Estimates of the ocular wave aberration from pairs of double-pass retinal images

Ignacio Iglesias; Esther Berrio; Pablo Artal

doi:10.1364/JOSAA.15.002466

Journal of the Optical Society of America A
Vol. 15,
Issue 9,
pp. 2466-2476
(1998)
•https://doi.org/10.1364/JOSAA.15.002466

Estimates of the ocular wave aberration from pairs of double-pass retinal images

Ignacio Iglesias, Esther Berrio, and Pablo Artal

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Ignacio Iglesias, Esther Berrio, and Pablo Artal, "Estimates of the ocular wave aberration from pairs of double-pass retinal images," J. Opt. Soc. Am. A 15, 2466-2476 (1998)

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Abstract

We apply a computational technique to retrieve the wave aberration of the eye from the point-spread function obtained from pairs of double-pass retinal images. The method consists of an adapted pyramidal version of a nonlinear least-squares fitting procedure to a wave aberration expressed as an expansion in Zernike polynomials. Although the procedure provides accurate estimates of the wave aberration, it presents several drawbacks that are discussed in detail. In particular, since a great deal of computational time is necessary to retrieve a single wave aberration, this technique is not useful for real-time applications. We present results of wave aberrations in five normal subjects in the fovea for a 4-mm-pupil diameter. In every case there is a clear presence of comalike aberrations, while the third-order spherical aberration is usually smaller than previous estimates. The root-mean-square error in the retrieved wave aberration, when defocus and astigmatism were corrected, ranges from 0.24 to 0.5 wavelength. The particular values of the aberration coefficients present a large intersubject variability.

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$a_{k}$	$Z_{k} (r, θ)$	Correspondence with Seidel Aberrations
$a_{1}$	1	Constant
$a_{2}$	$2 r cos θ$	Tilt
$a_{3}$	$2 r sin θ$	Tilt
$a_{4}$	$\sqrt{3} (2 r^{2} - 1)$	Defocus
$a_{5}$	$\sqrt{6} r^{2} sin 2 θ$	Astigmatism
$a_{6}$	$\sqrt{6} r^{2} cos 2 θ$	Astigmatism
$a_{7}$	$\sqrt{8} (3 r^{3} - 2 r) sin θ$	Coma
$a_{8}$	$\sqrt{8} (3 r^{3} - 2 r) cos θ$	Coma
$a_{9}$	$\sqrt{8} r^{3} sin 3 θ$
$a_{10}$	$\sqrt{8} r^{3} cos 3 θ$
$a_{11}$	$\sqrt{5} (6 r^{4} - 6 r^{2} + 1)$	Third-order spherical
$a_{12}$	$\sqrt{10} (4 r^{4} - 3 r^{2}) cos 2 θ$
$a_{13}$	$\sqrt{10} (4 r^{4} - 3 r^{2}) sin 2 θ$
$a_{14}$	$\sqrt{10} r^{4} cos 4 θ$
$a_{15}$	$\sqrt{10} r^{4} sin 4 θ$

$a_{k}$	Data from PA
$a_{k}$	(2)	(3)
$a_{1}$ CTEb	0.000000	0.000000
$a_{2}$ Tilt $x$	0.119168	0.120095
$a_{3}$ Tilt $y$	0.039403	0.067154
$a_{4}$ Defocus	$- 0.046165$	$- 0.036906$
$a_{5}$ Astigmatism $y$	$- 0.181802$	$- 0.145588$
$a_{6}$ Astigmatism $x$	0.087442	0.095624
$a_{7}$ Coma $y$	$- 0.006237$	$- 0.013968$
$a_{8}$ Coma $x$	0.048557	0.066044
$a_{9}$	$- 0.078176$	$- 0.108839$
$a_{10}$	$- 0.084068$	$- 0.022084$
$a_{11}$ Third-order spherical	$- 0.003645$	0.002921
$a_{12}$	$- 0.017268$	0.002602
$a_{13}$	$- 0.007635$	0.006830
$a_{14}$	$- 0.001140$	$- 0.030166$
$a_{15}$	0.014478	0.017230

$a_{k}$	Subjects
$a_{k}$	AP	PA	AG	NN	PR
$a_{1} CTE$	0.000000	0.000000	0.000000	0.000000	0.000000
$a_{2} Tilt x$	0.184799	0.119168	$- 0.147765$	$- 0.111866$	$- 0.018726$
$a_{3} Tilt y$	0.356953	0.039403	0.024901	$- 0.059382$	0.038468
$a_{4} Defocus$	0.038801	$- 0.046165$	0.072728	$- 0.100268$	$- 0.2001$
$a_{5} Astigmatism y$	$- 0.211828$	$- 0.181802$	$- 0.080422$	0.186981	$- 0.037951$
$a_{6} Astigmatism x$	$- 0.349898$	0.087442	$- 0.263914$	0.293286	$- 0.032981$
$a_{7} Coma y$	0.178249	$- 0.006237$	$- 0.004541$	0.038017	$- 0.007575$
$a_{8} Coma x$	0.065504	0.048557	0.008972	0.008533	$- 0.052184$
$a_{9}$	$- 0.188917$	$- 0.078176$	$- 0.139822$	$- 0.160408$	0.068636
$a_{10}$	0.055095	$- 0.084068$	$- 0.163935$	$- 0.125630$	0.144763
$a_{11} Third - order spherical$	$- 0.009450$	$- 0.003645$	$- 0.012590$	$- 0.005709$	$- 0.035096$
$a_{12}$	0.041647	$- 0.017268$	0.015568	$- 0.001830$	0.002124
$a_{13}$	0.048223	$- 0.007635$	$- 0.010445$	$- 0.007950$	$- 0.010593$
$a_{14}$	$- 0.078782$	$- 0.001140$	0.034643	0.017266	$- 0.044503$
$a_{15}$	$- 0.036367$	0.014478	0.062210	0.033638	$- 0.061089$

Parameter (in λ)	Subjects
Parameter (in λ)	AP	PA	AG	NN	PR
Spherical aberration	-0.126	-0.048	-0.208	-0.076	-0.47
Coma	1.272	0.328	0.067	0.261	0.447

Parameter	Subjects
Parameter	AP	PA	AG	NN	PR
Strehl ratio	0.14	0.3	0.2	0.12	0.16
P–V values of the WA (λ)	3.65	1.67	2.74	2.71	1.49
Rms error of the WA (λ)	0.504	0.242	0.364	0.418	0.279

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Journal of the Optical Society of America A