**National Standard of Length**

Standard Code: ECM 110-1/08-036

Declared in: 2008

Department: 8014 ČMI LPM Praha 5

responsible: RNDr. Petr Balling, Ph.D.

Number of CMCs: 15

Measurand: Range: Expanded Uncertainty (k = 2):

*Primary wavelength standards (MeP method c):*

vacuum wavelength ≈ 532,245 nm 0,000 000 002 0 nm

vacuum wavelength ≈ 543,516 nm 0,000 000 005 4 nm

vacuum wavelength ≈ 632,991 nm 0,000 000 006 7 nm

vacuum wavelength ≈ 1 542,384 nm 0,000 000 080 nm

*fs comb (MeP mehtod b):*

frequency (optical) (281 – 576) THz 2,0∙10^{-13}∙f

vacuum wavelength (520 – 1064) nm 2,0∙10^{-13}∙λ

*interferometry*

displacement *L* (comparator IK-1) (0 – 1,8) m Q[1 nm, 1,2∙10^{-7}∙*L*]

length *L* (gauge blocks) (0,1 – 1) m Q[70 nm, 8,5∙10^{-8}∙*L*]

thermal expansivity α of long gauge block

-1∙10^{-5}/K – 3∙10^{-5}/K Q[3∙10^{-9}/*L*, 2∙10^{-8}, 8∙10^{-4}∙α]/K, α in 1/K

line scales, line spacing *L* 10µm – 200 mm Q[28 nm, 3,77∙10^{-7}∙*L*]

line scales, line spacing *L* (200 – 500) mm Q[68 nm, 2,13∙10^{-7}∙*L*]

National Standard of Length consists of several primary wavelength standards and equipment enabling the realization of the SI definition of the metre: *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*. According to Mise en pratique (*MeP*) [1] one of following three methods can be used:

a) measurement of time needed by light to travel measured distance

b) using wavelength of electromagnetic radiation the frequency of which is measured

c) using wavelength of electromagnetic radiation from the list given with *MeP* for which the wavelength and uncertainty is stated in *MeP*.

Quantum standards of length - helium-neon lasers 633 nm (red) stabilized to hyperfine spectral components of iodine molecule – were developed in ČSMÚ and later in ČMI by group lead by Ing. Jana Blably, CSc. since 1978. These standards were first internationally compared in BIPM in 1981 with very good agreement with reference value which was later (in 1983) used for adopting the current SI definition of the metre. The group of primary standards of wavelengths 633nm served as National wavelength standard of Czechoslovakia since 1980s.

The other primary wavelength standards were developed in following years: iodine stabilized He-Me lasers 612 nm (orange, 1994) and 543,5 nm (green, 1996), iodine stabilized Nd:YAG laser 1064 nm/532 nm (infrared/green, 2001) and acetylene-stabilized DFB laser 1542 nm (infrared, 2004).

The combined expanded relative uncertainty of these primary standards is in the order of 10^{‑11} and stability in the order 10^{‑11} to 10^{‑14}. These standards have participated in more than 10 international comparisons, always successfully – with deviation less than uncertainty given in MeP.

The properties of all primary wavelength standards were studied carefully and some new methods enabling the increase of precision were developed. ČMI has contributed several times to the improvement of uncertainty of the MeP by participation of newly developed standards in absolute frequency measurement – i.e by realisation of the definition of the metre by method b). Wavelength standards 543 nm, 532 nm, 633 nm and 1542 nm developed in CMI were absolutely measured by fs combs in BIPM, BEV and MPQ. In 2005 CMI acquired femtosecond frequency comb generator MenloSystems FC 8004 and supporting instruments and started and started absolute frequency measurements of optical frequency standards. The CMI comb was also internationally compared several times and since 2009 the this CMC is recognized and published in KCDB with relative expanded uncertainty 2∙10^{‑13}.

The radiation of above mentioned wavelength standards is use as reference for dimensional measurements using interferometers. Two such interferometers – IK-1 and IDKM, both developed in CMI are also part of National Standard of Length. The vacuum wavelength has to be corrected for refractive index of air according to actual temperature, pressure, humidity and CO_{2} content in air which limits the relative uncertainty of dimensional measurements to few parts in 10^{8} in best case. Interferometric comparator IK-1 is mainly used for calibration of industrial interferometers but can be also used for precision calibrations of length transducers, actuators and linescales. The long gauge block interferometer IDKM was developed as complementary to short gauge block interferometer NPL-TESA which is operated in ČMI Liberec. IDKM measures up to four gauges up to 1m long; both the central length and the thermal expansivity are measured. IK-1 and IDKM took part in international comparison EURAMET 610, EUROMET.L-K2 and APMP.L-S1.

The National Standard of Length is described in more detail in references [2] to [11] below.

References:

[1] QUINN, T.J.: Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001), *Metrologia, 2003,* **40** pp.103-133 (2003) and R. FELDER “Practical realization of the definition of the metre”, *Metrologia*, 42 (2005) p.323-325 http://www.bipm.org/en/publications/mises-en-pratique/standard-frequencies.html

[2] BALLING, P.:„Primární etalonáž délky“, *Metrologie*, Tematická příloha č. 4/2009, p. 3-10

[3] BLABLA J., PICARD-FREDIN S., RAZET A.: "On the Fifth-Derivative Spectrum of the Hyperfine Structure of 127I2 at the 633nm Wavelength of the Helium-Neon Laser", *Journal of Molecular Spectroscopy*, 159 (1993) p. 282-285 (reference)

[4] BALLING P., BLABLA J., CHARTIER A., CHARTIER J.-M., ZIEGLER M.: "International Comparison of ^{127}I_{2} - Stabilized He-Ne Lasers at l»633nm Using the Third and the Fifth Harmonic Locking Technique", *IEEE Transactions on Instrumentation and Measurement*, , Vol. 44 No.2 (1995), p.173-176

[5] BALLING P.:, “Simple Measurement of Frequency Modulation of Laser with 0.1% Precision”, *Metrologia *2001, 38(4), pp. 297-299

[6] MATUS M., BALLING P., ŠMÍD M., WALCZUK J., BÁNRÉTI E., TOMANYICZKA K., POPESCU G.H., CHARTIER A. and CHARTIER J.M.: International comparisons of He-Ne lasers stabilized with ^{127}I_{2} at l » 633 nm (September 1999), *Metrologia*, , 39 n°1 (2002), 83-89

[7] PICARD S., ROBERTSSON L., MA L.-S., NYHOLM K., MERIMAA M., AHOLA T. E., BALLING P., KŘEN P., WALLERAND J.-P.: A comparison of ^{127}I_{2}-stabilized frequency-doubled Nd:YAG lasers at the BIPM, comparison in May 2001*, **Applied Optic, *42, No.6 (2003)

[8] MA L. S., PICARD S., ZUCCO M., CHARTIER J.-M. and ROBERTSSON L., BALLING P. and KREN P., QIAN J., LIN ZHONG Y., SHI CH., ALONSO M. V., XU G. and TAN S. L., NYHOLM K., HENNINGSEN J. and HALD J., WINDELER R.: Absolute Frequency Measurement of the R(12) 26-0 and R(106) 28-0 Transitions in ^{127}I_{2} at l=543 nm*, **IEEE Transactions on Instrumentation and Measurement*, Vol. 55 No.3 (2006).

[9] BALLING P., FISCHER M., KUBINA P., AND HOLZWARTH R.: "Absolute frequency measurement of wavelength standard at 1542nm: acetylene stabilized DFB laser," *Opt. Express*, 13, 9196-9201 (2005),

[10] BALLING P., KREN P.: Absolute frequency measurements of wavelength standards 532 nm, 543 nm, 633 nm and 1540 nm, *Eur. Phys. J. D*, 48** (**2008).

[11] KŘEN P., BALLING P.: Common path two-wavelength homodyne counting interferometer development, *Meas. Sci. Technol.*, 20 084009 (2009) (4pp)

[12] M. Matus *et al.*, „The CCL-K11 ongoing key comparison: final report for the year 2010", *Metrologia*, roč. 48, č. 1A, s. 04001–04001, led. 2011.

[13] P. Balling, P. Mašika, P. Křen, a M. Doležal, „Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy", *Measurement Science and Technology*, roč. 23, č. 9, s. 094001, zář. 2012.

[14] P. Balling, „Laser frequency stabilization and measurement of optical frequencies". Lambert Academic Publishing, 03-led-2012.

[15] M. Pisani *et al.*, „Comparison of the performance of the next generation of optical interferometers", *Metrologia*, roč. 49, č. 4, s. 455–467, srp. 2012.

[16] M. Zeitouny *et al.*, „Multi-correlation Fourier transform spectroscopy with the resolved modes of a frequency comb laser: Multi-correlation Fourier transform spectroscopy with the resolved modes of a frequency comb laser", *Annalen der Physik*, roč. 525, č. 6, s. 437–442, čer. 2013.

[17] M. Wisniewski *et al.*, „Final report on supplementary comparison EURAMET.L-S20: Comparison of laser distance measuring instruments", *Metrologia*, roč. 51, č. 1A, s. 04002–04002, led. 2014.

[18] M. Doležal *et al.*, „Analysis of thermal radiation in ion traps for optical frequency standards", *Metrologia*, roč. 52, č. 6, s. 842–856, pro. 2015.

[19] H. Wu *et al.*, „Absolute Distance Measurement Using Frequency Comb and a Single-Frequency Laser", *IEEE Photonics Technology Letters*, roč. 27, č. 24, s. 2587–2590, pro. 2015.

[20] M. Matus *et al.*, „Measurement of gauge blocks by interferometry", *Metrologia*, roč. 53, č. 1A, s. 04003–04003, led. 2016.

[21] P. B. R. Nisbet-Jones *et al.*, „A single-ion trap with minimized ion–environment interactions", *Applied Physics B*, roč. 122, č. 3, bře. 2016.

[22] H. Wu, F. Zhang, T. Liu, P. Balling, J. Li, a X. Qu, „Long distance measurement using optical sampling by cavity tuning", *Optics Letters*, roč. 41, č. 10, s. 2366, kvě. 2016.

[23] H. Wu, F. Zhang, T. Liu, P. Balling, a X. Qu, „Absolute distance measurement by multi-heterodyne interferometry using a frequency comb and a cavity-stabilized tunable laser", *Applied Optics*, roč. 55, č. 15, s. 4210, kvě. 2016.

[24] S. Quabis *et al.*, „Intercomparison of flatness measurements of an optical flat at apertures of up to 150 mm in diameter", *Metrologia*, roč. 54, č. 1, s. 85, led. 2017.