1、BS EN ISO24157:2008ICS 11.040.70NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBRITISH STANDARDOphthalmic opticsand instruments Reporting aberrationsof the human eye (ISO24157:2008)This British Standardwas published under theauthority of the StandardsPolicy and StrategyCommitt
2、ee on 31 July 2008 BSI 2008ISBN 978 0 580 61237 4Amendments/corrigenda issued since publicationDate CommentsBS EN ISO 24157:2008National forewordThis British Standard is the UK implementation of EN ISO 24157:2008.The UK participation in its preparation was entrusted to TechnicalCommittee CH/172/6, O
3、phthalmic instruments.A list of organizations represented on this committee can be obtained onrequest to its secretary.This publication does not purport to include all the necessary provisionsof a contract. Users are responsible for its correct application.Compliance with a British Standard cannot c
4、onfer immunityfrom legal obligations.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 - Mthodes deprsentation des aberrations d
5、e loeil humain (ISO24157:2008)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 stip
6、ulate the conditions for 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 ex
7、ists in three official 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 bo
8、dies of Austria, Belgium, 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.EURO
9、PEAN COMMITTEE FOR STANDARDIZATIONCOMIT 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: EBS EN ISO 2415
10、7:2008EN ISO 24157:2008 (E) 3 Foreword This document (EN ISO 24157:2008) has been prepared 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
11、 be given the status of a national standard, either by publication of an identical text or 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 docum
12、ent may be the subject of patent rights. CEN and/or CENELEC shall not be held responsible 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: A
13、ustria, Belgium, 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 the United Kingdom. Endors
14、ement notice The text of ISO 24157:2008 has been approved by CEN as a EN ISO 24157:2008 without any modification. BS EN ISO 24157:2008ISO 24157:2008(E) ISO 2008 All rights reserved iiiContents Page Foreword iv 1 Scope . 1 2 Normative references . 1 3 Terms and definitions. 1 4 Coordinate system 5 5
15、Representation of wavefront data. 6 5.1 Representation of wavefront data with the use of Zernike polynomial function coefficients 6 5.2 Representation of wavefront data in the form of wavefront gradient fields or wavefront error function values 9 5.3 Gradient fit error . 10 6 Presentation of data re
16、presenting the aberrations of the human eye 10 6.1 General. 10 6.2 Aberration data presented in the form of normalized Zernike coefficients 11 6.3 Aberration data presented in the form of normalized Zernike coefficients given in magnitude/axis form. 11 6.4 Aberration data presented in the form of to
17、pographical maps . 12 6.5 Presentation of pooled aberration data 14 Annex A (informative) Methods of generating Zernike coefficients . 15 Annex B (informative) Conversion of Zernike coefficients to account for differing aperture sizes, decentration and coordinate system rotation . 17 Annex C (inform
18、ative) Conversion between Zernike coefficients represented in different systems of notation . 25 Annex D (informative) Computer algorithm to generate partial derivative weighting matrices for un-normalized Zernike polynomial functions 27 Annex E (informative) Table of normalized Zernike polynomial f
19、unctions (to 6th radial order) 29 Bibliography . 31 BS EN ISO 24157:2008ISO 24157:2008(E) iv ISO 2008 All rights reservedForeword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International S
20、tandards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, als
21、o take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committe
22、es is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possi
23、bility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 24157 was prepared by Technical Committee ISO/TC 172, Optics and photonics, Subcommittee SC 7, Ophthalmic optics and instruments
24、. BS EN ISO 24157:2008INTERNATIONAL STANDARD ISO 24157:2008(E) ISO 2008 All rights reserved 1Ophthalmic optics and instruments Reporting aberrations of the human eye 1 Scope This International Standard specifies standardized methods for reporting aberrations of the human eye. 2 Normative references
25、The following referenced documents are indispensable for the application of this document. For 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 Ophthalm
26、ology Graduated dial scale 3 Terms and definitions For the purposes of this document, the following 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 fro
27、m the centre of the exit pupil to the retinal point of fixation (generally the foveola) 3.2 Zernike 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
28、 by a dimensionless radial parameter, , and a dimensionless meridional parameter, , designated 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 mer
29、idional term; the parameter is a real number continuous over its range of 0 to 1,0; the parameter 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, , n2 and n. BS EN ISO 24157:2008ISO 24157:2008(E)
30、2 ISO 2008 All rights reserved3.2.1 radial term Zernike polynomial function term with indices n and m given by the 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 val
31、ues between 0 and 1, its value at any radial distance, r, from the aperture centre being given by the expression 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
32、= if m =(11) NOTE 1 Piston and average tilt should be excluded from this calculation because they correspond to lateral 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
33、the Zernike coefficients and standard statistical methods. When this is done it might be found that this RMS value 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 n
34、on-uniformly spaced grid. Then the data set does not lead to the formation of discrete, orthogonal Zernike functions. 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 expr
35、essed in terms of Zernike polynomial function coefficients, those of order 3 and higher BS EN ISO 24157:2008ISO 24157:2008(E) ISO 2008 All rights reserved 53.8 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 e
36、xpressed in terms of Zernike polynomial coefficients, given by: ( )all and ,(, )mm nnnmWxyZ xycxx=and ( )all and ,(, )mm nnnmWxyZ xycyy=(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 m
37、agnitude/axis Zernike functions 5.1.9 mnc Zernike coefficient 3.3 nmc Zernike coefficient magnitude 5.1.9 m meridional index for Zernike 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
38、 radial term for Zernike functions 3.2.1 mnZ Zernike function alternate notation: Z(n,m) 3.2 nmZ Zernike function magnitude/axis form 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
39、,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 5.3 4 Coordinate system The coordinate system used to represent wavefront surfaces shall be the standard ophthalmic coordinate system in accordance with ISO 8429 in whic
40、h 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 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 pos
41、itive sense in the direction from the eye toward the examiner. The horizontal and vertical origin of the coordinate system is the centre 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 t
42、hrough the pupil). This coordinate system is illustrated in Figure 1. BS EN ISO 24157:2008ISO 24157:2008(E) 6 ISO 2008 All rights reservedThe sign convention used for wavefront error values reported at any location on a wavefront shall be that used for this coordinate system. When Zernike coefficien
43、ts are used to represent a wavefront or to report wavefront error, the sign convention used to describe the individual Zernike functions shall be that used for this coordinate system. a) Coordinate system b) Clinicians view of patient Key OD right eye OS left eye Figure 1 Ophthalmic coordinate syste
44、m (ISO 8429) 5 Representation of wavefront data 5.1 Representation of wavefront data with the use of Zernike polynomial function coefficients 5.1.1 Symbols for Zernike polynomial functions Zernike polynomial functions shall be designated by the upper case letter Z followed by a superscript and a sub
45、script. 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 function, n. Therefore a Zernike polynomial function shall be designated by the formmnZ . If, for reasons of font
46、 availability, it is not possible to write superscript and subscripts, the Zernike polynomial functions may be represented as a upper case letter Z followed 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 inde
47、x 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 letter m. 5.1.4 Radial parameter The radial parameter shall be designated by the Greek letter . 5.1.5 Meridional parameter The meridional parameter sha
48、ll be designated by the Greek letter . BS EN ISO 24157:2008ISO 24157:2008(E) ISO 2008 All rights reserved 75.1.6 Coefficients When a surface is represented by Zernike coefficients, these coefficients shall be designated by the lower case letter c followed by a superscript and a subscript. The supers
49、cript 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 function, 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 comm
