Weighted Zernike expansion with applications to the optical aberration of
               the human eye

Jayoung Nam; Jacob Rubinstein

doi:10.1364/JOSAA.22.001709

Weighted Zernike expansion with applications to the optical aberration of the human eye

Jayoung Nam and Jacob Rubinstein

Journal of the Optical Society of America A
Vol. 22,
Issue 9,
pp. 1709-1716
(2005)
•https://doi.org/10.1364/JOSAA.22.001709

Get Citation
Copy Citation Text
Jayoung Nam and Jacob Rubinstein, "Weighted Zernike expansion with applications to the optical aberration of the human eye," J. Opt. Soc. Am. A 22, 1709-1716 (2005)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Get PDF (125 KB)
Set citation alerts
Save article

Related Topics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Vision - acuity (330.1070)
- Ophthalmic optics and devices (330.4460)

About this Article
History
- Original Manuscript: December 10, 2004
- Revised Manuscript: February 18, 2005
- Manuscript Accepted: March 4, 2005
- Published: September 1, 2005

Not Accessible

Your account may give you access

Abstract

We propose to use weighted Zernike functions to represent the aberrations of an eye. Methods for computing the phase of an aberrated ophthalmic wavefront in terms of weighted Zernike functions are discussed. In particular, we consider several options for integrating the phase out of its measured slopes. The weighted functions involve a free parameter. Clinical data on subjective refraction and aberration maps of individual subjects are used to determine an estimate for this parameter.

Full Article | PDF Article

OSA Recommended Articles

Statistical variation of aberration structure and image quality in a normal population of healthy eyes

Larry N. Thibos, Xin Hong, Arthur Bradley, and Xu Cheng
J. Opt. Soc. Am. A 19(12) 2329-2348 (2002)

Statistical description of wave-front aberration in the human eye

Manuel P. Cagigal, Vidal F. Canales, José F. Castejón-Mochón, Pedro M. Prieto, Norberto López-Gil, and Pablo Artal
Opt. Lett. 27(1) 37-39 (2002)

Zernike radial slope polynomials for wavefront reconstruction and refraction

Jayoung Nam, Larry N. Thibos, and D. Robert Iskander
J. Opt. Soc. Am. A 26(4) 1035-1048 (2009)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (2)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (2)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (31)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

n	m	$ρ^{4}$	$ρ^{3}$	$ρ^{2}$	$ρ^{1}$	$ρ^{0}$ ^a
0	0					1.4142 (1.5942)
1	1				2 (2.3544)
2	0			4.8990 (5.5570)		$- 2.4495 (- 2.5479)$
2	2			2.4495 (2.9475)
3	1		8.4853 (9.6935)		$- 5.6569 (- 6.1845)$
3	3		2.8284 (3.4487)
4	0	18.9737 (21.5032)		$- 18.9737 (- 20.7860)$		3.1623 (3.2402)
4	2	12.6491 (14.6235)		$- 9.4868 (- 10.6820)$
4	4	3.1623 (3.8898)

n	m	$n^{'}$	$m^{'}$	Expected Value	Computed Inner Product
n	m	$n^{'}$	$m^{'}$	Expected Value	$(V_{n}^{m}, V_{n^{'}}^{m^{'}})$	${(V_{n}^{m}, V_{n^{'}}^{m^{'}})}_{new}$
3	3	0	0	0	$5.8634 \cdot 10^{- 16}$	$3.5388 \cdot 10^{- 16}$
3	3	1	1	0	$- 0.26529$	0.020655
3	3	2	0	0	$5.1348 \cdot 10^{- 16}$	$1.8041 \cdot 10^{- 16}$
3	3	2	2	0	$- 8.8124 \cdot 10^{- 16}$	$- 1.0408 \cdot 10^{- 16}$
3	3	3	1	0	$- 0.7017$	0.080579
3	3	3	3	π	7.5334	3.3612
3	3	4	0	0	$1.5821 \cdot 10^{- 15}$	$- 2.0123 \cdot 10^{- 16}$
3	3	4	2	0	$- 4.1633 \cdot 10^{- 17}$	$- 2.0123 \cdot 10^{- 16}$
3	3	4	4	0	$1.7347 \cdot 10^{- 15}$	$3.5041 \cdot 10^{- 16}$
3	3	5	1	0	$- 1.8595$	0.21174
3	3	5	3	0	8.9007	0.75456
3	3	5	5	0	$- 0.78488$	0.074048

n	m	$ρ^{4}$	$ρ^{3}$	$ρ^{2}$	$ρ^{1}$	$ρ^{0}$ ^a
0	0					1.4142 (1.5942)
1	1				2 (2.3544)
2	0			4.8990 (5.5570)		$- 2.4495 (- 2.5479)$
2	2			2.4495 (2.9475)
3	1		8.4853 (9.6935)		$- 5.6569 (- 6.1845)$
3	3		2.8284 (3.4487)
4	0	18.9737 (21.5032)		$- 18.9737 (- 20.7860)$		3.1623 (3.2402)
4	2	12.6491 (14.6235)		$- 9.4868 (- 10.6820)$
4	4	3.1623 (3.8898)

n	m	$n^{'}$	$m^{'}$	Expected Value	Computed Inner Product
n	m	$n^{'}$	$m^{'}$	Expected Value	$(V_{n}^{m}, V_{n^{'}}^{m^{'}})$	${(V_{n}^{m}, V_{n^{'}}^{m^{'}})}_{new}$
3	3	0	0	0	$5.8634 \cdot 10^{- 16}$	$3.5388 \cdot 10^{- 16}$
3	3	1	1	0	$- 0.26529$	0.020655
3	3	2	0	0	$5.1348 \cdot 10^{- 16}$	$1.8041 \cdot 10^{- 16}$
3	3	2	2	0	$- 8.8124 \cdot 10^{- 16}$	$- 1.0408 \cdot 10^{- 16}$
3	3	3	1	0	$- 0.7017$	0.080579
3	3	3	3	π	7.5334	3.3612
3	3	4	0	0	$1.5821 \cdot 10^{- 15}$	$- 2.0123 \cdot 10^{- 16}$
3	3	4	2	0	$- 4.1633 \cdot 10^{- 17}$	$- 2.0123 \cdot 10^{- 16}$
3	3	4	4	0	$1.7347 \cdot 10^{- 15}$	$3.5041 \cdot 10^{- 16}$
3	3	5	1	0	$- 1.8595$	0.21174
3	3	5	3	0	8.9007	0.75456
3	3	5	5	0	$- 0.78488$	0.074048

Abstract

References

Cited By

Figures (2)

Tables (2)

Equations (31)

Metrics

Login or Create Account