<i>ABCD</i> matrix of the human lens gradient-index profile: applicability of the calculation methods

José Antonio Díaz

doi:10.1364/AO.47.000195

Applied Optics
Vol. 47,
Issue 2,
pp. 195-205
(2008)
•https://doi.org/10.1364/AO.47.000195

ABCD matrix of the human lens gradient-index profile: applicability of the calculation methods

José Antonio Díaz

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José Antonio Díaz, "ABCD matrix of the human lens gradient-index profile: applicability of the calculation methods," Appl. Opt. 47, 195-205 (2008)

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- Vision, color, and visual optics
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About this Article
History
- Original Manuscript: September 24, 2007
- Revised Manuscript: November 20, 2007
- Manuscript Accepted: November 25, 2007
- Published: January 8, 2008
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 3, Iss. 2

Abstract

The applicability of different approximate methods proposed to determine the paraxial properties of the gradient-index (GRIN) distribution resembling that of the human lens, by means of the system ABCD matrix, is tested. Thus, the parabolic-ray-path approximation has been extended to provide the ABCD matrix of a slab lens comprised of a rotationally GRIN medium. The results show that this method has good numerical stability, and it is also the easiest one in determining the Gaussian constants of the human lens GRIN profile.

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Lens	Method^b	Φ′	$Φ_{b}'$	$\bar{V' H'}$	$\bar{V' N'}$	$\bar{H' N'}$	Φ	Φ_f	$\bar{V H}$	$\bar{V N}$	$\bar{H N}$
Example 1	EX	5.90	5.95	−1.640	−1.642	0.002	−5.90	−5.95	1.931	1.930	−0.001
	SS	5.90	5.95	−1.640	−1.642	0.002	−5.90	−5.95	1.931	1.930	−0.001
	WI	—	—	—	—	—	—	—	—	—	—
	PA	5.89	5.93	−1.799	−1.801	0.002	−5.89	−5.93	1.801	1.799	−0.002
Example 2	EX	10.10	10.22	−1.626	−1.626	0.001	−10.10	−10.27	2.266	2.266	0
	SS	—	—	—	—	—	—	—	—	—	—
	WI	—	—	—	—	—	—	—	—	—	—
	PA	10.01	10.15	−1.996	−1.996	0	−10.01	−10.15	1.996	1.996	0
Example 3	EX	15.98	15.95	−1.982	−1.937	−0.045	−15.99	−16.18	1.978	2.023	0.045
	SS	—	—	—	—	—	—	—	—	—	—
	WI	15.99	16.02	−0.154	−0.154	0	−15.99	−16.72	3.805	3.805	0
	PA	16.06	16.44	−2.011	−2.008	−0.003	−16.06	−16.44	2.008	2.011	0.003

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Applied Optics