Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 17
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Sci. Instrum. 65 576–58[34] Brenan C J H, Charette P G, Hunter I W 1992 Environmental isolation platform for microrobot system development Rev. Sci. Instrum. 63 3492–349853This page intentionally left blankCHAPTER 4Length traceability usinginterferometryDr. Han HaitjemaMitutoyo Research Centre Europe4.1 Traceability in lengthA short historical overview of length measurement was given in chapter 2.This chapter will take one small branch of length measurement, that of staticlength standards, and discuss in detail how the most accurate lengthmeasurements are made on macro-scale length standards using the technique of interferometry. These macro-scale length standards and thespecialist equipment used for their measurement may not appear, at firstsight, to have much relevance to MNT.
However, macro-scale length standards are measured to nanometre uncertainties and many of the conceptsdiscussed in this chapter will have relevance in later chapters. For example,much of the information here that relates to static surface-based interferometry will be developed further or modified in chapter 5, which discussesthe development of displacement interferometry.It is also important to discuss traditional macro-scale length standards,both specification standards and artefact standards, because the subject ofthis book is engineering nanometrology. In other words, this book is concerned with the tools, theory and practical application of nanometrology inan engineering context, rather than as an academic study.
It is anticipatedthat the development of standards for engineering nanometrology will verymuch follow the route taken for macro-scale engineering in that problemsconcerning the interoperability of devices, interconnections, tolerancing andstandardization will lead to the requirement for testing and calibration, andthis in turn will lead to the writing of specification standards and the preparation of nanoscale artefact standards and the metrology tools with which tocalibrate them. It may well be that a MNT version of the ISO GeometricalFundamental Principles of Engineering NanometrologyCopyright Ó 2010 by Elsevier Inc.
All rights reserved.CONTENTSTraceability in lengthGauge blocks – both apractical andtraceable artefactIntroduction tointerferometryInterferometer designsGauge blockinterferometryReferences5556C H A P T ER 4 : Length traceability using interferometryProduct Specification (GPS) matrix [1] will evolve to serve the needs fordimensional metrology at these small scales. A discussion on this subject isas presented in [2].There is a large range of macro-scale length standards and lengthmeasuring instruments that are used throughout engineering, for examplesimple rulers, callipers, gauge blocks, setting rods, micrometers, step gauges,coordinate measuring machines, linescales, ring and plug gauges, verniers,stage micrometers, depth gauges, ball bars, laser trackers, ball plates, threadgauges, angle blocks, autocollimators, etc.; the list is quite extensive [3]. Forany of these standards or equipment to be of any practical application toengineers, end users or metrologists, the measurements have to be traceable.Chapter 2 explained the concept of traceability and described the comparisonchain for some quantities.
In this chapter we will examine in detail thetraceable measurement of some of the length standards with the most basicconcepts known as gauge blocks and, in doing so, we will show many of thebasic principles of interferometry – perhaps the most directly traceablemeasurement technique for length metrology.4.2 Gauge blocks – both a practical and traceable artefactAs discussed in section 2.3, the end standard is one of the basic forms ofmaterial length artefact (a line standard being the alternative form of artefact). It is not only the basic form of an end standard that makes them sopopular, but also the fact that Johannsson greatly enhanced the practicalusability of end standards by defining gauge block sizes so that they could beused in sets and be combined to give any length with micrometre accuracy[3,4].
For these reasons the end standard found its way from the NMIsthrough to the shop floor.In summary, the combination of direct traceability to the level of primarystandards, the flexibility of combining them to produce any length witha minimal loss of accuracy, their availability in a range of accuracy classes andmaterials and the standardization of sizes and accuracies make end standardswidespread, and their traceability well established and respected.The most commonly used gauge blocks have a standardized cross-section of9 mm by 35 mm for a nominal length ln > 10 mm and 9 mm by 30 mm fornominal length 0.5 mm < ln < 10 mm. The flatness of the surfaces (less than0.1 mm) is such that gauge blocks can be wrung on top of each other withoutcausing a significant additional uncertainty in length.1 This is due to the1Wringing is the process of attaching two flat surfaces together by a sliding action [6]Gauge blocks – both a practical and traceable artefactdefinition of a gauge block, which states that the length is defined as the distancefrom the measurement (reference) point on the top surface to the plane ofa platen (a flat plate) adjacent to the wrung gauge block [5].
This platen should bemanufactured from the same material as the gauge block and have the samesurface properties (surface roughness and refractive index). Figure 4.1 isa schematic, and Figure 4.2 is a photograph, of a gauge block wrung to a platen.The definition of the length of a gauge block enables the possibility ofrelating the length to optical wavelengths by interferometry. Also, there is noadditional uncertainty due to the wringing as the auxiliary platen could bereplaced by another gauge block, where the wringing would have the sameeffect as the wringing to the platen, which is included in the length definition.Gauge blocks are classified into accuracy classes. The less accurate classesare intended to be used in the workshop. Using mechanical comparators,these gauge blocks can be compared to reference gauge blocks that are relatedto wavelengths using gauge block interferometers.Table 4.1 gives the tolerances for gauge block classes K, 0, 1 and 2according to ISO 3650 [5].
For those to be calibrated by interferometry (classK) the absolute length is not so critical as this length is explicitly measured.However, the demands on parallelism needed for good wringing, and anaccurate length definition, are highest. ISO 3650 gives the basis of demands,tolerances and definitions related to gauge blocks.The method of gauge block calibration by interferometry is a basicexample of how the bridge between the metre definition by wavelength anda material reference artefact can be made.
It will be the main subject of therest of this chapter.FIGURE 4.1 Definition of the length of a gauge block.5758C H A P T ER 4 : Length traceability using interferometryFIGURE 4.2 A typical gauge block wrung to a platen.Table 4.1ClassK012Gauge block classes according to ISO 3650 [5]Tolerance on length, L0.200.120.200.45mmmmmmmmþþþþ4248610106106106LLLLTolerance on parallelism for length, L0.050.100.160.30mmmmmmmmþþþþ2357107107107107LLLL4.3 Introduction to interferometry4.3.1 Light as a waveThis chapter will introduce the aspects of optics that are required to understand interferometry. For a more thorough treatment of optics the reader isreferred to [7].Introduction to interferometryFor the treatment of light we will restrict ourselves to electromagneticwaves of optical frequencies, usually called ‘visible light’.
From Maxwell’sequations it follows that the electric field of a plane wave, with speed, c,frequency, f, and wavelength, l, travelling in the z-direction, is given by ExeiðkzutÞEðz; tÞ ¼(4.1)Eywhere u ¼ 2pf ¼ 2pc/l is the circular frequency and k is the circular wavenumber, k ¼ 2p/l.Here we use the convention that a measurable quantity, for example theamplitude, Ex, can be obtained by taking the real part of equation (4.1) and weassume that Ey ¼ 0, i.e. the light is linearly polarized in the x direction. At thelocation z ¼ 0, the electric field E ¼ Excosut. This means that the momentaryelectric field oscillates with a frequency f.
For visible light, for example greenlight (l ¼ 500 nm), this gives, with the speed of light defined as c ¼ 299 792458 m$s1, a frequency of f ¼ 6 1014 Hz. No electric circuit can directlyfollow such a high frequency; therefore light properties are generallymeasured by averaging the cosine function over time. The intensity is givenby the square of the amplitude, thusIðzÞ ¼ hE,Ei ¼ ðE2x Þhcos2 uti:(4.2)A distortion at t ¼ 0, z ¼ 0, for example of the amplitude Ex in equation(4.1), will be the same as at time, t, at location z ¼ ut/k ¼ ct, so the propagation velocity is c indeed.In equation (4.1), the amplitudes Ex and Ey can both be complex. In thatgeneral case we speak of elliptical polarization; the E-vector describes anellipse in space.
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