/j.acm.20221103.11

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Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems

Psang Dain Lin

Published in Applied and Computational Mathematics (Volume 11, Issue 3)

Received: 17 April 2022 Accepted: 5 May 2022 Published: 12 May 2022

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Abstract

The design and development of optical systems relies on a thorough theoretical understanding of optical aberrations. However, determining the values of the various-order wavefront aberrations in an optical system is extremely challenging. Accordingly, the present study proposes a methodology for determining the numerical values of the secondary wavefront aberrations of an axis-symmetrical optical system by expanding the optical path length of its general ray using a Taylor series expansion. The determined values of the secondary wavefront aberration coefficients are given. They are distortion W511, field curvature W420, astigmatism W422, coma W331, oblique spherical aberration W240, spherical aberration W060, and six still un-named secondary wavefront aberrations. It is shown that three components (i.e., W244, W153, and W155) are not included among the secondary wavefront aberrations given in the literature despite satisfying the equations of axis-symmetrical nature of axis-symmetrical systems. In other words, the equation of existing literature fails to provide all the components needed to fully compute the secondary wavefront aberrations. By extension, some components of the higher-order wavefront aberrations may also be incompletely presented. The proposed method in this study provides the opportunity to compute all components of various-order wavefront aberrations for rotationally-symmetric optical systems, indicating it is a robust approach for aberration determination.

Published in	Applied and Computational Mathematics (Volume 11, Issue 3)
DOI	10.11648/j.acm.20221103.11
Page(s)	60-68
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Wavefront Aberrations, Geometrical Optics, Taylor Series Expansion, Optical Path Length

References

[1]	W. J. Smith, Modern Optical Engineering, 3rd ed., (Edmund Industrial Optics, Barrington, N. J., (2001), p. 62.
[2]	W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1986).
[3]	V. N. Mahajan, Optical Imaging and Aberrations, Part I Ray Geometrical Optics (SPIE Press, 1998).
[4]	R. Kingslake and R. B. Johnson, Lens Design Fundamentals, Second Edition (Academic, 2010).
[5]	J. Sasián, Introduction to Aberrations in Optical Imaging Systems (Cambridge, 2013).
[6]	H. A. Buchdahl, Optical Aberration Coefficients (Dover, 1968).
[7]	G. W. Hopkins, “Proximate ray tracing and optical aberration coefficients,” J. Opt. Soc. Am. 66 (5), 405–410 (1976).
[8]	W. T. Welford, “A new total aberration formula,” J. Mod. Opt. 19, 719–727 (1972).
[9]	B. Chen and A. M. Herkommer, “High order surface aberrations contributions from phase space analysis of differential rays,” Opt. Express 24, 5934–5945 (2016).
[10]	D. Claus, J. Watson, and J. Rodenburg, “Analysis and interpretation of the Seidel aberration coefficients in digital holography,” Appl. Opt. 50 (34), H220–H229 (2011).
[11]	R. S. Chang, J. Y. Sheu, and C. H. Lin, “Analysis of Seidel aberration by use of the discrete wavelet transform,” Appl. Opt. 41 (13), 2408–2413 (2002).
[12]	R. B. Johnson, “Polynomial ray aberrations computed in various lens design programs,” Appl. Opt. 12 (9), 2079–2082 (1973).
[13]	M. Oleszko, R. Hambach, and H. Gros, “Decomposition of the total wave aberration in generalized optical systems,” J. Opt. Soc. Am. 34 (10), 1856–1864 (2017).
[14]	R. B. Johnson, “Balancing the astigmatic fields when all other aberrations are absent,” Applied Optics 32 (19), 3494–3496 (1993).
[15]	P. D. Lin and R. B. Johnson, ”Seidel Aberration Coefficients: an Alternative Computation Method,” Opt. Express 27 (14), 19712–19725 (2019).
[16]	P. D. Lin, ” Seidel primary ray aberration coefficients for objects placed at finite and infinite distances,” Opt. Express 28 (9), 19740–19754 (2020).
[17]	P. D. Lin, “Alternative method for computing primary wavefront aberrations using Taylor series expansion of optical path length”, OPTIK - International Journal for Light and Electron Optics, Vol. 248, Article 168134, November 2021.
[18]	“Zemax OpticStudio 18.9 User Manual,” (Zemax LLC, 2018).
[19]	S. Jibrin and I. Abdullahi, “Search directions in infeasible newton’s method for computing weighted analytic center for linear matrix inequalities,” Applied and Computational Mathematics. 8 (1), 21–28 (2019).
[20]	BA Demba Bocar, ”Uniform convergence of the series expansion of the multifractional brownian motion,” Applied and Computational Mathematics. 9 (6), 195–200 (2020).
[21]	M. M. Aliyev, “Exact, polynomial, determination solution method of the subset sum problem,” Applied and Computational Mathematics. 3 (5), 262-267 (2014).

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APA Style

Psang Dain Lin. (2022). Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems. Applied and Computational Mathematics, 11(3), 60-68. https://doi.org/10.11648/j.acm.20221103.11

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Psang Dain Lin. Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems. Appl. Comput. Math. 2022, 11(3), 60-68. doi: 10.11648/j.acm.20221103.11

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AMA Style

Psang Dain Lin. Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems. Appl Comput Math. 2022;11(3):60-68. doi: 10.11648/j.acm.20221103.11

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@article{10.11648/j.acm.20221103.11,
  author = {Psang Dain Lin},
  title = {Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems},
  journal = {Applied and Computational Mathematics},
  volume = {11},
  number = {3},
  pages = {60-68},
  doi = {10.11648/j.acm.20221103.11},
  url = {https://doi.org/10.11648/j.acm.20221103.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20221103.11},
  abstract = {The design and development of optical systems relies on a thorough theoretical understanding of optical aberrations. However, determining the values of the various-order wavefront aberrations in an optical system is extremely challenging. Accordingly, the present study proposes a methodology for determining the numerical values of the secondary wavefront aberrations of an axis-symmetrical optical system by expanding the optical path length of its general ray using a Taylor series expansion. The determined values of the secondary wavefront aberration coefficients are given. They are distortion W511, field curvature W420, astigmatism W422, coma W331, oblique spherical aberration W240, spherical aberration W060, and six still un-named secondary wavefront aberrations. It is shown that three components (i.e., W244, W153, and W155) are not included among the secondary wavefront aberrations given in the literature despite satisfying the equations of axis-symmetrical nature of axis-symmetrical systems. In other words, the equation of existing literature fails to provide all the components needed to fully compute the secondary wavefront aberrations. By extension, some components of the higher-order wavefront aberrations may also be incompletely presented. The proposed method in this study provides the opportunity to compute all components of various-order wavefront aberrations for rotationally-symmetric optical systems, indicating it is a robust approach for aberration determination.},
 year = {2022}
}

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TY  - JOUR
T1  - Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems
AU  - Psang Dain Lin
Y1  - 2022/05/12
PY  - 2022
N1  - https://doi.org/10.11648/j.acm.20221103.11
DO  - 10.11648/j.acm.20221103.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 60
EP  - 68
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20221103.11
AB  - The design and development of optical systems relies on a thorough theoretical understanding of optical aberrations. However, determining the values of the various-order wavefront aberrations in an optical system is extremely challenging. Accordingly, the present study proposes a methodology for determining the numerical values of the secondary wavefront aberrations of an axis-symmetrical optical system by expanding the optical path length of its general ray using a Taylor series expansion. The determined values of the secondary wavefront aberration coefficients are given. They are distortion W511, field curvature W420, astigmatism W422, coma W331, oblique spherical aberration W240, spherical aberration W060, and six still un-named secondary wavefront aberrations. It is shown that three components (i.e., W244, W153, and W155) are not included among the secondary wavefront aberrations given in the literature despite satisfying the equations of axis-symmetrical nature of axis-symmetrical systems. In other words, the equation of existing literature fails to provide all the components needed to fully compute the secondary wavefront aberrations. By extension, some components of the higher-order wavefront aberrations may also be incompletely presented. The proposed method in this study provides the opportunity to compute all components of various-order wavefront aberrations for rotationally-symmetric optical systems, indicating it is a robust approach for aberration determination.
VL  - 11
IS  - 3
ER  -

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Author Information

Psang Dain Lin

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan

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Psang Dain Lin. (2022). Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems. Applied and Computational Mathematics, 11(3), 60-68. https://doi.org/10.11648/j.acm.20221103.11

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ACS Style

Psang Dain Lin. Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems. Appl. Comput. Math. 2022, 11(3), 60-68. doi: 10.11648/j.acm.20221103.11

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AMA Style

Psang Dain Lin. Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems. Appl Comput Math. 2022;11(3):60-68. doi: 10.11648/j.acm.20221103.11

Copy | Download

@article{10.11648/j.acm.20221103.11,
  author = {Psang Dain Lin},
  title = {Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems},
  journal = {Applied and Computational Mathematics},
  volume = {11},
  number = {3},
  pages = {60-68},
  doi = {10.11648/j.acm.20221103.11},
  url = {https://doi.org/10.11648/j.acm.20221103.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20221103.11},
  abstract = {The design and development of optical systems relies on a thorough theoretical understanding of optical aberrations. However, determining the values of the various-order wavefront aberrations in an optical system is extremely challenging. Accordingly, the present study proposes a methodology for determining the numerical values of the secondary wavefront aberrations of an axis-symmetrical optical system by expanding the optical path length of its general ray using a Taylor series expansion. The determined values of the secondary wavefront aberration coefficients are given. They are distortion W511, field curvature W420, astigmatism W422, coma W331, oblique spherical aberration W240, spherical aberration W060, and six still un-named secondary wavefront aberrations. It is shown that three components (i.e., W244, W153, and W155) are not included among the secondary wavefront aberrations given in the literature despite satisfying the equations of axis-symmetrical nature of axis-symmetrical systems. In other words, the equation of existing literature fails to provide all the components needed to fully compute the secondary wavefront aberrations. By extension, some components of the higher-order wavefront aberrations may also be incompletely presented. The proposed method in this study provides the opportunity to compute all components of various-order wavefront aberrations for rotationally-symmetric optical systems, indicating it is a robust approach for aberration determination.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Determination of Secondary Wavefront Aberrations in Axis-Symmetrical Optical Systems
AU  - Psang Dain Lin
Y1  - 2022/05/12
PY  - 2022
N1  - https://doi.org/10.11648/j.acm.20221103.11
DO  - 10.11648/j.acm.20221103.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 60
EP  - 68
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20221103.11
AB  - The design and development of optical systems relies on a thorough theoretical understanding of optical aberrations. However, determining the values of the various-order wavefront aberrations in an optical system is extremely challenging. Accordingly, the present study proposes a methodology for determining the numerical values of the secondary wavefront aberrations of an axis-symmetrical optical system by expanding the optical path length of its general ray using a Taylor series expansion. The determined values of the secondary wavefront aberration coefficients are given. They are distortion W511, field curvature W420, astigmatism W422, coma W331, oblique spherical aberration W240, spherical aberration W060, and six still un-named secondary wavefront aberrations. It is shown that three components (i.e., W244, W153, and W155) are not included among the secondary wavefront aberrations given in the literature despite satisfying the equations of axis-symmetrical nature of axis-symmetrical systems. In other words, the equation of existing literature fails to provide all the components needed to fully compute the secondary wavefront aberrations. By extension, some components of the higher-order wavefront aberrations may also be incompletely presented. The proposed method in this study provides the opportunity to compute all components of various-order wavefront aberrations for rotationally-symmetric optical systems, indicating it is a robust approach for aberration determination.
VL  - 11
IS  - 3
ER  -

Copy | Download