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Refractive Index of Air and Precision Length Measurements

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Refractive Index of Air and Precision Length Measurements Refractive Index of Air and Precision Length Measurements Jennifer E. Decker Science, Technology & Innovation Division Foreign Affairs & International Trade Canada 13 May 2011 Vancouver © Government of Canada, 2011 Introduction • Historical overview of International System of Units (SI) definition of the metre • Interferometric length measurement / calibration • Impact of refractive index of air on accurate length measurement – What is the magnitude of the correction? – How is the correction applied? – Recent Developments © Government of Canada, 2011 Brief History of the metre 1872 prototype Kilogramme des Archives and Mètre des Archives (c.1799) 1875 Convention of the Metre signed 1887 Michelson proposed using optical interferometers for length measurement; received 1907 Nobel Prize for physics 1892 Michelson interferometer at BIPM (Michelson & Benoît) measured the metre in terms of red line of cadmium; confirmed in 1906 by Benoît, Fabry & Perot 1960 Definition of the metre in terms of wavelength in vacuum of specific radiation from krypton 86 1975 CGPM recommended value for speed of light in vacuum based on wavelength and frequency of laser radiation 1983 Definition of the metre as length of path travelled by light in vacuum during a specific fraction of a second © Government of Canada, 2011 SI Definition of the metre (m) The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. • Consultative Committee for Length (CCL) formed in 1952 – Provides recommendations for practical realization of the metre (Mise en Pratique) – Provides wavelengths, frequencies and associated uncertainties of recommended laser radiations, spectral lamps http://www.bipm.org/en/si/base_units/ © Government of Canada, 2011 Definition Gauge Block Length • “. the perpendicular distance between point of the measuring face and the plane surface of an auxiliary plate of the same material and surface texture upon which the other measuring face has been wrung …includes the effect of one face wringing.” ISO 3650(E) • lengths of gauge blocks directly compared with internationally- recommended wavelength standards • traceability established via comparison measurements © Government of Canada, 2011 Accuracy (Uncertainty) 10-14 Time Frequency standards c 10-12 Laser frequency stabilized on molecular transition (Mise en Pratique) 10-9 Polarization-stabilized lasers c 299792458 m/s (distance measuring) 10-8 Equation for Air Refractive Index of Air 10-6 Gauge Block length nair • 25 mm ± 20 nm • 1 m ± 70 nm 10-6 Frequency of a free-running laser © Government of Canada, 2011 Optical Interferometry • Main influences: – air temperature, pressure and humidity on the wavelength of light refractive index, n – gauge block temperature deviation from 20ºC – optical phase change on reflection of light from surface – wringing Gauge length – design parameters of the optical Block instrument (obliquity correction) Optical Flat © Government of Canada, 2011 Refractive Index © Government of Canada, 2011 Twyman-Green Interferometer Schödel PTB-Mitteilungen 120 (2010), Heft 1 © Government of Canada, 2011 Method of Exact Fractions • ‘Fringe fraction’ fi observed with wavelength i for several laser sources, each in turn • Length evaluation by finding the best match for integer interference orders to satisfy: lf() i ii2 © Government of Canada, 2011 Method of Exact Fractions Wavelength Measured Example of a 10 mm gauge block: /nm fraction 1st Step: Measure fractions from the 543 0.2 interference patterns 612 0.7 633 0.5 Interference Orders Length Red Orange Green /mm 31592.5 32676.6 36828.8 9.999 03 31593.5 32677.6 36830.0 9.999 35 2nd Step: Evaluate 31594.5 32678.7 36831.2 9.999 67 gauge length based on 31595.6 32679.7 36832.4 10.000 00 Fractions and “known” 31596.6 32680.8 36833.6 10.000 31 Nominal length. 31597.6 32681.8 36834.8 10.000 64 31598.6 32682.9 36835.9 10.000 96 Decker et al., Applied Optics 42 (2003) 5670-5678 © Government of Canada, 2011 Edlén Equation - Brief History • 1966: Edlén published empirical equation for n of standard dry air and corrections for water vapour, based on experimental data (Barrell and Sears 1939, Hilsenrath 1955) • 1988: Birch and Downs revise water vapour constants - higher accuracy • 1994: Updated by Birch and Downs (1993, 1994) – accommodates the SI units (Pascal vs. Torr) – replaced IPTS-1948 temperature scale with ITS-90 – corrects for increased levels of CO2 in laboratory air (62 ppm) – includes improved experimental data on density of air and the refractivity of water vapour 1 ppm 1 part per million = 1x10-6 © Government of Canada, 2011 An Empirical Equation 8 1 2 1 2 n 1 N 10 8091.37 2333983/130 / m 15518/38.9 / m n 1 x n 1 N 1 0.5327x 0.0004 n 1 p / Pa 1108 0.5953 0.009876t /C p / Pa n 1 x tp 93214.60 1 0.0036610 t/C 1 2 10 ntpf ntp f / Pa 3.8020 0.0384 / m 10 Bönsch & Potulski, Metrologia 35 (1998) 133-139 © Government of Canada, 2011 Empirical Equations Bönsch & Potulski, 1998, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia, 35, 133-139 Ciddor P. E., 1996, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt., 35, 1566-1573. Birch K. P. and Downs M. J., 1994, “Correction to the Updated Edlén Equation for the Refractive Index of Air,” Metrologia, 31, 315-316. Decker et al., NRC Document No. 42753 (2000) Edlén B., 1966, “The Refractive Index of Air,” Metrologia, 2, 72-80. © Government of Canada, 2011 Wavelength of light compensation • Vacuum wavelengths are adjusted for refractive index of air, n vac = n air • Correction for refractive index of air = (n-1)L n 1.000 27 ~300L nm for L [mm] (about 300 nm on 1 mm) Change for which Nominal Value -6 n=+1x10 Temperature 20.0°C -1.0°C Pressure 101.3 kPa +0.4 kPa (760 Torr) (+3 Torr) Relative Humidity 40% -100% Estler Applied Optics 24 (1985) 808 © Government of Canada, 2011 Wavelength of light compensation NRC Gauge Block Interferometer Pressure Measurement 101800 Rate of change = 101700 200 Pa in 30 minutes 101600 50 nm for L=100 mm 101500 101400 101300 Pressure /Pa Pressure 101200 101100 101000 8:09 9:38 11:08 12:37 14:06 15:36 Time of Day © Government of Canada, 2011 Principal Constituent Gases Molar Concentrations N2 O2 Ar CO2 0.781 0.209 0.009 0.0004 Other gases such as He, CH4, etc. make up the remaining air composition. Pendrill Metrologia 25 (1988) 87-93 © Government of Canada, 2011 Variation in Lab Air Composition •CO2 largest single source of variation & significant contaminant • Operators are not at rest up to 5 ~5 nm on times higher respiration rate! 100 mm • Operator near the instrument • CO2 paired with O2 results in additional change in composition Birch and Downs “The Precise Determination of the Refractive Index of Air,” National Physical Laboratory (NPL) Report MOM90 (1988) Teddington, UK © Government of Canada, 2011 PTB Kösters Interferometer • Kösters design allows real time evaluation of the refractive index of air in the proximity of the gauge block by direct comparison with vacuum. • Frequency-stabilized laser sources. • High-accuracy thermometry equipment: thermocouples paired with Pt-25 and precision bridge. • Cooled CCD camera. © Government of Canada, 2011 Correction via Refractometer • Refractive index of air is the largest single correction to 1 n length measurements by m 2L interferometry (3x10-4 L) v Cell mair 2LCell v v • Measure fringe fractions – determine the difference in m m m number of interference orders n air v mn between air and vacuum 1 • More accurate than estimation v n 1 mn by empirical formulas (Edlén LCell 2 equations). 1 v n fn C LCell 2 © Government of Canada, 2011 © Government of Canada, 2011 Phase Stepping Interferometry • Popular technique for interference fringe analysis – flatness-measuring interferometers – optical component evaluation • Displacement of fringes when the optical path length is changed – Sample interferogram at each of 5 phase steps – Change in grey-scale is related to the change in optical path length and the wavelength of light • Fringe fraction measurand for: – Gauge block length – Refractive index of air © Government of Canada, 2011 Length-Dependent Influences Influence Type dy/dxi ui Refractive index of air -9 Window optics correction 3 nm B L/ 3x10 L -9 Fringe fraction 0.007 fringe B L/2 2x10 L -9 -11 3.7x10 L Vacuum cell length, 250 nm B (n-1)L/ 7x10 L -10 Vacuum wavelength 10 B (n-1)L/ negl. Influence Type dy/dxi ui Refractive index of air -8 -8 Edlen Equation 1x10 BL1x10 L -7 -9 Air Temperature 4 mK B -9.5x10 L3x10L -9 -8 -8 Air Pressure 6 Pa B 2.7x10 L1.6x10L 2.4x10 L -9 -8 Relative Humidity 2% B -8.5x10 L1.3x10L -8 Vacuum Wavelength 10 B -1.2x10-5Lnegl. Decker et al., Metrologia 41 (2004) L11-L17 © Government of Canada, 2011 End Effect vs. Length-Dependent Influences 120 Ciddor Equation 100 Refractometer 80 60 /nm 40 84 20 0 Expanded (k=2) Uncertainty 0 200 400 600 800 1000 Nominal Gauge Block Length /mm © Government of Canada, 2011 Atmospheric Bath • Gauge block length is defined at the standard atmospheric P pressure of P0=101325 Pa LP L ISO 3650 3K P1 2 • Artifact length can change LP as L a result of a change in pressure E • Gauge block length increases with Example: 900 mm gauge block decreasing pressure P (higher measured in Boulder, CO (altitude altitude = lower pressure) 1500 m; 83 kPa) is 34 nm longer than when measured in Paris (at sea level, 101 kPa) Bayer-Helms Über den Einfluss von Luftdruck und Gewichtskraft auf Endmasse PTB-Mitt.
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