ISO INTERNATIONAL STANDARD 24157 First edition 2008-07-01 Ophthalmic optics and instruments - Reporting aberrations of the human eye Optique et instruments ophtalmiques - Methodes de presentation des aberrations de I'ceil humain Reference number ISO 24157:2008(E) @ ISO 2008 ISO 24157:2008(E) PDFdisclaimer This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In accepts no liability in this area. Adobe is a trademark of Adobe Systems Incorporated. Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by IsO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. COPYRIGHTPROTECTEDDOCUMENT @ISO2008 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, Iso's member body in the country of the requester. ISO copyright office Case postale 56 : CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyright@iso.org Web www.iso.org Published in Switzerland ii ISO2008-All rights reserved ISO24157:2008(E) Contents Page Foreword. 1 Scope 2 Normative references 3 Terms and definitions. 4 Coordinate system 5 5 Representation of wavefront data.. 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 errorfunctionvalues. 5.3 Gradient fit error 10 6 Presentation of data representing the aberrations of the human eye . 6.1 General... .10 6.2 Aberration data presented in the form of normalized Zernike coefficients. .11 6.3 AberrationdatapresentedintheformofnormalizedZernikecoefficientsgivenin magnitude/axis form.. .11 6.4 Aberration data presented in the form of topographical maps 12 6.5 Presentation of pooled aberration data...... Annex A (informative) Methods of generating Zernike coefficients Annex B (informative) Conversion of Zernike coefficients to account for differing aperture sizes, decentration and coordinate system rotation .. Annex C (informative) Conversion between Zernike coefficients represented in different systems of notation .... 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 @ IS0 2008 - All rights reserved ili