1、April 2016 English price group 12No part of this translation 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 01.100.20; 37.020!%Q-“2469710www.d
2、in.deDIN ISO 10110-12Optics and photonics Preparation of drawings for optical elements and systems Part 12: Aspheric surfaces (ISO 10110-12:2007 + Amd 1:2013),English translation of DIN ISO 10110-12:2016-04Optik und Photonik Erstellung von Zeichnungen fr optische Elemente und Systeme Teil 12: Asphri
3、sche Oberflchen (ISO 10110-12:2007 + Amd 1:2013),Englische bersetzung von DIN ISO 10110-12:2016-04Optique et photonique Prparation des dessins pour lments et systmes optiques Partie 12: Surfaces asphriques (ISO 10110-12:2007 + Amd 1:2013),Traduction anglaise de DIN ISO 10110-12:2016-04SupersedesDIN
4、ISO 10110-12:2009-01www.beuth.deDTranslation by DIN-Sprachendienst.In case of doubt, the German-language original shall be considered authoritative.Document comprises 23 pages 04.16 DIN ISO 10110-12:2016-04 2 A comma is used as the decimal marker. Contents Page National foreword . 3 National Annex N
5、A (informative) Bibliography 5 1 Scope 6 2 Normative references 6 3 Mathematical description of aspheric surfaces . 6 3.1 General 6 3.1.1 Coordinate system 6 3.1.2 Sign conventions 7 3.2 Classification of surface type 8 3.3 Special surface types 8 3.3.1 Surfaces of second order 8 3.3.2 Surfaces of h
6、igher order 10 4 Indications in drawings . 12 4.1 Indication of the theoretical surface . 12 4.2 Indication of surface form tolerances . 12 4.3 Indication of centring tolerances . 13 4.4 Indication of surface imperfection and surface texture tolerances 13 5 Examples . 13 5.1 Parts with a symmetric a
7、spheric surface, coincident mechanical and optical axes 13 5.2 Parts with a symmetric aspheric surface, with the optical and mechanical axes not coincident . 16 5.3 Parts with a non-rotationally-symmetric aspheric surface 18 Annex A (normative) Summary of aspheric surface types . 20 Annex B (normati
8、ve) !Description of an orthogonal polynomial“ . 21 Bibliography . 23 DIN ISO 10110-12:2016-04 3 National foreword This document (ISO 10110-12:2007 + Amd.1:2013) has been prepared by Technical Committee ISO/TC 172 “Optics and photonics”, Subcommittee SC 1 “Fundamental standards” (Secretariat: DIN, Ge
9、rmany). The responsible German body involved in its preparation was DIN-Normenausschuss Feinmechanik und Optik (DIN Standards Committee Optics and Precision Mechanics), Working Committee NA 027-01-02 AA Grundnormen fr die Optik, Working Group Zeichnungen fr die Optik. Attention is drawn to the possi
10、bility that some elements of this document may be the subject of patent rights. DIN and/or DKE shall not be held responsible for identifying any or all such patent rights. DIN ISO 10110 consists of the following parts, under the general title Optics and photonics Preparation of drawings for optical
11、elements and systems: Part 1: General Part 2: Material imperfections Stress birefringence Part 3: Material imperfections Bubbles and inclusions Part 4: Material imperfections Inhomogeneity and striae Part 5: Surface form tolerances Part 6: Centring tolerances Part 7: Surface imperfection tolerances
12、Part 8: Surface texture Roughness and waviness Part 9: Surface treatment and coating Part 10: Table representing data of optical elements and cemented assemblies Part 11: Non-toleranced data Part 12: Aspheric surfaces Part 14: Wavefront deformation tolerance Part 17: Laser irradiation damage thresho
13、ld Part 19: General description of surfaces and components The DIN Standards corresponding to the International Standards referred to in this document are as follows: ISO 1101 DIN EN ISO 1101 ISO 10110-1 DIN ISO 10110-1 ISO 10110-5 DIN ISO 10110-5 ISO 10110-6 DIN ISO 10110-6 ISO 10110-7 DIN ISO 1011
14、0-7 ISO 10110-8 DIN ISO 10110-8 DIN ISO 10110-12:2016-04 4 Amendments This standard differs from DIN ISO 10110-12:2009-01 as follows: a) Subclause 3.3.2.4 “Combined surface based on an orthogonal polynomial” has been added; b) in the table in Annex A, a new row for “Sphere” has been added; c) Amendm
15、ent 1 to International Standard ISO 10110-12:2007 (ISO 10110-12:2007/Amd.1:2013) has been incorporated. Previous editions DIN ISO 10110-12: 2000-02, 2009-01 DIN ISO 10110-12:2016-04 5 National Annex NA (informative) Bibliography DIN EN ISO 1101, Geometrical Product Specifications (GPS) Geometrical t
16、olerancing Tolerances of form, orientation, location and run-out DIN EN ISO 4288, Geometrical Product Specifications (GPS) Surface texture: Profile method Rules and procedures for the assessment of surface texture DIN ISO 10110-1, Optics and photonics Preparation of drawings for optical elements and
17、 systems Part 1: General DIN ISO 10110-2, Optics and optical instruments Preparation of drawings for optical elements and systems Part 2: Material imperfections Stress birefringence DIN ISO 10110-3, Optics and optical instruments Preparation of drawings for optical elements and systems Part 3: Mater
18、ial imperfections Bubbles and inclusions DIN ISO 10110-4, Optics and optical instruments Preparation of drawings for optical elements and systems Part 4: Material imperfections Inhomogeneity and striae DIN ISO 10110-5, Optics and photonics Preparation of drawings for optical elements and systems Par
19、t 5: Surface form tolerances DIN ISO 10110-5 Supplement 1, Optics and photonics Preparation of drawings for optical elements and systems Part 5: Surface form tolerances Surface form tolerance inspection using testing glasses DIN ISO 10110-6, Optics and photonics Preparation of drawings for optical e
20、lements and systems Part 6: Centring tolerances DIN ISO 10110-7, Optics and photonics Preparation of drawings for optical elements and systems Part 7: Surface imperfection tolerances DIN ISO 10110-8, Optics and photonics Preparation of drawings for optical elements and systems Part 8: Surface textur
21、e Roughness and waviness DIN ISO 10110-9, Optics and optical instruments Preparation of drawings for optical elements and systems Part 9: Surface treatment and coating DIN ISO 10110-10, Optics and photonics Preparation of drawings for optical elements and systems Part 10: Table representing data of
22、optical elements and cemented assemblies DIN ISO 10110-11, Optics and optical instruments Preparation of drawings for optical elements and systems Part 11: Non-toleranced data DIN ISO 10110-14, Optics and photonics Preparation of drawings for optical elements and systems Part 14: Wavefront deformati
23、on tolerance DIN ISO 10110-17, Optics and photonics Preparation of drawings for optical elements and systems Part 17: Laser irradiation damage threshold DIN ISO 10110-19, Optics and photonics Preparation of drawings for optical elements and systems Part 19: General description of surfaces and compon
24、ents DIN ISO 10110 Supplement 1, Optics and photonics Preparation of drawings for optical elements and systems Supplement 1: Comparison DIN ISO 10110 DIN 3140, Index DIN Taschenbuch 304, Technische Produktdokumentation Erstellung von Zeichnungen fr optische Elemente und Systeme DIN ISO 10110-12:2016
25、-04 6 Optics and photonics Preparation of drawings for optical elements and systems Part 12: Aspheric surfaces 1 Scope The ISO 10110 series specifies the presentation of design and functional requirements for optical elements in technical drawings used for manufacturing and inspection. This part of
26、ISO 10110 specifies rules for presentation, dimensioning and tolerancing of optically effective surfaces of aspheric form. This part of ISO 10110 does not apply to discontinuous surfaces such as Fresnel surfaces or gratings. This part of ISO 10110 does not specify the method by which compliance with
27、 the specifications is to be tested. 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
28、) applies. ISO 1101:2004, Geometrical Product Specifications (GPS) Geometrical tolerancing Tolerances of form, orientation, location and run-out ISO 10110-1, Optics and photonics Preparation of drawings for optical elements and systems Part 1: General ISO 10110-5, Optics and photonics Preparation of
29、 drawings for optical elements and systems Part 5: Surface form tolerances ISO 10110-6, Optics and optical instruments Preparation of drawings for optical elements and systems Part 6: Centring tolerances ISO 10110-7, Optics and photonics Preparation of drawings for optical elements and systems Part
30、7: Surface imperfection tolerances ISO 10110-8, Optics and optical instruments Preparation of drawings for optical elements and systems Part 8: Surface texture 3 Mathematical description of aspheric surfaces 3.1 General 3.1.1 Coordinate system Aspheric surfaces are described in a right-handed, ortho
31、gonal coordinate system in which the Z axis is the optical axis. DIN ISO 10110-12:2016-04 7 Unless otherwise specified, the Z axis is in the plane of the drawing and runs from left to right; if only one cross-section is drawn, the Y axis is in the plane of the drawing and is oriented upwards. If two
32、 cross-sections are drawn, the XZ cross-section shall appear below the YZ cross-section (see Figure 5). For clarity the X- and Y-axes may be shown on the drawing. The origin of the coordinate system is at the vertex of the aspheric surface (see Figure 1). Figure 1 Coordinate system 3.1.2 Sign conven
33、tions NOTE !1“ As will be shown later in this part of ISO 10110, the various types of aspheric surface are given by mathematical equations. In drawings the chosen equation and the corresponding constants and coefficients are specified. To achieve unambiguous indications of the surfaces, sign convent
34、ions for the constants and coefficients need to be introduced. !NOTE 2 In this case, “left” and “right” presume z is increasing from left to right. When the Z-axis is reversed as a result of a reflection (a 180 rotation about the Y-axis), the sign convention for radius and sagitta is also reversed.
35、This is discussed further in 3.3.2.3.“ A radius of curvature (commonly given for the vertex) has a positive sign if the centre of curvature is to the right of the vertex and a negative sign if the centre of curvature is to the left of the vertex. The sagitta of a point of the aspheric surface is pos
36、itive if this point is to the right of the vertex (XY plane) and negative if it is to the left of the vertex (XY plane). DIN ISO 10110-12:2016-04 8 3.2 Classification of surface type Two types of surface are of particular importance because of their common application in applied optics: generalized
37、surfaces of second order; surfaces of higher order. Generalized surfaces of second order contain conical surfaces, centred quadrics and parabolic surfaces. Surfaces of higher order contain polynomials, toric surfaces and combinations of surface types, e.g. by adding polynomials to other surface type
38、s. 3.3 Special surface types 3.3.1 Surfaces of second order 3.3.1.1 Centred quadrics and parabolic surfaces In the coordinate system given in 3.1.1, the equation of the surfaces of second order which fall within the scope of this part of ISO 10110 are derived from the canonical forms nullnullnullnul
39、l+nullnullnullnull+nullnullnullnull=1 for centred quadrics (1)where a, b are real or imaginary constants; c is a real constant. nullnullnullnull+nullnullnullnull+2null=0 for parabolic surfaces (2)where a, b are real or imaginary constants, and can be written as null=null(null,null) =nullnullnullX+nu
40、llnullnullY1+null1(1+nullX)nullnullnullXnullnull (1+nullY)nullnullnullYnullnull(3)where RXis the radius of curvature in the XZ plane; RYis the radius of curvature in the YZ plane; X, Yare conic constants. DIN ISO 10110-12:2016-04 9 Using curvatures CX= 1/RXand CY= 1/RYinstead of radii yields null=nu
41、ll(null,null) =nullnullnullX+nullnullnullY1+null1(1+nullX)(nullnullX)null (1+nullY)(nullnullY)null(4)If the surface according to Equations (3) or (4) is intersected with the XZ plane (y = 0) or the YZ plane (x = 0), then, depending on the value of Y(or X), intersection lines of the following types a
42、re produced: 0 oblate ellipse; = 0 circle; 1 0 prolate ellipse; = 1 parabola; 1 hyperbola. The following special cases of Equations (3) and (4) should be mentioned: a) Rotationally symmetric surfaces: Using radii: Using curvatures:For R = RX= RY, = X= Yand h2= x2+ y2Equation (3) gives For C = CX= CY
43、, = X= Yand h2= x2+ y2Equation (4) gives null=null() =nullnullnull1+null1(1+null)nullnullnullnullnull(5)null=null() =nullnull1+null1(1+null)nullnullnull(6)Equations (5) and (6) describe a surface rotationally symmetric about the Z axis. b) Cylindrical surfaces: Using radii: Using curvatures:For RX=
44、or RY= Equation (3) gives For CX=0 or CY=0 Equation (4) gives null=null(null) =nullnullnullUnull1+null1(1+nullU)nullnullnullUnullnullnull(7)null=null(null) =nullnullnullU1+null1(1+nullU)nullnullnullUnull(8)Equations (7) and (8) describe a cylinder (due to Unot necessarily of circular cross-section),
45、 the axis of which for u = x is perpendicular to the XZ plane, and the axis of which for u = y is perpendicular to the YZ plane. DIN ISO 10110-12:2016-04 10 3.3.1.2 Conical surfaces The canonical form nullnullnullnull+nullnullnullnull+nullnullnullnull=0 (9)where a, b are imaginary constants; c is a
46、real constant. leads to Equation (10) null=null(null,null) =nullnullnullnullnullnull+nullnullnullnull(10)where a, b, c are real constants. This equation describes a cone with its tip at the origin, with elliptical cross-section (if a b) or with circular cross-section (if a = b). 3.3.2 Surfaces of hi
47、gher order 3.3.2.1 Polynomials The equation for polynomial surfaces is null=null(null,null) = nullnullnullnull+nullnullnullnull+ nullnullnullnull+nullnullnullnull+.+nullnull|null|null+.+nullnull|null|null+. (11)A special case of Equation (11) with h2= x2+ y2is null=null() = nullnullnull+ nullnullnul
48、l+ nullnullnull+. (12)!The first order and second order aspheric terms, A1h and A2h2, may be added to Equation (12).“ Equation (12) describes a rotational symmetric polynomial surface, known as Schmidt surface. 3.3.2.2 Toric surfaces A toric surface is generated by the rotation of a defining curve, contained in a plane, about an axis which lies in the same plane. The equation of a toric surface having its defining curve, z = g(x), in the XZ plane and its axis of rotation parallel to the X axis is null=null(null,null) =nullY nullnullnullYnull(null)nullnullnullnull(13
