DOCSLIB.ORG

Standards for Reporting the Optical Aberrations of Eyes

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Standards for Reporting the Optical Aberrations of Eyes Standards for Reporting the Optical Aberrations of Eyes Larry N. Thibos, PhD; Raymond A. Applegate, OD, PhD; James T. Schwiegerling, PhD; Robert Webb, PhD; VSIA Standards Taskforce Members ABSTRACT tional standards for reporting aberration data and In response to a perceived need in the vision to specify test procedures for evaluating the accura- community, an OSA taskforce was formed at the cy of data collection and data analysis methods. 1999 topical meeting on vision science and its appli- 1 cations (VSIA-99) and charged with developing con- Following a call for participation , approximately sensus recommendations on definitions, conven- 20 people met at VSIA-99 to discuss the proposal to tions, and standards for reporting of optical aber- form a taskforce that would recommend standards rations of human eyes. Progress reports were pre- for reporting optical aberrations of eyes. The group sented at the 1999 OSA annual meeting and at VSIA- agreed to form three working parties that would 2000 by the chairs of three taskforce subcommittees on (1) reference axes, (2) describing functions, and take responsibility for developing consensus recom- (3) model eyes. [J Refract Surg 2002;18:S652-S660] mendations on definitions, conventions and stan- dards for the following three topics: (1) reference axes, (2) describing functions, and (3) model eyes. It he recent resurgence of activity in visual was decided that the strategy for Phase I of this pro- optics research and related clinical disciplines ject would be to concentrate on articulating defini- T(eg, refractive surgery, ophthalmic lens tions, conventions, and standards for those issues design, ametropia diagnosis) demands that the which are not empirical in nature. For example, sev- vision community establish common metrics, termi- eral schemes for enumerating the Zernike polyno- nology, and other reporting standards for the speci- mials have been proposed in the literature. fication of optical imperfections of eyes. Currently Selecting one to be the standard is a matter of there exists a plethora of methods for analyzing and choice, not empirical investigation, and therefore representing the aberration structure of the eye but was included in the charge to the taskforce. On the no agreement exists within the vision community on other hand, issues such as the maximum number of a common, universal method for reporting results. Zernike orders needed to describe ocular aberra- In theory, the various methods currently in use by tions adequately is an empirical question which was different groups of investigators all describe the avoided for the present, although the taskforce may same underlying phenomena and therefore it should choose to formulate recommendations on such be possible to reliably convert results from one rep- issues at a later time. Phase I concluded at the resentational scheme to another. However, the prac- VSIA-2000 meeting. tical implementation of these conversion methods is computationally challenging, is subject to error, and REFERENCE AXIS SELECTION reliable computer software is not widely available. All of these problems suggest the need for opera- Summary It is the committee’s recommendation that the ophthalmic community use the line-of-sight as the From the School of Optometry, Indiana University, Bloomington, IN reference axis for the purposes of calculating and (Thibos); College of Optometry, University of Houston, TX (Applegate); measuring the optical aberrations of the eye. The Department of Ophthalmology, University of Arizona, Tucson, AZ rationale is that the line-of-sight in the normal eye (Schweigerling); Schepens Research Institute, Boston, MA (Webb). This is an expanded version of a report originally published as: Thibos is the path of the chief ray from the fixation point to LN, Applegate RA, Schwiegerling JT, Webb R. Standards for Reporting the the retinal fovea. Therefore, aberrations measured Optical Aberrations of Eyes. In: Lakshminarayanan V, ed (Optical Society with respect to this axis will have the pupil center of America, Washington, D.C., 2000). Vision Science and Its Applications. TOPS-35:232-244. as the origin of a Cartesian reference frame. S652 Journal of Refractive Surgery Volume 18 September/October 2002 Standards for Reporting Optical Aberrations of Eyes/Thibos et al Figure 1. The cornea, pupil, and crystalline lens are decentered and tilted with respect to each other, rendering the eye a decentered optical system that is different between individuals and eyes within the same individual. Figure 2. An anatomical view of the macular region as viewed from the front and in cross section (below). a: foveola, b: fovea, Secondary lines-of-sight may be similarly construct- c: parafoveal area, d: perifoveal area. (From Histology of the Human ed for object points in the peripheral visual field. Eye by Hogan MJ, Alvarado JA, and Weddell JE. W.B. Saunders Because the exit pupil is not readily accessible in Company Publishers, 1971, page 491.) the living eye whereas the entrance pupil is, the committee recommends that calculations for speci- designed to form an in-focus inverted image on a fying the optical aberration of the eye be referenced screen. In the case of the eye, the imaging screen is to the plane of the entrance pupil. the retina. However, unlike film, the “grain” of the retina is not uniform over its extent. Instead, the Background grain is finest at the foveola and falls off quickly as Optical aberration measurements of the eye from the distance from the foveola increases. Conse- various laboratories or within the same laboratory quently, when viewing fine detail, we rotate our eye are not comparable unless they are calculated with such that the object of regard falls on the foveola respect to the same reference axis and expressed in (Fig 2). Thus, aberrations at the foveola have the the same manner. This requirement is complicated greatest impact on an individual’s ability to see fine by the fact that, unlike a camera, the eye is a decen- details. tered optical system with non-rotationally symmet- Two traditional axes of the eye are centered on ric components (Fig 1). The principle elements of the the foveola, the visual axis and the line-of-sight, but eye’s optical system are the cornea, pupil, and the only the latter passes through the pupil center. In crystalline lens. Each can be decentered and tilted object space, the visual axis is typically defined as with respect to other components, thus rendering an the line connecting the fixation object point to the optical system that is typically dominated by coma eye’s first nodal point. In image space, the visual at the foveola. axis is the parallel line connecting the second nodal The optics discipline has a long tradition of spec- point to the center of the foveola (Fig. 3, left). In con- ifying the aberration of optical systems with respect trast, the line-of-sight is defined as the (broken) line to the center of the exit pupil. In a centered optical passing through the center of the eye’s entrance and system (eg, a camera, or telescope) using the center exit pupils connecting the object of regard to the of the exit pupil as a reference for measurement of foveola (Fig. 3, right). The line-of-sight is equivalent on-axis aberration is the same as measuring the to the path of the foveal chief ray and therefore is optical aberrations with respect to the chief ray the axis which conforms to optical standards. The from an axial object point. However, because the visual axis and the line of sight are not the same exit pupil is not readily accessible in the living eye, and in some eyes the difference can have a large it is more practical to reference aberrations to the impact on retinal image quality.2 For a review of the entrance pupil. This is the natural choice for objec- axes of the eye see.3 (To avoid confusion, we note tive aberrometers which analyze light reflected from that Bennett and Rabbetts4 re-define the visual axis the eye. to match the traditional definition of the line of Like a camera, the eye is an imaging device sight. The Bennett and Rabbetts definition is Journal of Refractive Surgery Volume 18 September/October 2002 S653 Standards for Reporting Optical Aberrations of Eyes/Thibos et al Figure 3. Left panel illustrates the visual axis and right panel illus- trates the line of sight. counter to the majority of the literature and is not used here.) Figure 4. Schematic of a generic objective alignment system When measuring the optical properties of the eye designed to place the line of sight on the optical axis of the mea- for objects which fall on the peripheral retina out- surement system. BS: beam splitter, FP: on axis fixation point. side the central fovea, a secondary line-of-sight may be constructed as the broken line from object point to center of the entrance pupil and from the center of the exit pupil to the retinal location of the image. This axis represents the path of the chief ray from the object of interest and therefore is the appropri- ate reference for describing aberrations of the peripheral visual field. METHODS FOR ALIGNING THE EYE DURING MEASUREMENT Summary The committee recommends that instruments Figure 5. Schematic of a generic subjective alignment system designed to measure the optical properties of the eye designed to place the line of sight on the optical axis of the mea- and its aberrations be aligned co-axially with the surement system. BS: beam splitter, FP: fixation point source. eye’s line-of-sight. co-axial with the optical axis of the measurement Background system. There are numerous ways to align the line of sight to the optical axis of the measuring instru- Subjective Method ment.
Load more

Recommended publications
  • Quaternion Zernike Spherical Polynomials
    MATHEMATICS OF COMPUTATION Volume 84, Number 293, May 2015, Pages 1317–1337 S 0025-5718(2014)02888-3 Article electronically published on August 29, 2014 QUATERNION ZERNIKE SPHERICAL POLYNOMIALS J. MORAIS AND I. CAC¸ AO˜ Abstract. Over the past few years considerable attention has been given to the role played by the Zernike polynomials (ZPs) in many different fields of geometrical optics, optical engineering, and astronomy. The ZPs and their applications to corneal surface modeling played a key role in this develop- ment. These polynomials are a complete set of orthogonal functions over the unit circle and are commonly used to describe balanced aberrations. In the present paper we introduce the Zernike spherical polynomials within quater- nionic analysis ((R)QZSPs), which refine and extend the Zernike moments (defined through their polynomial counterparts). In particular, the underlying functions are of three real variables and take on either values in the reduced and full quaternions (identified, respectively, with R3 and R4). (R)QZSPs are orthonormal in the unit ball. The representation of these functions in terms of spherical monogenics over the unit sphere are explicitly given, from which several recurrence formulae for fast computer implementations can be derived. A summary of their fundamental properties and a further second or- der homogeneous differential equation are also discussed. As an application, we provide the reader with plot simulations that demonstrate the effectiveness of our approach. (R)QZSPs are new in literature and have some consequences that are now under investigation. 1. Introduction 1.1. The Zernike spherical polynomials. The complex Zernike polynomials (ZPs) have long been successfully used in many different fields of optics.
    [Show full text]
  • Higher-Order Wavefront Aberration and Letter-Contrast Sensitivity In
    Eye (2008) 22, 1488–1492 & 2008 Macmillan Publishers Limited All rights reserved 0950-222X/08 $32.00 www.nature.com/eye 1 1 2 2 CLINICAL STUDY Higher-order C Okamoto , F Okamoto , T Samejima , K Miyata and T Oshika1 wavefront aberration and letter-contrast sensitivity in keratoconus Abstract Keywords: keratoconus; wavefront aberration; higher-order aberration; contrast sensitivity; Aims To evaluate the relation between letter-contrast sensitivity higher-order aberration of the eye and contrast sensitivity function in eyes with keratoconus. Methods In 22 eyes of 14 patients with Introduction keratoconus (age 30.578.4 years, means7SD) and 26 eyes of 13 normal controls (age Keratoconus is a chronic, non-inflammatory 29.276.7 years), ocular higher-order wavefront disease of the cornea associated with aberration for a 6-mm pupil was measured progressive thinning and anterior protrusion of with the Hartmann-Schack aberrometer the central cornea.1,2 Irregular astigmatism is (KR-9000 PW, Topcon). The root mean square often the first and most apparent clinical finding (RMS) of third- and fourth-order Zernike in keratoconus, and this is evidenced by a coefficients was used to represent higher-order distortion of the corneal image as noted with aberrations. The letter-contrast sensitivity was the placido disc, retinoscope, keratometer, examined using the CSV-1000LV contrast chart keratoscope, and computerized (Vector Vision). videokeratograph. Previous studies using Results In the keratoconus group, the videokeratography have quantitatively 1 Department of letter-contrast sensitivity showed significant demonstrated that corneal irregular Ophthalmology, Institute of correlation with third-order (Spearman’s astigmatism is significantly greater in eyes with Clinical Medicine, University correlation coefficient ¼À0.736, 0.001) 3–6 of Tsukuba, Ibaraki, Japan r Po keratoconus than in normal eyes.
    [Show full text]
  • Higher-Order Aberrations
    Higher-order aberrations Lens Design OPTI 517 Prof. Jose Sasian Higher order Aberrations • Aberration function • Six-order terms (fifth-order transverse) • Wavefront shapes and field dependence • Coefficients • Pupil matching • References. Prof. Jose Sasian References • 1) J. Sasian, “Theory of sixth-order wave aberrations,” Applied Optics, June 2010. • 2) O. N. Stavroudis, “Modular Optical Design” • 3) Buchdahl, “Optical Aberration Coefficients” • 4) M. Herzberger, “Modern Geometrical Optics” Prof. Jose Sasian “Back of the envelope” Prof. Jose Sasian Coordinate system and reference sphere y' E ' yI H Exit pupil plane Image plane Prof. Jose Sasian Aberration function Prof. Jose Sasian Prof. Jose Sasian Aberration orders Roland Shack’s aberration diagram Prof. Jose Sasian Terminology •W240 Oblique spherical aberration •W331 Cubic coma •W422 Quartic astigmatism •W420 Six order field curvature •W511 Six order distortion •W600 Six order piston •W060 Six order spherical aberration •W151 •W242 •W333 Prof. Jose Sasian Some earlier terminology • Oblique spherical aberration • Elliptical coma • Line coma • Secondary spherical aberration • Secondary coma • Lateral coma • Lateral image curvature/astigmatism •Trefoil Prof. Jose Sasian Wavefront deformation shapes Prof. Jose Sasian Spherical aberration: W060 Prof. Jose Sasian W151 & W333 Prof. Jose Sasian W242 Prof. Jose Sasian Higher-order aberration coefficients • Harder to derive/calculate than fourth- order • Intrinsic coefficients • Extrinsic coefficients • Depend highly on coordinate system Prof. Jose Sasian Intrinsic spherical aberration 1 2 u W040 A y 8 n 2 1 y 1 u' u y 8 y W060I W040 2 A 2 u W040 W040 2 r 2 n' n r y 2 1 y 1 u' u y 8 y W060I W040 2 A 2 u' W040 W040 2 r 2 n' n r y 3 5 7 y Y y c3 y c5 y c7 y ..
    [Show full text]
  • Correction of the Eye's Wave Aberration
    Adaptive Optics for Vision Science and Astronomy ASP Conference Series, Vol. **VOLUME**, **PUBLICATION YEAR** A. Quirrenbach Correction of the Eye’s Wave Aberration Yasuki Yamauchi∗, David R. Williams∗,, Jason Porter∗,, and Antonio Guirao∗,† ∗ Center for Visual Science, University of Rochester, Rochester, New York, 14627, USA The Institute of Optics, University of Rochester, Rochester, New York, 14627, USA † Laboratorio de Optica, Universidad de Murcia, Campus de Espinardo (Edificio C), 30071 Murcia, SPAIN 1. Introduction We have seen in the previous two chapters that the human eye is not a perfect optical system and contains a host of different aberrations. If the eye’s opti- cal quality is poor, i.e. if the images formed on the retina are blurred or have low contrast, vision will be deficient even if the rest of the visual system were perfect. Several methods to improve the optics of the human eye have been proposed and developed, the earliest written reports of which originated at least 700 years ago. Spectacles that corrected defocus were invented as early as the 13th century (Willoughby Cashell, 1971; Rubin, 1986) while spectacles that cor- rected defocus and astigmatism were conceived in the 19th century (Helmholtz, 1924). Since then, there has been relatively little work on exploring techniques to correct additional aberrations in the eye. In 1961, Smirnov suggested that it might be possible to manufacture customized contact lenses that would com- pensate for the higher order aberrations found in individual eyes. Recently, technological advances in measuring and compensating for the aberrations of the human eye have made it possible to provide the eye with unprecedented optical quality (Liang et al., 1997).
    [Show full text]
  • Measuring Higher Order Optical Aberrations of the Human Eye: Techniques and Applications
    Brazilian Journal of Medical and Biological Research (2002) 35: 1395-1406 Optical aberrations of the human eye 1395 ISSN 0100-879X Measuring higher order optical aberrations of the human eye: techniques and applications L. Alberto V. Carvalho1, 1Grupo de Óptica, Instituto de Física de São Carlos, Universidade de São Paulo, J.C. Castro1 and São Carlos, SP, Brasil L. Antonio V. Carvalho2 2Departamento de Matemática, Universidade Estadual de Maringá, Maringá, PR, Brasil Abstract Correspondence In the present paper we discuss the development of wave-front, an Key words L. Alberto V. Carvalho instrument for determining the lower and higher optical aberrations of · Optical aberrations Grupo de Óptica, IFSC, USP the human eye. We also discuss the advantages that such instrumenta- · Corneal topography 13560-900 São Carlos, SP tion and techniques might bring to the ophthalmology professional of · Zernike polynomials Brasil the 21st century. By shining a small light spot on the retina of subjects · Refractive surgery E-mail: [email protected] and observing the light that is reflected back from within the eye, we are able to quantitatively determine the amount of lower order aberra- Research partially supported by FAPESP (Nos. 01/03132-8 and tions (astigmatism, myopia, hyperopia) and higher order aberrations 00/06810-4). L. Antonio V. Carvalho (coma, spherical aberration, etc.). We have measured artificial eyes is partially supported by CNPq with calibrated ametropia ranging from +5 to -5 D, with and without (No. 304041/85-8). 2 D astigmatism with axis at 45º and 90º. We used a device known as the Hartmann-Shack (HS) sensor, originally developed for measuring the optical aberrations of optical instruments and general refracting surfaces in astronomical telescopes.
    [Show full text]
  • Total, Corneal, and Internal Ocular Optical Aberrations in Patients with Keratoconus
    Total, Corneal, and Internal Ocular Optical Aberrations in Patients With Keratoconus Zuzana Schlegel, MD; Yara Lteif, MD; Harkaran S. Bains; Damien Gatinel, MD, PhD he front corneal surface is a major refracting com- ABSTRACT ponent of the eye and is considerably distorted in 1 PURPOSE: To measure and compare total, corneal, and T patients with keratoconus. Asymmetric corneal internal ocular aberrations using combined wavefront protrusion is the primary cause of irregular astigmatism in analysis and corneal topography in eyes with keratoco- keratoconus.2 This deformity affects both the anterior and nus and eyes with normal corneas. posterior corneal surfaces.3-5 Recent studies have investigated the contribution of the posterior surface to the overall corneal METHODS: This prospective study comprised eyes of optical performance by analyzing data obtained with slit- patients with keratoconus and myopic patients seeking 6 7 refractive surgery. Patients diagnosed with keratoconus scanning or Scheimpfl ug topography. Signifi cantly larger and with a classifi cation of “normal” or “keratoconus” amounts of posterior corneal aberrations and higher compen- on the NIDEK Corneal Navigator corneal disease screen- sation effects were observed in keratoconic eyes compared ing software were selected for inclusion in this study. to normal eyes.6,7 Both the posterior corneal aberrations and The normal group comprised eyes with a “normal” clas- crystalline lens aberrations contribute to the internal aberra- sifi cation with 99% similarity. In the normal group, only one eye per patient was randomly selected based on tion component. a randomization schedule. Corneal, internal, and total Recent studies have found that in pre-presbyopic patients, wavefront measurements were provided by the NIDEK the magnitude of higher order aberrations for the cornea or OPD-Scan II.
    [Show full text]
  • Wavefront Parameters Recovering by Using Point Spread Function
    Wavefront Parameters Recovering by Using Point Spread Function Olga Kalinkina[0000-0002-2522-8496], Tatyana Ivanova[0000-0001-8564-243X] and Julia Kushtyseva[0000-0003-1101-6641] ITMO University, 197101 Kronverksky pr. 49, bldg. A, Saint-Petersburg, Russia [email protected], [email protected], [email protected] Abstract. At various stages of the life cycle of optical systems, one of the most important tasks is quality of optical system elements assembly and alignment control. The different wavefront reconstruction algorithms have already proven themselves to be excellent assistants in this. Every year increasing technical ca- pacities opens access to the new algorithms and the possibilities of their appli- cation. The paper considers an iterative algorithm for recovering the wavefront parameters. The parameters of the wavefront are the Zernike polynomials coef- ficients. The method involves using a previously known point spread function to recover Zernike polynomials coefficients. This work is devoted to the re- search of the defocusing influence on the convergence of the algorithm. The method is designed to control the manufacturing quality of optical systems by point image. A substantial part of the optical systems can use this method with- out additional equipment. It can help automate the controlled optical system ad- justment process. Keywords: Point Spread Function, Wavefront, Zernike Polynomials, Optimiza- tion, Aberrations. 1 Introduction At the stage of manufacturing optical systems, one of the most important tasks is quality of optical system elements assembly and alignment control. There are various methods for solving this problem, for example, interference methods. However, in some cases, one of which is the alignment of the telescope during its operation, other control methods are required [1, 2], for example control by point image (point spread function) or the image of another known object.
    [Show full text]
  • Representation of Wavefront Aberrations
    Slide 1 4th Wavefront Congress - San Francisco - February 2003 Representation of Wavefront Aberrations Larry N. Thibos School of Optometry, Indiana University, Bloomington, IN 47405 [email protected] http://research.opt.indiana.edu/Library/wavefronts/index.htm The goal of this tutorial is to provide a brief introduction to how the optical imperfections of a human eye are represented by wavefront aberration maps and how these maps may be interpreted in a clinical context. Slide 2 Lecture outline • What is an aberration map? – Ray errors – Optical path length errors – Wavefront errors • How are aberration maps displayed? – Ray deviations – Optical path differences – Wavefront shape • How are aberrations classified? – Zernike expansion • How is the magnitude of an aberration specified? – Wavefront variance – Equivalent defocus – Retinal image quality • How are the derivatives of the aberration map interpreted? My lecture is organized around the following 5 questions. •First, What is an aberration map? Because the aberration map is such a fundamental description of the eye’ optical properties, I’m going to describe it from three different, but complementary, viewpoints: first as misdirected rays of light, second as unequal optical distances between object and image, and third as misshapen optical wavefronts. •Second, how are aberration maps displayed? The answer to that question depends on whether the aberrations are described in terms of rays or wavefronts. •Third, how are aberrations classified? Several methods are available for classifying aberrations. I will describe for you the most popular method, called Zernike analysis. lFourth, how is the magnitude of an aberration specified? I will describe three simple measures of the aberration map that are useful for quantifying the magnitude of optical error in a person’s eye.
    [Show full text]
  • Articles Induced Optical Aberrations Following Formation of a Laser in Situ Keratomileusis Flap
    articles Induced optical aberrations following formation of a laser in situ keratomileusis flap Ioannis G. Pallikaris, MD, PhD, George D. Kymionis, MD, PhD, Sophia I. Panagopoulou, Charalambos S. Siganos, MD, PhD, Michalis A. Theodorakis, Aristofanis I. Pallikaris Purpose: To determine how refractive error, visual acuity, and high-order aberra- tions (3rd- and 4th-order) are affected by the formation of a lamellar corneal flap during laser in situ keratomileusis (LASIK). Setting: University refractive surgery center. Methods: The effect of lamellar corneal flap formation was analyzed in 15 myopic eyes (mean preoperative refraction Ϫ4.72 diopters [D] [range Ϫ1.25 to Ϫ7.25 D]). The flap was created using a 2-step procedure: (1) a nasally hinged lamellar cor- neal flap was created; (2) the flap was lifted and stromal ablation performed 2 months after the flap was made. A Hartmann-Shack aberrometer was used to measure the aberrations. Results: There was no significant change in the refractive error (spherical equiva- lent pre-flap Ϫ4.72 Ϯ 1.99 D and post-flap Ϫ4.62 Ϯ 1.99 D [P ϭ .28]) or visual acuity (pre-flap uncorrected visual acuity [UCVA] 0.07 and best corrected visual acuity [BCVA] 0.96; post-flap UCVA 0.08 and BCVA 0.95 [P ϭ .16 and P ϭ .33, respectively]). A statistically significant increase in total higher-order wavefront aberrations was observed following flap formation (root mean square pre-flap 0.344 Ϯ 0.125 and post-flap 0.440 Ϯ 0.221 [P ϭ .04]). Conclusion: Flap formation during LASIK can modify the eye’s existing natural higher-order aberrations (especially spherical and coma-like aberrations along the axis of the flap’s hinge), while visual acuity and refractive error remain unaffected.
    [Show full text]
  • Wavefront Aberrations
    11 Wavefront Aberrations Mirko Resan, Miroslav Vukosavljević and Milorad Milivojević Eye Clinic, Military Medical Academy, Belgrade, Serbia 1. Introduction The eye is an optical system having several optical elements that focus light rays representing images onto the retina. Imperfections in the components and materials in the eye may cause light rays to deviate from the desired path. These deviations, referred to as optical or wavefront aberrations, result in blurred images and decreased visual performance (1). Wavefront aberrations are optical imperfections of the eye that prevent light from focusing perfectly on the retina, resulting in defects in the visual image. There are two kinds of aberrations: 1. Lower order aberrations (0, 1st and 2nd order) 2. Higher order aberrations (3rd, 4th, … order) Lower order aberrations are another way to describe refractive errors: myopia, hyperopia and astigmatism, correctible with glasses, contact lenses or refractive surgery. Lower order aberrations is a term used in wavefront technology to describe second-order Zernike polynomials. Second-order Zernike terms represent the conventional aberrations defocus (myopia, hyperopia and astigmatism). Lower order aberrations make up about 85 per cent of all aberrations in the eye. Higher order aberrations are optical imperfections which cannot be corrected by any reliable means of present technology. All eyes have at least some degree of higher order aberrations. These aberrations are now more recognized because technology has been developed to diagnose them properly. Wavefront aberrometer is actually used to diagnose and measure higher order aberrations. Higher order aberrations is a term used to describe Zernike aberrations above second-order. Third-order Zernike terms are coma and trefoil.
    [Show full text]
  • Ocular Higher-Order Aberrations and Mesopic Pupil Size in Individuals
    HOAsandpupilsizeinindividuals 窑ClinicalResearch窑 Ocularhigher-orderaberrationsandmesopicpupil sizeinindividualsscreenedforrefractivesurgery 1EyeResearchcenter,RasoulAkramHospitalTehran hyperopescomparedtomyopes.Mesopicpupilsizewas UniversityofMedicalSciences,Tehran,Iran largerinmyopicgroup. 2DepartmentofEpidemiologyandBiostatistics,Schoolof ·KEYWORDS:cornealwavefrontaberration;pupil;mesopic PublicHealth,TehranUniversityofMedicalSciences, vision;race;myopia;hyperopia Tehran,Iran DOI:10.3980/j.issn.2222-3959.2012.02.21 Correspondenceto: MohammadSoleimani.EyeResearch Center,RassoulAkramHospital,TehranUniversityof HashemianSJ,SoleimaniM,ForoutanA,JoshaghaniM,Ghaempanah MedicalSciences,Tehran,[email protected] MJ,JafariME,YaseriM.Ocularhigher-orderaberrationsand Received:2011-08-23Accepted:2012-03-10 mesopicpupilsizeinindividualsscreenedforrefractivesurgery. 2012;5(2):222-225 Abstract INTRODUCTION AIM:Tostudythedistributionofocularhigher-order · cularaberrationsmayplayamajorroleintheimage aberrations(HOAs)andmesopicpupilsizeinindividuals O formationintheocularopticalsystem.Lowerorder screenedforrefractivesurgery. aberrationssuchasastigmatismanddefocuscaneasilybe · METHODS:OcularHOAsandmesopicpupilsizewere correctedandmaybelessproblematic,howeverhigher studiedin2458eyesof1240patientswithmyopia,myopic orderaberrations(HOAs)cancausemoredegradationofthe astigmatismandcompoundmyopicastigmatismand215eyes visualperformance[1-5]. of110patientswithhyperopia,hyperopicastigmatismand Customizedcornealablationhasbeensuccessfullyusedto compoundhyperopic
    [Show full text]
  • Zernike Polynomials: a Guide
    See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/241585467 Zernike polynomials: A guide Article in Journal of Modern Optics · April 2011 DOI: 10.1080/09500340.2011.633763 CITATIONS READS 41 12,492 2 authors: Vasudevan Lakshminarayanan Andre Fleck University of Waterloo Grand River Hospital 399 PUBLICATIONS 1,806 CITATIONS 40 PUBLICATIONS 1,210 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Theoretical and bench color and optics work View project Quantum Relational Databases View project All content following this page was uploaded by Vasudevan Lakshminarayanan on 13 May 2014. The user has requested enhancement of the downloaded file. Journal of Modern Optics Vol. 58, No. 7, 10 April 2011, 545–561 TUTORIAL REVIEW Zernike polynomials: a guide Vasudevan Lakshminarayanana,b*y and Andre Flecka,c aSchool of Optometry, University of Waterloo, Waterloo, Ontario, Canada; bMichigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI, USA; cGrand River Hospital, Kitchener, Ontario, Canada (Received 5 October 2010; final version received 9 January 2011) In this paper we review a special set of orthonormal functions, namely Zernike polynomials which are widely used in representing the aberrations of optical systems. We give the recurrence relations, relationship to other special functions, as well as scaling and other properties of these important polynomials. Mathematica code for certain operations are given in the Appendix. Keywords: optical aberrations; Zernike polynomials; special functions; aberrometry 1. Introduction the Zernikes will not be orthogonal over a discrete set The Zernike polynomials are a sequence of polyno- of points within a unit circle [11].
    [Show full text]