EN ISO 24157:2008
(Main)Ophthalmic optics and instruments - Reporting aberrations of the human eye (ISO 24157:2008)
Ophthalmic optics and instruments - Reporting aberrations of the human eye (ISO 24157:2008)
ISO 24157:2008 specifies standardized methods for reporting aberrations of the human eye.
Augenoptik und ophthalmische Instrumente - Verfahren zur Darstellung von Abbildungsfehlern des menschlichen Auges (ISO 24157:2008)
Diese Internationale Norm legt genormte Verfahren zur Darstellung der Aberrationen des menschlichen Auges fest.
Optique et instruments ophtalmiques - Méthodes de présentation des aberrations de l'oeil humain (ISO 24157:2008)
L'ISO 24157:2008 spécifie les méthodes normalisées permettant de consigner les aberrations de l'œil humain.
Očesna optika in instrumenti - Postopek prikaza aberacije človeškega očesa (ISO 24157:2008)
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-september-2008
2þHVQDRSWLNDLQLQVWUXPHQWL3RVWRSHNSULND]DDEHUDFLMHþORYHãNHJDRþHVD ,62
Ophthalmic optics and instruments - Reporting aberrations of the human eye (ISO
24157:2008)
Augenoptik und ophthalmische Instrumente - Verfahren zur Darstellung von
Abbildungsfehlern des menschlichen Auges (ISO 24157:2008)
Optique et instruments ophtalmiques - Méthodes de présentation des aberrations de
l'oeil humain (ISO 24157:2008)
Ta slovenski standard je istoveten z: EN ISO 24157:2008
ICS:
11.040.70 Oftalmološka oprema Ophthalmic equipment
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EUROPEAN STANDARD
EN ISO 24157
NORME EUROPÉENNE
EUROPÄISCHE NORM
July 2008
ICS 11.040.70
English Version
Ophthalmic optics and instruments - Reporting aberrations of
the human eye (ISO 24157:2008)
Optique et instruments ophtalmiques - Méthodes de Augenoptik und ophthalmische Instrumente - Verfahren zur
présentation des aberrations de l'oeil humain (ISO Darstellung von Abbildungsfehlern des menschlichen
24157:2008) Auges (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 for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the
official versions.
CEN members are the national standards bodies 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.
EUROPEAN COMMITTEE FOR STANDARDIZATION
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EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36 B-1050 Brussels
© 2008 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 24157:2008: E
worldwide for CEN national Members.
Contents Page
Foreword.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 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 document 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: 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 the United Kingdom.
Endorsement notice
The text of ISO 24157:2008 has been approved by CEN as a EN ISO 24157:2008 without any modification.
INTERNATIONAL ISO
STANDARD 24157
First edition
2008-07-01
Ophthalmic optics and instruments —
Reporting aberrations of the human eye
Optique et instruments ophtalmiques — Méthodes de présentation des
aberrations de l'œil humain
Reference number
ISO 24157:2008(E)
©
ISO 2008
ISO 24157:2008(E)
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ii © ISO 2008 – All rights reserved
ISO 24157:2008(E)
Contents Page
Foreword. iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 Coordinate system. 5
5 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 representing 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 topographical 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 (informative) 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 functions (to 6th radial order). 29
Bibliography . 31
ISO 24157:2008(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards 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, also 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 committees 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 possibility 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.
iv © ISO 2008 – All rights reserved
INTERNATIONAL STANDARD ISO 24157:2008(E)
Ophthalmic 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
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 — Ophthalmology — 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 from
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 by a dimensionless radial parameter, ρ,
and a dimensionless meridional parameter, θ, designated by a non-negative radial integer index, n, and a
signed meridional index, m, and given by the equation
m
mm
Z =NR ρ M mθ (1)
() ( )
nnn
where
m
N is the normalization term;
n
m
R is the radial term;
n
M(mθ) is the meridional term;
the parameter ρ is a real number continuous over its range of 0 to 1,0;
the parameter θ is a real number continuous over its range of 0 to 2π.
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.
ISO 24157:2008(E)
3.2.1
radial term
Zernike polynomial function term with indices n and m given by the equation
0,5nm−
( ) s
()−−1!(ns)
m
ns−2
Rρρ= (2)
()
n ∑
⎡⎤⎡ ⎤
sn!0,5 +−m s ! 0,5n−m−s !
() ()
s=0
⎣⎦⎣ ⎦
where s is an integer summation index incremented by one unit
3.2.2
radial parameter
ρ
dimensionless number taking values between 0 and 1, its value at any radial distance, r, from the aperture
centre being given by the expression
r
ρ = (3)
a
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
Mmmθ = cos θ if m W 0 (4)
( ) ( )
Mm()θ = sin m θ if m < 0 (5)
()
NOTE The meridional term is also known as the azimuthal term.
3.2.4
meridional parameter
θ
angular value taking values between 0 and 2π (0° and 360°), expressed in the coordinate system defined in
Clause 4
NOTE This is also called the azimuthal angle.
3.2.5
normalization term
Zernike polynomial function term with indices n and m, equal to 1,0 for “un-normalized” functions (3.2.7) and
for “normalized” functions (3.2.6) by the equation
m
Nn=−21δ + (6)
()
()
nm0,
where δ = 1 if m = 0, δ = 0 if m ≠ 0.
0,m 0,m
3.2.6
normalized Zernike polynomial function
Zernike polynomial function whose normalization term takes the form given in 3.2.5 for “normalized” functions
defined as orthogonal in the sense that it satisfies the following equation
12π
...
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