ISO TR 14999-1-2005 Optics and photonics - Interferometric measurement of optical elements and optical systems - Part 1 Terms definitions and fundamental relati.pdf

1、 Reference number ISO/TR 14999-1:2005(E) ISO 2005TECHNICAL REPORT ISO/TR 14999-1 First edition 2005-03-01 Optics and photonics Interferometric measurement of optical elements and optical systems Part 1: Terms, definitions and fundamental relationships Optique et photonique Mesurage interfromtrique d

2、e composants et systmes optiques Partie 1: Termes, dfinitions et relations fondamentales ISO/TR 14999-1:2005(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobes licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces whi

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7、ii ISO 2005 All rights reservedISO/TR 14999-1:2005(E) ISO 2005 All rights reserved iiiContents Page Foreword iv Introduction v 1 Scope 1 2 Wave propagation and some topics on electromagnetic theory . 1 2.1 Parameters, symbols, units and constants, operators and computational procedures . 1 2.2 Maxwe

8、lls equations 2 2.3 Electromagnetic fields in a medium 3 2.4 Velocity of the wave 3 2.5 Refractive index 3 2.6 Scalar wave equation 3 2.7 Amplitude, angular frequency, wavelength, wave number 4 2.8 Complex notation, complex amplitude. 4 2.9 Irradiance . 5 2.10 Poynting vector . 5 2.11 Propagation of

9、 plane waves 6 2.12 Propagation of spherical wave 8 2.13 Propagation of waves with limited extent 9 2.14 Propagation of aspherical waves 10 3 General description of interference and different types of interferometers. 12 3.1 Interference between two waves . 12 3.2 Coherence 14 3.3 Different arrangem

10、ents of interference between two beams . 19 3.4 Characteristic features for interferometer structures . 25 4 Coupled ray-paths in interferometers. 33 4.1 Aperture stops and field stops; telecentric imaging. 33 4.2 Coupled ray-path. 34 4.3 Difference of coherent/incoherent optical imaging. 34 4.4 Pri

11、ncipal layout of an interferometer 35 4.5 Consequences of not properly imaging the test piece onto the detector 39 5 Random and systematic error sources 39 Annex A (informative) Visibility of fringes . 41 Bibliography . 42 ISO/TR 14999-1:2005(E) iv ISO 2005 All rights reservedForeword ISO (the Inter

12、national 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

13、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 st

14、andardization. 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

15、for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. In exceptional circumstances, when a technical committee has collected data of a different kind from that which is normally published as an International Standard (“state of t

16、he art”, for example), it may decide by a simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely informative in nature and does not have to be reviewed until the data it provides are considered to be no longer valid or useful. Attention is dra

17、wn 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/TR 14999-1 was prepared by Technical Committee ISO/TC 172, Optics and photonics, Subcommittee SC 1, Fundamental s

18、tandards. 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 and evaluation techniques (Technical

19、Report) Part 3: Calibration and validation of interferometric test equipment (Technical Report) Part 4: Interpretation and evaluation of tolerances specified by ISO 10110 ISO/TR 14999-1:2005(E) ISO 2005 All rights reserved vIntroduction A series of International Standards on “Indications in technica

20、l drawings for the representation of optical elements and optical systems” has been prepared by ISO/TC 172/SC 1, and published as ISO 10110 under the title “Optics and photonics Preparation of drawings for optical elements and systems”. When drafting this series and especially its Part 5, Surface fo

21、rm tolerances, and Part 14, Wavefront deformation tolerance, it became evident to the experts involved that additional complementary documentation is required to describe how the necessary information on the conformance of the fabricated parts with the stated tolerances can be demonstrated. Therefor

22、e, the responsible ISO Committee ISO/TC 172/SC 1 decided to prepare an ISO Technical Report on Interferometric measurement of optical wavefronts and surface form of optical elements. When discussing the topics which had to be included into or excluded from such a Technical Report, it was envisaged t

23、hat it might be the first time, where an ISO Technical Report or Standard is prepared which deals with wave-optics, i.e. which is based more in the field of physical optics than in the field of geometrical optics. As a consequence, only fewer references than usual were available, which made the task

24、 more difficult. Envisaging the situation, that the topic of interferometry has so far been left blank in ISO, it was the natural wish to now be as comprehensive as possible. Therefore there was discussion, whether important techniques such as interference microscopy (for characterizing the micro-ro

25、ughness of optical parts), shearing interferometry (e.g. for characterizing corrected optical systems), multiple beam interferometry, coherence sensing techniques or phase conjugation techniques should be included or not. Other techniques, which are related to the classical two beam interferometry,

26、like holographic interferometry, Moir techniques and profilometry were also mentioned as well as Fourier transform spectroscopy or the polarization techniques, which are mainly for microscopic interferometry. In order to complement ISO 10110, the guideline adopted was to include what presently are c

27、ommon techniques used for the purpose of characterizing the quality of optical parts. Decision was made to complete a first Technical Report, and to then up-date it by supplementing new parts, as required. It is very likely that more material will be added in the near future as more stringent tolera

28、nces (two orders of magnitude) for optical parts and optical systems become mandatory when dealing with optics for the EUV range (wavelength range 6 nm to 13 nm) for microlithography. Also, testing optics with EUV radiation (the same wavelength as they are later used, e.g. at-wavelength testing) can

29、 be a new challenge, and is not covered by any current standards. This Technical Report should cover the need for qualifying optical parts and complete systems regarding the wavefront error produced by them. Such errors have a distribution over the spatial frequency scale; in this Technical Report o

30、nly the low- and mid-frequency parts of this error-spectrum are covered, not the very high end of the spectrum. These high-frequency errors can be measured only by microscopy, measurement of the scattered light or by non-optical probing of the surface. A similar statement can be made regarding the w

31、avelength range of the radiation used for testing: ISO 14999 considers test methods with visible light as the typical case. In some cases, infrared radiation from CO 2 -lasers in the range of 10,6 m is used for testing rough surfaces after grinding or ultraviolet radiation from excimer- lasers in th

32、e range of 193 nm or 248 nm are used for at-wavelength testing of microlithography optics. However, these are still rare cases, which are included in standards, that will not be dealt with in detail. The wavelength range outside these borders is not covered. TECHNICAL REPORT ISO/TR 14999-1:2005(E) I

33、SO 2005 All rights reserved 1Optics and photonics Interferometric measurement of optical elements and optical systems Part 1: Terms, definitions and fundamental relationships 1 Scope This part of ISO/TR 14999 gives terms, definitions and fundamental physical and technical relationships for interfero

34、metric measurements of optical wavefronts and surface form of optical elements. It explains why some principles of the construction and use of interferometers are important due to the wave nature of the wavefronts to be measured. Since all wavefronts with the exception of very extended plane waves d

35、o alter their shape when propagating, this part of ISO/TR 14999 also includes some basic information about wave propagation. In practice, interferometric measurements can be done and are done by use of various configurations; this part of ISO/TR 14999 outlines the basic configurations for two-beam i

36、nterference. The mathematical formulation of optical waves by the concept of the complex amplitude as well as the basic equations of two-beam interference are established to explain the principles of deriving the phase information out of the measured intensity distribution, either in time or in spac

37、e. Both random and systematic errors may affect the results of interferometric measurements and error types to be clearly differentiated are therefore described in this part of ISO/TR 14999. 2 Wave propagation and some topics on electromagnetic theory 2.1 Parameters, symbols, units and constants, op

38、erators and computational procedures Basic parameters, symbols, units and constants are given in Table 1. Operators and computational procedures are given in Table 2. ISO/TR 14999-1:2005(E) 2 ISO 2005 All rights reservedTable 1 Parameters, symbols, units and constants Parameters Symbols Recommended

39、unit, constant Electric field vector E V/m Magnetic field vector H A/m Electric displacement or electric flux density D C/m 2 = As/m 2Magnetic induction or magnetic flux density B T = Wb/m 2= Vs/m 2Dielectric constant or permittivity a F/m = As/Vm Dielectric constant in the vacuum 08,854 10 12 F/m R

40、elative dielectric constant (relative permittivity) r1 Magnetic permeability b H/m = Vs/Am Magnetic permeability in the vacuum 01,257 10 6H/m Relative magnetic permeability r1 Velocity of the wave in the medium c m/s Velocity of the wave in the vacuum c 02,997 924 58 10 8m/s Absolute refractive inde

41、x n 1 aMathematical relationship: = 0 r . bMathematical relationship: = 0 r .Table 2 Operators and computational procedures Operator Definition/Computational procedures Name (type) , xyz Nabla (vector) 222 222 2 xyz + =Laplacian (scalar) 2.2 Maxwells equations Maxwells equations are the fundamentals

42、 for the electromagnetic wave propagation. Maxwells equations for an electromagnetic wave propagating in a medium which does not involve any charge or current and has vanishing conductivity are expressed by: 0 0 0 0+ = t= t= = B E D H D B(1) ISO/TR 14999-1:2005(E) ISO 2005 All rights reserved 3The m

43、athematical relation between D and E as well as between B and H is given by: = = D E B H(2) in a linear medium. 2.3 Electromagnetic fields in a medium For media in which the dielectric constant and magnetic permeability are uniform, Equation (1) gives the following wave equations: 2 2 2 2 2 2 0 0= t

44、 t E E H H(3) 2.4 Velocity of the wave The velocity in an optically homogeneous and isotropic medium is given by: 0 c c = (4) Analogously, in a vacuum the velocity is given by: 00 0 1 c = (5) 2.5 Refractive index The ratio of the propagation velocities in vacuum and in the medium with and 0 c n = c

45、6) is called the refractive index of the medium or the absolute refractive index. 2.6 Scalar wave equation As mentioned before, E and H are vectors. In many applications one deals with linearly polarized light, which can be fully described by one vector component. Equation (3) then reduces to the s

46、calar wave equation. In the general form, the scalar wave equation may be written as: 2 2 22 10 = ct (7) Equation (7) is in conformity with a second-order differential equation. is called the light disturbance. The basic problem of light propagation is thus simply the determination of the manner in

47、which a wave propagates from one surface to another. ISO/TR 14999-1:2005(E) 4 ISO 2005 All rights reserved2.7 Amplitude, angular frequency, wavelength, wave number We suppose a sinusoidal plane electromagnetic wave propagating in the z direction. The light disturbance is determined as a function of

48、position z and time t () c o s( ) z z,t = U t + c (8) where U is the amplitude; is the angular frequency; is the phase constant of the wave. The angular frequency is defined as 2 , where is the frequency, i.e. the number of waves per unit time. The wavelength is given from Equation (9): 0 2 2 c v= = n (9) The wave number k is defined as 2 k = (10) In many applications of the concept of waves, as in diffraction or in interferometry, Equation (8) is used to define “wavefronts”. In this case for a given position z the phase constant is a function of the lateral spatial coor