1、November 2008DEUTSCHE NORM English price group 16No part of this standard may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS 11.040.70!$Rdn“147657
2、5www.din.deDDIN EN ISO 24157Ophthalmic optics and instruments Reporting aberrations of the human eye (ISO 24157:2008)English version of DIN EN ISO 24157:2008-11Augenoptik und ophthalmische Instrumente Verfahren zur Darstellung von Abbildungsfehlern des menschlichen Auges(ISO 24157:2008)Englische Fas
3、sung DIN EN ISO 24157:2008-11www.beuth.deDocument comprises 36 pagesDIN EN ISO 24157:2008-11 2 National foreword This standard has been prepared by Technical Committee ISO/TC 172 “Optics and photonics”, Subcommittee SC 7 “Ophthalmic optics and instruments” in collaboration with Technical Committee C
4、EN/TC 170 “Ophthalmic optics” (Secretariat: DIN, Germany). The responsible German body involved in its preparation was the Normenausschuss Feinmechanik und Optik (Optics and Precision Mechanics Standards Committee). The DIN Standard corresponding to the International Standard referred to in this doc
5、ument is as follows: ISO 8429 DIN EN ISO 8429 Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. DIN shall not be held responsible for identifying any or all such patent rights. National Annex NA (informative) Bibliography DIN EN ISO
6、 8429, Optics and optical instruments Ophthalmology Graduated dial scale EUROPEAN STANDARDNORME EUROPENNEEUROPISCHE NORMEN ISO 24157July 2008ICS 11.040.70English VersionOphthalmic optics and instruments - Reporting aberrations ofthe human eye (ISO 24157:2008)Optique et instruments ophtalmiques - Mth
7、odes de Augenoptik und ophthalmische Instrumente - Verfahren zurDarstellung von Abbildungsfehlern des menschlichenAuges (ISO 24157:2008)This European Standard was approved by CEN on 29 May 2008.CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions f
8、or giving this EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such nationalstandards may be obtained on application to the CEN Management Centre or to any CEN member.This European Standard exists in three official
9、 versions (English, French, German). A version in any other language made by translationunder the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as theofficial versions.CEN members are the national standards bodies of Austria, Belgi
10、um, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STA
11、NDARDIZATIONCOMIT EUROPEN DE NORMALISATIONEUROPISCHES KOMITEE FR NORMUNGManagement Centre: rue de Stassart, 36 B-1050 Brussels 2008 CEN All rights of exploitation in any form and by any means reservedworldwide for CEN national Members.Ref. No. EN ISO 24157:2008: Eprsentation des aberrations de loeil
12、 humain(ISO 24157:2008)Contents Page 1 2 3 4 5 5.1 5.2 Representation of wavefront data in the form of wavefront gradient fields or wavefront 5.3 6 6.1 6.2 6.3 Aberration data presented in the form of normalized Zernike coefficients given in 6.4 6.5 Annex B (informative) Conversion of Zernike coeffi
13、cients to account for differing aperture sizes, Annex C (informative) Conversion between Zernike coefficients represented in different systems Annex D (informative) Computer algorithm to generate partial derivative weighting matrices for 2 DIN EN ISO 24157:2008-11 EN ISO 24157:2008 (E)Foreword. 3 Sc
14、ope . 4 Normative references . 4 Terms and definitions. 4 Coordinate system 8 Representation of wavefront data. 9 Representation of wavefront data with the use of Zernike polynomial function coefficients 9 error function values 12 Gradient fit error . 13 Presentation of data representing the aberrat
15、ions of the human eye 13 Aberration data presented in the form of normalized Zernike coefficients 14 General. 13 magnitude/axis form. 14 Aberration data presented in the form of topographical maps . 15 Annex A (informative) Methods of generating Zernike coefficients . 18 Presentation of pooled aberr
16、ation data 17 decentration and coordinate system rotation . 20 of notation . 28 un-normalized Zernike polynomial functions 30 Annex E (informative) Table of normalized Zernike polynomial functions (to 6th radial order) 32 Bibliography . 34 Foreword This document (EN ISO 24157:2008) has been prepared
17、 by Technical Committee ISO/TC 172 “Optics and optical instruments“ in collaboration with Technical Committee CEN/TC 170 “Ophthalmic optics” the secretariat of which is held by DIN. This European Standard shall be given the status of a national standard, either by publication of an identical text or
18、 by endorsement, at the latest by January 2009, and conflicting national standards shall be withdrawn at the latest by January 2009. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN and/or CENELEC shall not be held responsible
19、for identifying any or all such patent rights. According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germ
20、any, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the United Kingdom. Endorsement notice The text of ISO 24157:2008 has been approved by CEN as a EN ISO 24157:2008 wi
21、thout any modification. 3 DIN EN ISO 24157:2008-11 EN ISO 24157:2008 (E)1 Scope This International Standard specifies standardized methods for reporting aberrations of the human eye. 2 Normative references The following referenced documents are indispensable for the application of this document. For
22、 dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 8429, Optics and optical instruments Ophthalmology Graduated dial scale 3 Terms and definitions For the purposes of this document, the foll
23、owing terms and definitions apply. Symbols used are summarized in Table 1. 3.1 line of sight line from the point of interest in object space to the centre of the entrance pupil of the eye and continuing from the centre of the exit pupil to the retinal point of fixation (generally the foveola) 3.2 Ze
24、rnike polynomial function one of a complete set of functions defined and orthogonal over the unit circle, the product of three terms, a normalization term, a radial term and a meridional term, parameterized by a dimensionless radial parameter, , and a dimensionless meridional parameter, , designated
25、 by a non-negative radial integer index, n, and a signed meridional index, m, and given by the equation () ( )mmmnnnZ NR Mm = (1) where mnN is the normalization term; mnR is the radial term; M(m) is the meridional term; the parameter is a real number continuous over its range of 0 to 1,0; the parame
26、ter is a real number continuous over its range of 0 to 2. NOTE For a given value of radial index n, the meridional index m may only take the values n, n+2, , n 2 and n. 4 DIN EN ISO 24157:2008-11 EN ISO 24157:2008 (E)3.2.1 radial term Zernike polynomial function term with indices n and m given by th
27、e equation ()()( )() ()( )0,5201!0,5 ! 0,5 !nm smnsnsnsRsnms nms=+ (2) where s is an integer summation index incremented by one unit 3.2.2 radial parameter dimensionless number taking values between 0 and 1, its value at any radial distance, r, from the aperture centre being given by the expression
28、ra = (3) where a is the value of the aperture radius 3.2.3 meridional term Zernike polynomial function term with index m given by the equations ( ) ( )cosM mm = if m W 0 (4) () ()sinMm m = if m =(11) NOTE 1 Piston and average tilt should be excluded from this calculation because they correspond to l
29、ateral displacements of the image rather than image degradation per se. NOTE 2 The RMS error can also be found using the discrete set of wavefront error values that were used to generate the Zernike coefficients and standard statistical methods. When this is done it might be found that this RMS valu
30、e does not exactly match the value found using the formula given above. This is more likely to happen in cases where the locations in the pupil used to sample the wavefront error form a non-uniformly spaced grid. Then the data set does not lead to the formation of discrete, orthogonal Zernike functi
31、ons. 3.7 higher-order aberrations those aberrations experienced by the eye in addition to sphero-cylindrical refractive errors and prismatic error and thus, if the wavefront error is expressed in terms of Zernike polynomial function coefficients, those of order 3 and higher 7 DIN EN ISO 24157:2008-1
32、1 EN ISO 24157:2008 (E)3.8 wavefront gradient W(x,y) vector giving the values of the gradient of the wavefront, W(x,y)/x and W(x,y)/y, at locations x and y and, when expressed in terms of Zernike polynomial coefficients, given by: ( )all and ,(, )mm nnnmWxyZ xycxx=and ( )all and ,(, )mm nnnmWxyZ xyc
33、yy=(12) NOTE Measured gradient values are referred to by x(x,y) and y(x,y) at locations x,y. Table 1 Symbols Symbol Name Definition given in(),Am meridional term for magnitude/axis Zernike functions 5.1.9 mnc Zernike coefficient 3.3 nmc Zernike coefficient magnitude 5.1.9 m meridional index for Zern
34、ike functions 3.2 ()mnM m meridional term for Zernike functions 3.2.3 n radial index for Zernike functions 3.2 mnN normalization term for Zernike functions 3.2.5 ()mnR radial term for Zernike functions 3.2.1 mnZ Zernike function alternate notation: Z(n,m) 3.2 nmZ Zernike function magnitude/axis form
35、 5.1.9 axis parameter for magnitude/axis form Zernike functions 5.1.9 radial parameter for Zernike functions 3.2.2 meridional parameter for Zernike functions 3.2.4 W(x,y) wavefront error 3.4 x,y measured gradient at a location x,y 3.8 Wx,y wavefront gradient at a location x,yfitgradient fit error 5.
36、3 4 Coordinate system The coordinate system used to represent wavefront surfaces shall be the standard ophthalmic coordinate system in accordance with ISO 8429 in which the x-axis is local horizontal with its positive sense to the right as the examiner looks at the eye under measurement, the y-axis
37、is local vertical with its positive sense superior with respect to the eye under measurement, the z-axis is the line of sight of the eye under measurement with its positive sense in the direction from the eye toward the examiner. The horizontal and vertical origin of the coordinate system is the cen
38、tre of the visible pupil of the eye. The coordinate system origin lies in the plane of the exit pupil of the eye (for light originating on the retina and passing out through the pupil). This coordinate system is illustrated in Figure 1. 8 DIN EN ISO 24157:2008-11 EN ISO 24157:2008 (E)The sign conven
39、tion used for wavefront error values reported at any location on a wavefront shall be that used for this coordinate system. When Zernike coefficients are used to represent a wavefront or to report wavefront error, the sign convention used to describe the individual Zernike functions shall be that us
40、ed for this coordinate system. a) Coordinate system b) Clinicians view of patient Key OD right eye OS left eye Figure 1 Ophthalmic coordinate system (ISO 8429) 5 Representation of wavefront data 5.1 Representation of wavefront data with the use of Zernike polynomial function coefficients 5.1.1 Symbo
41、ls for Zernike polynomial functions Zernike polynomial functions shall be designated by the upper case letter Z followed by a superscript and a subscript. The superscript shall be a signed integer representing the meridional index of the function, m. The subscript shall be a non-negative integer rep
42、resenting the radial index of the function, n. Therefore a Zernike polynomial function shall be designated by the formmnZ . If, for reasons of font availability, it is not possible to write superscript and subscripts, the Zernike polynomial functions may be represented as a upper case letter Z follo
43、wed by parentheses in which the radial index, n, appears first, followed, after a comma, by the meridional index, m, thus Z(n,m). 5.1.2 Radial index The radial index shall be designated by the lower case letter n. 5.1.3 Meridional index The meridional index shall be designated by the lower case lett
44、er m. 5.1.4 Radial parameter The radial parameter shall be designated by the Greek letter . 5.1.5 Meridional parameter The meridional parameter shall be designated by the Greek letter . 9 DIN EN ISO 24157:2008-11 EN ISO 24157:2008 (E)5.1.6 Coefficients When a surface is represented by Zernike coeffi
45、cients, these coefficients shall be designated by the lower case letter c followed by a superscript and a subscript. The superscript shall be a signed integer representing the meridional index of the function, m. The subscript shall be a non-negative integer representing the radial index of the func
46、tion, n. Therefore, a Zernike coefficient shall be designated by the formmnc . 5.1.7 Common names of Zernike polynomial functions Zernike polynomial functions are often referred to by their common names. These names are given in Table 2 in so far as the functions have been given a common name. Table
47、 2 Common names of Zernike polynomial functions Zernike function Common name 00Z piston 11Zvertical tilt11Z horizontal tilt 22Zoblique astigmatism 02Z myopic defocus (positive coefficient value) hyperopic defocus (negative coefficient value) 22Z against the rule astigmatism (positive coefficient val
48、ue) with the rule astigmatism (negative coefficient value) 33Zoblique trefoil 13Zvertical coma superior steepening (positive coefficient value) vertical coma inferior steepening (negative coefficient value) 13Z horizontal coma 33Z horizontal trefoil 44Zoblique quatrefoil 24Zoblique secondary astigma
49、tism 04Z spherical aberration positive coefficient value pupil periphery more myopic than centre negative coefficient value pupil periphery more hyperopic than centre 24Z with/against the rule secondary astigmatism 44Z quatrefoil 15Zsecondary vertical coma 15Z secondary horizontal coma 10 DIN EN ISO 24157:2008-11 EN ISO 24157:2008 (E)5.1.8 Comparison of data expressed as Zernike coefficients generated using different aperture sizes The Zernike coefficient value
