1、BSI Standards PublicationBS ISO 14999-4:2015Optics and photonics Interferometric measurementof optical elements and opticalsystemsPart 4: Interpretation and evaluation oftolerances specified in ISO 10110BS ISO 14999-4:2015 BRITISH STANDARDNational forewordThis British Standard is the UK implementati
2、on of ISO 14999-4:2015.It supersedes BS ISO 14999-4:2007 which is withdrawn.The UK participation in its preparation was entrusted to TechnicalCommittee CPW/172, Optics and Photonics.A list of organizations represented on this committee can beobtained on request to its secretary.This publication does
3、 not purport to include all the necessaryprovisions of a contract. Users are responsible for its correctapplication. The British Standards Institution 2015. Published by BSI StandardsLimited 2015ISBN 978 0 580 79515 2ICS 37.020Compliance with a British Standard cannot confer immunity fromlegal oblig
4、ations.This British Standard was published under the authority of theStandards Policy and Strategy Committee on 31 July 2015.Amendments issued since publicationDate Text affectedBS ISO 14999-4:2015 ISO 2015Optics and photonics Interferometric measurement of optical elements and optical systems Part
5、4: Interpretation and evaluation of tolerances specified in ISO 10110Optique et photonique Mesurage interfromtrique de composants et de systmes optiques Partie 4: Directives pour lvaluation des tolrances spcifies dans lISO 10110INTERNATIONAL STANDARDISO14999-4Second edition2015-08-01Reference number
6、ISO 14999-4:2015(E)BS ISO 14999-4:2015ISO 14999-4:2015(E)ii ISO 2015 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2015, Published in SwitzerlandAll rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form or by any means, ele
7、ctronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISOs member body in the country of the requester.ISO copyright officeCh. de Blandonnet 8 CP 401CH-1214 Verni
8、er, Geneva, SwitzerlandTel. +41 22 749 01 11Fax +41 22 749 09 47copyrightiso.orgwww.iso.orgBS ISO 14999-4:2015ISO 14999-4:2015(E)Foreword ivIntroduction v1 Scope .12 Normative references 13 Terms and definitions .13.1 Mathematical definitions . 13.2 Definition of optical functions . 23.3 Definition
9、of values related to the optical functions defined in 3.2 . 43.4 Definition of Zernike polynomials 73.5 Definitions of functions and terms for tolerancing the slope deviation 73.6 Definitions of values for tolerancing the slope deviation. 84 Relating interferometric measurements to surface form devi
10、ation or transmitted wavefront deformation .114.1 Test areas 114.2 Quantities . 114.3 Single-pass transmitted wavefront deformation 114.4 Double-pass transmitted wavefront deformation .114.5 Surface form deviation 114.6 Conversion to other wavelengths 115 Representation of the measured wavefront dev
11、iation as Zernike coefficients 126 Tolerancing of the slope deviation 126.1 One-dimensional measurement of the slope deviation 126.2 Two-dimensional measurement of the slope deviation .15Annex A (normative) Visual interferogram analysis 16Annex B (normative) Zernike polynomials 24Bibliography .27 IS
12、O 2015 All rights reserved iiiContents PageBS ISO 14999-4:2015ISO 14999-4:2015(E)ForewordISO (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
13、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
14、 closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular the different approval crite
15、ria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).Attention is drawn to the possibility that some of the elements of this document may be the subject of
16、patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents).Any trade name u
17、sed in this document is information given for the convenience of users and does not constitute an endorsement.For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISOs adherence to the WTO principles in the Technical B
18、arriers to Trade (TBT) see the following URL: Foreword - Supplementary information.The committee responsible for this document is ISO/TC 172, Optics and photonics, Subcommittee SC 1, Fundamental standards.This second edition cancels and replaces the first edition (ISO 14999-4:2007), which constitute
19、s the following changes:a) clauses for tolerancing cylindrical and torical wavefronts, the representation of the measured wavefront deformation in terms of Zernike coefficients, and for tolerancing of the slope deviation have been added;b) the name of quantity A has been changed to power deviation.
20、For further details, see 3.3.1, Note 2 to entry.ISO 14999 consists of the following parts, under the general title Optics and photonics Interferometric measurement of optical elements and optical systems: Part 1: Terms, definitions and fundamental relationships Technical Report Part 2: Measurement a
21、nd evaluation techniques Technical Report Part 3: Calibration and validation of interferometric test equipment and measurements Technical Report Part 4: Interpretation and evaluation of tolerances specified in ISO 10110iv ISO 2015 All rights reservedBS ISO 14999-4:2015ISO 14999-4:2015(E)Introduction
22、This part of ISO 14999 provides a theoretical frame upon which are based indications from ISO 10110-5 and/or ISO 10110-14.A table listing the corresponding nomenclature, functions, and values used in ISO 10110-5 and ISO 14999-4 is given in ISO 10110-5, Annex B.ISO 10110-5 refers to deformations in t
23、he form of an optical surface and provides a means for specifying tolerances for certain types of surface deformations in terms of “nanometers”.ISO 10110-14 refers to deformations of a wavefront transmitted once through an optical system and provides a means of specifying similar deformation types i
24、n terms of optical “wavelengths”.As it is common practice to measure the surface form deviation interferometrically as the wavefront deformation caused by a single reflection from the optical surface at normal (90 to surface) incidence, it is possible to describe a single definition of interferometr
25、ic data reduction that can be used in both cases. One “fringe spacing” (as defined in ISO 10110-5) is equal to a surface deformation that causes a deformation of the reflected wavefront of one wavelength.Certain scaling factors apply depending on the type of interferometric arrangement, e.g. whether
26、 the test object is being measured in single pass or double pass.Due to the potential for confusion and misinterpretation, units of nanometres rather than units of “fringe spacings” or “wavelengths” are to be used for the value of surface form deviation or the value of wavefront deformation, where p
27、ossible. Where “fringe spacings” or “wavelengths” are used as units, the wavelength is also to be specified. ISO 2015 All rights reserved vBS ISO 14999-4:2015BS ISO 14999-4:2015Optics and photonics Interferometric measurement of optical elements and optical systems Part 4: Interpretation and evaluat
28、ion of tolerances specified in ISO 101101 ScopeThis part of ISO 14999 applies to the interpretation of interferometric data relating to the measurement of optical elements.This part of ISO 14999 gives definitions of the optical functions and values specified in the preparation of drawings for optica
29、l elements and systems, made in accordance with ISO 10110-5 and/or ISO 10110-14 for which the corresponding nomenclature, functions, and values are listed in ISO 10110-5, Annex B. It also provides guidance for their interferometric evaluation by visual analysis.2 Normative referencesThe following do
30、cuments, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 10110-5, Optics and
31、photonics Preparation of drawings for optical elements and systems Part 5: Surface form tolerancesISO 10110-14, Optics and photonics Preparation of drawings for optical elements and systems Part 14: Wavefront deformation toleranceISO/TR 14999-2, Optics and photonics Interferometric measurement of op
32、tical elements and optical systems Part 2: Measurement and evaluation techniques3 Terms and definitions3.1 Mathematical definitions3.1.1functionmathematical description of the measured wavefront deformation and its decomposition into componentsNote 1 to entry: The functions used in this part of ISO
33、14999 are scalar functions.3.1.2peak-to-valley valuePV ( f )maximum value of the function within the region of interest minus the minimum value of the function within the region of interest3.1.3root mean square valuerms ( f )value given by either of the following integral expressions:INTERNATIONAL S
34、TANDARD ISO 14999-4:2015(E) ISO 2015 All rights reserved 1BS ISO 14999-4:2015ISO 14999-4:2015(E)a) Cartesian variables x and yrms ()ddddwhereffxyxyxyxyxyx=(),212yyA()b) Polar variables r and rms (ddddwhereffr rrrrrr),=()212rA,()Note 1 to entry: This integral may be approximated by the standard devia
35、tion if the usage includes removal of the mean value of the wavefront (piston) and provided that the measurement resolution is specified and is sufficient.3.2 Definition of optical functionsNOTE 1 For the relationship of interferometric measurements to surface form deviation and transmitted wavefron
36、t deformation, see Clause 4.NOTE 2 The optical functions given in this subclause are used either for rotationally invariant (spherical or aspherical) wavefronts (depicted in Figure 1) or cylindrical wavefronts (depicted in Figure 2). The functions corresponding to each are grouped together; the func
37、tions for rotationally invariant wavefronts first and the functions for cylindrical wavefronts follow. The functions for rotationally invariant wavefronts are unchanged with respect to ISO 14999-4:2007.NOTE 3 The term cylindrical waveform is used here as synonym for circular cylindrical, non-circula
38、r cylindrical, and torical wavefronts. The functions can also be applied for general wavefronts that are close to cylindrical or torical ones.3.2.1measured wavefront deformationfMWDfunction representing the distances between the measured wavefront and the nominal theoretical wavefront, measured norm
39、al to the nominal theoretical wavefrontNote 1 to entry: See Figure 1 a) and Figure 2 a).Note 2 to entry: In case of tactile measurement where the measurement values are usually taken along z-direction, the measurement values have to be converted to the measured wavefront deformation fMWD(distance pe
40、rpendicular to the theoretical surface).3.2.2tiltfTLTplane function representing the best (in the sense of the rms fit) linear approximation to the measured wavefront deformation fMWDNote 1 to entry: See Figure 1 b) and Figure 2 b).3.2.3twist-function describing rotational misalignment for cylindric
41、al wavefrontsfTWSTfunction of the saddle form used for eliminating rotational misalignmentfxyconst xyTWST(,).*=2 ISO 2015 All rights reservedBS ISO 14999-4:2015ISO 14999-4:2015(E)Note 1 to entry: See Figure 2 c).Note 2 to entry: A rotational misalignment (twist) of the cylindrical axes of the test w
42、ave and the surface (respectively, the object under test and the optics generating or compensating the cylindrical or torical phase front) results in an additive term in the form of a saddle. This term could be eliminated or minimized by careful alignment of the setup. In most practical cases, it is
43、 more useful to eliminate this term by removing it mathematically.3.2.4wavefront deformationfWDfunction resulting after subtraction of the tilt fTLTfrom the measured wavefront deformation fMWDff fWD MWDTLT=Note 1 to entry: See Figure 1 c).3.2.5wavefront deformation for cylindrical wavefrontsfWD,CYfu
44、nction resulting after subtraction of the tilt fTLTand fTWSTfrom the measured wavefront deformation, fMWDfxyf xy fxyf xyWD,CYMWD TLTTWST(,)(,) (,)(,)=Note 1 to entry: See Figure 2 d).3.2.6wavefront spherical approximationfWSfunction of spherical form that best (in the sense of the rms fit) approxima
45、tes the wavefront deformation fWDNote 1 to entry: See Figure 1 d).3.2.7wavefront circular cylindrical approximationfWC, x, fWC, yfunctions of cylindrical form that best (in the sense of the rms fit) approximate the wavefront deformation fWD,CYfxyR RxconstWC,x x,fitx,fit(,).= +22fxyR RyconstWC,y y,fi
46、ty,fit(, = +22Note 1 to entry: See Figure 2 e) and Figure 2 f).3.2.8wavefront irregularityfWIfunction resulting after subtraction of the wavefront spherical approximation fWSfrom the wavefront deformation fWDff fWI WD WS=Note 1 to entry: See Figure 1 e). ISO 2015 All rights reserved 3BS ISO 14999-4:
47、2015ISO 14999-4:2015(E)3.2.9wavefront irregularity for cylindrical wavefrontsfWI, CYfunction resulting after subtraction of the wavefront circular cylindrical approximations fWC, xand fWC, yfxyf xy fxyf xyWI, CY WD, CY WC,xWC,y(,)(,) (,)(,)=Note 1 to entry: See Figure 2 g).3.2.10wavefront aspheric a
48、pproximationfWRIrotationally invariant aspherical function that best (in the sense of the rms fit) approximates the wavefront irregularity, fWINote 1 to entry: See Figure 1 f).3.2.11wavefront non-circular cylindrical approximationfWTI, x, fWTI, ytranslationally invariant non-circular cylindrical fun
49、ction that best (in the sense of the rms fit) approximates the wavefront irregularity for cylindrical wavefronts, fWI, CYin x and y direction, respectivelyfxyf xWTI,xWTI,x(,)=()fxyf yWTI,yWTI,y(,)=()Note 1 to entry: See Figure 2 h) and Figure 2 i).3.2.12rotationally varying wavefront deviationfWRVfunction resulting after subtraction of the wavefront aspheric approximation fWRIfrom the wavefront irregularity fWIfffWRVWIWRI=Note 1 to entry: See Figure 1 g)
