Pupil Scaling for the Estimation of Aberrations in Natural Pupils (original) (raw)
Related papers
Eye aberration analysis with Zernike polynomials
Ophthalmic Technologies VIII, 1998
PuDlic reporting Duroen tor this collection of information >s estimated to average i nour per response, including the tim< gatnennq ana maintaining the aata needed, and completing ana reviewing tne collection of information Send commen collection of information, including sugaestions for reducing tnis Duraen. :o Wasnmgton Headauarters Services, Directoi Davis Hignway. Suite 1204. Arlington. 7Ä 22202-4302 and to tne Office of Management and Budget. Paperwork Reducti Otfz,
Eye aberration analysis with Zernike polynomials
Proceedings of SPIE, 1998
New horizons for accurate photorefractive sight correction, afforded by novel flying spot technologies, require adequate measurements of photorefractive properties of an eye. Proposed techniques of eye refraction mapping present results of measurements for finite number of points of eye aperture, requiring to approximate these data by 3D surface. A technique of wave front approximation with Zernike polynomials is described, using optimization of the number of polynomial coefficients. Criterion of optimization is the nearest proximity of the resulted continuous surface to the values calculated for given discrete points. Methodology includes statistical evaluation of minimal root mean square deviation (RMSD) of transverse aberrations, in particular, varying consecutively the values of maximal coefficient indices of Zernike polynomials, recalculating the coefficients, and computing the value of RMSD. Optimization is finished at minimal value of RMSD. Formulas are given for computing ametropia, size of the spot of light on retina, caused by spherical aberratio n, coma, and astigmatism. Results are illustrated by experimental data, that could be of interest for other applications, where detailed evaluation of eye parameters is needed.
Eye aberrations analysis with zernike polynomials
Proceedings of SPIE - The International Society for Optical Engineering, 1998
Contents vii Conference Committee ix Introduction SESSION 1 OPHTHALMIC DIAGNOSTICS 2 Dual-purpose laser irradiation and perfusion testing system for in-vitro experiments using cultured trabecular meshwork endothelial cells [3246-01]
Journal of Optics A: Pure and Applied Optics, 2009
Aberrations of the eye and other image-forming systems are often analyzed by expanding the wavefront aberration function for a given pupil in Zernike polynomials. In previous articles explicit analytical formulae to transform Zernike coefficients of up to seventh order corresponding to wavefront aberrations for an original pupil into those related to a contracted transversally displaced new pupil are obtained. In the present paper, selection rules for the direct and inverse coefficients' transformation are given and missing modes associated with certain displacement directions are analyzed. Taking these rules into account, a graphical method to qualitatively identify which are the elements of the transformation matrix and their characteristic dependence on pupil parameters is presented. This method is applied to fictitious systems having only one non-zero original coefficient and, for completeness, the new coefficient values are also analytically evaluated.
Visual Impact of Zernike and Seidel Forms of Monochromatic Aberrations
Optometry and Vision Science, 2010
Purpose-To examine the impact on visual acuity of different aberrations modes (e.g. coma, astigmatism, spherical aberration (SA)) and different aberration basis functions (Zernike or Seidel). Methods-Computational optics was used to generate retinal images degraded by either the Zernike or Seidel forms of 2 nd through 4 th order aberrations for an eye with a 5mm pupil diameter. High contrast, photopic visual acuity was measured using method of constant stimuli for letters displayed on a computer-controlled, linearized, quasi-monochromatic (λ=556 nm) display. Results-Minimum angle of resolution (MAR) varied linearly with the magnitude (root mean square error, RMS) of all modes of aberration. The impact of individual Zernike lower and higher order aberrations (HOAs) varied significantly with mode, e.g. arc minutes of MAR/micron of RMS slopes varied from 7 (spherical defocus) to 0.5 (quadrafoil). Seidel forms of these aberrations always had a smaller visual impact. Notably, Seidel spherical aberration (SA) had 1/17 th the impact of Zernike SA with the same wavefront variance, and about 1/4 th the impact of Zernike SA with matching levels of r 4 wavefront error. With lower order components removed, HOAs near the center of the Zernike pyramid do not have a large visual impact. Conclusions-The majority of the visual impact of high levels of 4 th order Zernike aberrations can be attributed to the 2 nd order terms within these polynomials. Therefore, the impact of SA can be minimized by balancing it with a defocus term that flattens the central wavefront (paraxial focus) or maximizes the area of the pupil with a flat wavefront. Over this wide range of aberration types and levels, image quality metrics based upon the PSF and OTF can predict VA as reliably as VA measures can predict retests of VA, and thus such metrics may become valuable predictors of both VA and, via optimization, refractions.
Journal of Optics A: Pure and Applied Optics, 2007
An analytical method to convert the set of Zernike coefficients that fits the wavefront aberration for a pupil into another corresponding to a contracted and horizontally translated pupil is proposed. The underlying selection rules are provided and the resulting conversion formulae for a seventh-order expansion are given. These formulae are applied to calculate corneal aberrations referred to a given pupil centre in terms of those referred to the keratometric vertex supplied by the SN CT1000 topographer. Four typical cases are considered: a sphere and three eyes-normal, keratoconic and post-LASIK. When the pupil centre is fixed and the pupil diameter decreases from 6 mm to the photopic natural one, leaving aside piston, tilt and defocus, the difference between the root mean square wavefront error computed with the formulae and the topographer is less than 0.04 μm. When the pupil diameter is kept equal to the natural one and the pupil centre is displaced, coefficients vary according to the eye. For a 0.3 mm pupil shift, the variation of coma is at most 0.35 μm and that of spherical aberration 0.01 μm.
Journal of The Optical Society of America A-optics Image Science and Vision, 2006
In eye aberrometry it is often necessary to transform the aberration coefficients in order to express them in a scaled, rotated, and/or displaced pupil. This is usually done by applying to the original coefficients vector a set of matrices accounting for each elementary transformation. We describe an equivalent algebraic approach that allows us to perform this conversion in a single step and in a straightforward way. This approach can be applied to any particular definition, normalization, and ordering of the Zernike polynomials, and can handle a wide range of pupil transformations, including, but not restricted to, anisotropic scalings. It may also be used to transform the aberration coefficients between different polynomial basis sets.
Zernike phase spatial filter for measuring the aberrations of the optical structures of the eye
Journal of Biomedical Photonics & Engineering, 2015
To measure directly the wavefront aberration coefficients, we propose to use the multi-order diffractive element fitted with the set of Zernike polynomials. Polynomials of lowest degree describe defocusing (ametropy) and astigmatism. Coefficients of highest degree correspond to the spherical aberration of oblique rays that occurs as a consequence of misalignment of the crystalline lens and foveola, as well as deflection at the periphery of the crystalline lens. Multi-order elements allow several tens of expansion coefficients to be measured simultaneously, which will enable to investigate insufficiently known high-order aberrations for the differentiated diagnostics of eye diseases.
Mathematics of Zernike polynomials: a review
Clinical & Experimental Ophthalmology, 2011
Monochromatic aberrations of the eye principally originate from the cornea and the crystalline lens. Aberrometers operate via differing principles but function by either analysing the reflected wavefront from the retina or by analysing an image on the retina. Aberrations may be described as lower order or higher order aberrations with Zernike polynomials being the most commonly employed fitting method. The complex mathematical aspects with regards the Zernike polynomial expansion series are detailed in this review. Refractive surgery has been a key clinical application of aberrometers; however, more recently aberrometers have been used in a range of other areas ophthalmology including corneal diseases, cataract and retinal imaging.