Zernike coefficients for concentric, circular scaled pupils: an equivalent expression

Díaz, José A.; Fernández-Dorado, José; Pizarro, Carles; Arasa, Josep

doi:10.1080/09500340802531224

Cited by 21 publications

(8 citation statements)

References 18 publications

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“…Measurements at several pupil diameters for the same eye may be available. It is also possible to numerically transform Zernike coefficients from one pupil diameter to another (usually smaller) diameter (Bara et al, 2006;Dai, 2006;Díaz et al, 2009;Janssen & Dirksen, 2006;Mahajan, 2010;Schwiegerling, 2002). We make use of the formula of Dai (2006) for the new coefficients b based on the old coefficients a, b m n ¼ r n a m n þ…”

Section: Scaling Zernike Coefficients To a Different Pupil Sizementioning

confidence: 99%

“…These basic principles relating wavefront aberrations to the PSF are well known (Dai, 2008;Goodman, 2005;Mahajan, 2013) and were first introduced to computation of retinal images by Artal (1990). Methods to scale Zernike coefficients from one pupil size to another were developed by Schwiegerling (2002) and refined by others (Bara, Arines, Ares, & Prado, 2006;Dai, 2006;Díaz, Fernández-Dorado, Pizarro, & Arasa, 2009;Janssen & Dirksen, 2006;Mahajan, 2010). Methods to compute the polychromatic PSF from monochromatic data have also been developed (Artal, Santamaria, & Bescos, 1989;Coe, Bradley, & Thibos, 2014;Marcos, Burns, Moreno-Barriusop, & Navarro, 1999;Ravikumar, Thibos, & Bradley, 2008;Van Meeteren, 1974).…”

Section: Introductionmentioning

confidence: 99%

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Computing human optical point spread functions

Watson

2015

Journal of Vision

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There is renewed interest in the role of optics in human vision. At the same time there have been advances that allow for routine standardized measurement of the wavefront aberrations of the human eye. Computational methods have been developed to convert these measurements to a description of the human visual optical point spread function (PSF), and to thereby calculate the retinal image. However, tools to implement these calculations for vision science are not widely available or widely understood. In this report we describe software to compute the human optical PSF, and we discuss constraints and limitations.

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Section: Scaling Zernike Coefficients To a Different Pupil Sizementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computing human optical point spread functions

Watson

2015

Journal of Vision

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“…On the other hand, the actual aberrations a 0 in Π 0 can be easily related to the actual aberrations a in Π using the M 0 × M 0 Zernike transformation matrix T associated with a change of scale of the reference frame [8][9][10][11][12][13][14][15][16][17][18][19][20] as a 0 Ta. Hence, we have C a 0 TC a T T , and the aberration estimation error in Π 0 using the refitting procedure is finally given by…”

Section: Error Associated With the Refitting Approachmentioning

confidence: 99%

Estimating the eye aberration coefficients in resized pupils: is it better to refit or to rescale?

et al. 2013

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In order to work in a consistent way with Zernike aberration coefficients estimated in different pupils, it is necessary to refer them to a common pupil size. Two standard approaches can be used to that end: to rescale algebraically the coefficients estimated in the original pupil or to refit them anew using the wavefront slope measurements available within the new one. These procedures are not equivalent; they are affected by different estimation errors that we address in this work. Our results for normal eye populations show that in case of reducing the pupil size it is better to rescale the original coefficients than to refit them using the measurements contained within the smaller pupil. In case of enlarging the pupil size, as it can a priori be expected, the opposite holds true. We provide explicit expressions to quantify the errors arising in both cases, including the expected error incurred when extrapolating the Zernike estimation beyond the radius where the measurements were made.

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“…These expressions will be referred to here as fourth-order spherical, lateral (horizontal) coma, and H/V astigmatism, respectively. In addition, the fourth-order Zernike coefficients were scaled by using the relationships published elsewhere, [75][76][77] when compared with those found in the experimental works with a smaller pupil. Table 2 lists the notation corresponding to the different Zernike coefficients when used for calculating different contributions from surfaces or from GRIN lens profile, for analyzing the results, and it also shows how they were calculated.…”

Section: Zernike Coefficientsmentioning

confidence: 99%

Role of the human lens gradient-index profile in the compensation of third-order ocular aberrations

2012

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The open question regarding the compensation of the ocular aberrations between the cornea and the lens is currently being investigated. We report additional insights considering the role of the lens gradient-index (GRIN) profile in third-order ocular aberrations, since this profile changes through life. Thus, we have calculated the contribution of that profile to the ocular aberrations with aging by applying the Seidel third-order theory of tilted and decentered elements, and by using a schematic-eye model. The results show the GRIN profile is needed to account for the decoupling of the aberrations between the cornea and the lens because the geometrical changes of the ocular surfaces with aging are not enough. Therefore, the current developments of aging human-eye models, as well as the experimental studies, cannot neglect the changes of the lens GRIN structure through life when modelling mechanisms of the compensation of ocular aberrations.

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Zernike coefficients for concentric, circular scaled pupils: an equivalent expression

Cited by 21 publications

References 18 publications

Computing human optical point spread functions

Computing human optical point spread functions

Estimating the eye aberration coefficients in resized pupils: is it better to refit or to rescale?

Role of the human lens gradient-index profile in the compensation of third-order ocular aberrations

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