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

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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)

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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.

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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)

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