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MEASUREMENT UNCERTAINTY OF THE OPTICAL WAVELENGTH CALIBRATION 633 nm BY BEAT FREQUENCY MEASUREMENT METHODS
KETIDAKPASTIAN PENGUKURAN PADA KALIBRASI PANJANG GELOMBANG OPTIK 633 nm DENGAN METODE PENGUKURAN BEAT FREQUENCY
Asep Hapiddin*, Yulita Ika Pawestri, A. M. Boynawan, Ratnaningsih Center for Research and Human Resources Development,
National Standardization Agency of Indonesia
PUSPIPTEK area, Building 420, Setu, South Tangerang, Banten, Indonesia, 15314 Email: aseph@bsn.go.id
*This author contributed equally to this work
ABSTRACT
Measurement traceability is one of the critical aspects in metrology area. The measurement uncertainty had been evaluated to assure reliability of the optical wavelength calibration system for stabilized He-Ne laser 633 nm in SNSU-BSN. Beat frequency measurement was applied as a calibration method by utilizing KIM-1 as a reference standard that traceable to SI unit through CCL-K11 key comparison. Best measurement capability declares with a relative uncertainty of ±1.3×10-10 by excluding UUC effect. The calibration replica was performed as a validation process, dual mode laser head Agilent 5519B took a role as UUC. As calibration result, beat frequency of KIM-1 and UUC is (122.931±0.060) MHz. Among all of the uncertainty sources, KIM-1 uncertainty most significant influence to the beat frequency uncertainty and the optical wavelength of the UUC laser in vacuum condition. Based on the evaluation result, the calibration system of stabilized He-Ne laser can be validated and trace back with documented unbroken calibration chain to the primary standard of length, KIM-1 where established in SNSU-BSN.
Keywords— measurement uncertainty; wavelength calibration; beat frequency measurement;
stabilized He-Ne laser; SNSU-BSN INTISARI
Ketertelusuran pengukuran merupakan salah satu aspek penting di bidang metrologi. Telah dilakukan evaluasi ketidakpastian untuk menjamin keandalan dari kalibrasi panjang gelombang optik untuk stabilized He-Ne 633 nm di SNSU-BSN. Pengukuran beat frequency diterapkan sebagai metode kalibrasi dengan menggunakan KIM-1 sebagai standar referensi yang tertelusur ke Standar Internasional satuan melalui uji banding CCL-K11. Kemampuan pengukuran terbaik dinyatakan dengan ketidakpastian relatif ±1.3×10-10 dengan
mengecualikan efek dari UUC. Replika kalibrasi dilakukan sebagai proses validasi dengan laser dual mode Agilent 5519B berperan sebagai UUC. Sebagai hasil kalibrasi, beat frequency antara KIM-1 dan UUC adalah (122.931±0.060) MHz. Di antara semua sumber ketidakpastian, ketidakpastian standar KIM-1 berpengaruh paling signifikan terhadap ketidakpastian dari beat frequency dan panjang gelombang optik laser UUC dalam kondisi vakum. Berdasarkan hasil evaluasi, sistem kalibrasi laser stabilizes He-Ne laser dapat divalidasi dan tertelusur dengan rantai kalibrasi tak terputus yang didokumentasikan ke standar utama panjang, KIM-1 di SNSU-BSN.,
Keywords— ketidakpastian pengukuran; kalibrasi panjang gelombang; pengukuran beat frequency; stabilized He-Ne laser, SNSU-BSN
1. INTRODUCTION
Laser application is widely used in the metrology area, e.g. in length metrology.
Customized stabilized laser recommended as a primary standard in the realization of meter definition (Quinn, 2003), laser with specific wavelength also used in the interferometry system for the gauge block calibration (Lewis & Hughes, 2010) (Salbut, 2013), coordinate measuring machine (CMM) calibration (Maruyama &
Fusayasu, 2014) and step gauge calibration (Yan & Wang, 2006).
One of the recommended stabilized laser in the realization definition of the meter is iodine stabilized He-Ne laser with wavelength 633 nm (Quinn, 2003). KIM-1 is iodine stabilized He-Ne laser (Neoark 92SI) that belong to the National Measurement Standard Laboratory – National Standardization Agency (SNSU – BSN). Result of CCL-K11 key comparison
in 2014 validated KIM-1 wavelength and assure its traceability to SI with relative standard uncertainty 6.3×10-11, it concluded in the appropriate to be utilized as length primary standard in SNSU – BSN (Matus M., V. Gavalyugov, D. Tamakyarska, M.
Ranusawud, A. Tonmueanwai, F. L. Hong, J. Ishikawa, G. Moona, R. Sharma, A.
Hapiddin, A. M. Boynawan, N. Alqahtani, M. Alfohaid, L. Robertsson, 2017).
In order to disseminate wavelength value of KIM-1 and fulfill the constant calibration need to ensure the quality and uncertainty of the lasers in industries and laboratories, the optical wavelength calibration system has been established in SNSU-BSN, particularly for stabilized He- Ne laser as a unit under calibration (UUC).
Beat frequency measurement method (Leach, 2014) had been applied on the optical wavelength calibration in SNSU- BSN, i.e. frequency comparison between
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KIM-1 as reference laser and UUC laser (Hapiddin et al., 2020). The other method is a direct measurement method, usually for non-stabilized He-Ne laser calibration. It is not recommended for stabilized He-Ne laser calibration, due to limitation of readability and stability of the wavelength meter. (Ranusawud, Vacharanukul, &
Tonmeanwai, 2009) (Widya, Hapiddin, Ratnaningsih, Syahadi, & Juliastuti, 2017).
There is a requirement to evaluate and validate the calibration system through the uncertainty analysis. Measurement traceability is one of the critical aspects that should be established and maintained by means of a documented unbroken chain of calibrations, each contributing to the measurement uncertainty, linking them to an appropriate reference (ISO-IEC, 2017).
In this research, we focused on the evaluation and analysis work of the uncertainty in the optical wavelength calibration system for the stabilized He-Ne laser by a method of the beat frequency measurement, in SNSU-BSN.
2. MATERIALS AND METHODS A. Materials
The first step in the uncertainty evaluation was determining the mathematical formula for the optical wavelength calibration by beat frequency measurement. The optical frequency of UUC laser ( fUUC) can be obtained by formula in Eq. (1):
UUC std
f f f (1)
fstd is frequency of KIM-1 (Iodine stabilized He-Ne laser as the reference standard, i.e. 473 612 353 613.3 kH2 z taken from CCL-K11 key comparison result (Matus M., V. Gavalyugov, D.
Tamakyarska, M. Ranusawud, A.
Tonmueanwai, F. L. Hong, J. Ishikawa, G.
Moona, R. Sharma, A. Hapiddin, A. M.
Boynawan, N. Alqahtani, M. Alfohaid, L.
Robertsson, 2017). f is the frequency difference (beat frequency) between UUC laser and KIM-1 that obtained by the experimental work. The scheme of the measurement setup shown in Figure 1.
Stabilized He Ne Laser GPIB-USB-HS+
Figure 1. Scheme of the configuration setup for the beat frequency measurement in SNSU-BSN.
B. Method
The optical beat frequency between UUC laser and KIM-1 was measured by Universal Counter (Agilent 53132A), which has 10 MHz external reference from National Frequency Standard (NaFS) Cesium Atomic Clock HP5071A through Frequency Distribution Amplifier (FDA).
Selected polarized beam of UUC laser was aligned goes through beam splitter. Glan Thomson polarizer take a role in the selection process of the wanted polarized beam from UUC laser before reaching a beam splitter and combining with KIM-1 beam. The combined beam is focused by an objective lens to reach the aperture of
the photodetector (Thorlabs PDA10A) that connected to an optical spectrum analyzer (OSA) and a frequency counter using a power splitter. OSA (Agilent-DSO6052A) as the instrument in the spectral accuracy and signal-to-noise ratio observations of the beat signal in FFT mode.
The optical wavelength of UUC laser (UUC) expressed as vacuum wavelength and determined by formula in Eq. (2):
UUC UUC f
c0
(2)
where c is speed of light in vacuum 0 condition 299 792 458 m/s.
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Second step was the observation of the uncertainty sources for the beat frequency measurement (u(f)). Then, determine the uncertainty of fUUC as the source uncertainty of UUC. The experimental work on the calibration replica was conducted in the Optical Frequency Laboratory of SNSU-BSN. The UUC laser was laser head Agilent (dual mode laser) with central wavelength of
632.991 354 nm
in vacuum, frequency difference 3.4 to 4.0 MHz and 0.02 ppm stability for typical lifetime (“Laser Heads Agilent 5519B, User’s Manual,” 2002).
The beat frequency gathered once every second by automation program based on C++ while the counter was continuously performing processing of 102 measurement data.
In the beat frequency measurement, type A and type B evaluations were analyzed to determine the measurement uncertainty (u(f)). The estimated uncertainty was evaluated from the possible sources, mainly from environment, materials, devices used during the measurement. Based on the
measurement setup, beat frequency of UUC laser and KIM-1 measured by the frequency counter (Agilent 53132A) with 10 MHz external reference from NaFS through frequency distribution amplifier (FDA). Therefore, it is necessary to consider incremental uncertainty derived from KIM-1 (ustd) as a reference standard, universal counter Agilent 53132A (uCtr), NaFS (uNaFS), the insertion of FDA (uFDA), and the coaxial cable (u ) that used in the Cx connection of the measurement devices.
The uncertainty sources of the beat frequency measurement is figured out by Ishikawa diagram as shown in Figure 2.
Therefore, the actual of the beat frequency can be determined by mathematical model in Eq. (3):
(actual) ( )
f f u f
1
2 2 2 2
( ) 2 rep 2Std 2Ctr 2
NaFS FDA Cx
u u u
f f
u u u
actual
(3) The identified of each quantity and their uncertainties are shown in Table 1.
Figure 2. Ishikawa (Fishbone) diagram of the uncertainty sources in beat frequency measurement.
Table 1. The Uncertainty Sources of the Beat Frequency Measurement
Uncertainty Quantity Type Sensitivity Coefficient Probability
u(xi) Xi ci Distribution
urep Repeatability Type A 1 Normal
ustd Fractional Frequency Different of I2
stabilized He Ne Laser (KIM-1)
Type B
1 Normal
uCtr Error of Frequency Counter (Ctr) Type B 1 Rectangular
uNaFS National Frequency Standard (NaFs) Type B 1 Normal
uFDA Stability of Frequency Distribution Amplifier (FDA)
Type B
1 Normal
uCx Stability of Coaxial Cable (Cx) Type B 1 Normal
C. Uncertainty Evaluation (1) Uncertainty of the Frequency
Measurement of UUC
The actual frequency of the UUC laser was determined by formula in Eq. (1). The uncertainty for the actual frequency measurement of UUC laser is calculated based on the calculation of the standard uncertainty of the output estimate (JCGM, 2008) (European co-operation for Accreditation, 2013).
2 2
1 N
UUC i UUC
u f i u f
(4)
UUC
i
ii f cu x
u ; where c is the i sensitivity coefficient associate the input
estimatex , i.e. the partial derivative i fUUC of with respect to fstd andf .
2 2
2 UUC 2 UUC 2
UUC std
std
f f
u f u f u f
f f
f
u
f
u
fu2 UUC 2 std 2
So, the uncertainty for the actual frequency measurement of UUC is determined by formula in Eq. (5):
UUC
std
u f u f u f (5)
(2) Uncertainty of the Optical Wavelength of UUC Laser
The optical wavelength of UUC was determined by formula in Eq. (2). The uncertainty of the optical wavelength also
Measurement Uncertainty Of… | 147
can be determined based on ‘calculation of the standard uncertainty of the output estimate’ (JCGM, 2008) (European co- operation for Accreditation, 2013).
UUC
UUC UUC UUC
UUC u f
c f c u
u 2
2
0 2 2
0 2
UUC
UUC UUC
UUC u f
f c c
f u
u 2
2
2 0 0
2 2
2 1
c0 is speed of light in vacuum condition and there is no uncertainty for speed of light in vacuum, u(c0)0.
UUC
UUC
UUC u f
f
u c 2
4 2 0
2
20 2 2
4 2 0 2
2
c f f
u f
c
u UUC
UUC UUC
UUC UUC
UUC
UUC UUC
UUC u f
f
u 2
2 2
2 1
Thus, uncertainty of the optical wavelength of UUC is calculated by formula in Eq. (6):
UUC UUC
UUC
UUC f
f
u u
(6)
The actual optical wavelength of UUC laser is stated by formula in Eq. (7):
( ) ( )
UUC actual UUC u UUC
(7)
3. RESULTS AND DISCUSSION
The result of the beat frequency measurement of KIM-1 that lock on f absorption line and polarized beam of UUC
laser (Agilent 5519B) shown in Figure 3.
Based on the measurement result, the beat frequency of KIM-1 lock on f absorption line and polarized beam of UUC laser shows relatively stable with an average value of 122.931 MHz and 0.031 MHz of the standard deviation.
The type A uncertainty that called urep is determined by formula
n uA s with s is the standard deviation and n is number of measurement. So, the type A uncertainty is 0.003 1 MHz.
Type B uncertainty sources mainly from the meaning devices used during the measurement. The relative uncertainty of KIM-1 equal to 6.3×10–11 was obtained from the International Laboratory Comparison in 2014 by RCM-LIPI as a part of CCL-K11 key comparison of the optical frequency and wavelength standards (Matus M., V. Gavalyugov, D.
Tamakyarska, M. Ranusawud, A.
Tonmueanwai, F. L. Hong, J. Ishikawa, G.
Moona, R. Sharma, A. Hapiddin, A. M.
Boynawan, N. Alqahtani, M. Alfohaid, L.
Robertsson, 2017)
.
0 20 40 60 80 100 122.86
122.88 122.9 122.92 122.94 122.96 122.98 123 123.02
Beat Frequency (MHz)
No. of Measurement
Figure 3. Beat frequency of KIM-1 lock on f absorption line and polarized beam of Agilent 5519B.
As type B uncertainty, the relative uncertainty of NaFS was analyzed as a combined uncertainty of UTC uncertainty (uUTC), UTC-UTC(IDN) Link uncertainty (ulink), UTC(IDN) uncertainty (uUTC IDN( )), and stability of NaFS (uStability). All values of those parameters were taken from Circular T (July 2019 – March 2020) that published by BIPM as a result of key comparison CCTF-K001.UTC, describe with formula in Eq (8) (APMP Guideline, 2013):
1
2 2 2
2 2
( )
UTC link NaFS
UTC IDN stability
u u
u u u
(8) Under this study, we took to the account some physical parameters from Circular-T in the period of July 2019 –
March 2020 for case study of uNaFS calculation, e.g. the worst value for the fractional deviation and standard uncertainty of UTC were 6.7×10-16 and 2.1×10-16, respectively in relative form. UTC uncertainty (uUTC) equal to 7.0×10-16 based on the calculation with formula in Eq. (9):
1
2 2
2
fractional deviation standard uncertainty uUTC
(9)
In the Eq. (9), we assume frequency offset of UTC is always zero and fractional deviation is treated as an uncertainty.
UTC-UTC(IDN) uncertainty (ulink) is determined by formula in Eq. (10):
UTC-UTC(IDN) link uncertainty 86400 5 2
ulink
(10)
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The existence of a multiplicative factor 2 due to the consideration the link uncertainty on both sides of the calculation period for every five days. The worst value of type A uncertainty of UTC-UTC(IDN) uncertainty in the period of July 2019 – March 2020 was 0.7 ns. So, ulinkequal to 2.3×10-15.
UTC(IDN) (uUTC IDN( )) uncertainty was determined from the calculation of frequency difference between UTC and UTC(IDN) for every five days (dF). Based on Circular T published by BIPM (July 2019 – March 2020), average of dF (dF) equal 2.4×10-14 with 2.6×10-14 standard deviation. uUTC IDN( ) equal to 3.5×10-14 that calculated by formula in Eq. (11):
2 2
12( )
UTC IDN
u dF stdev dF (11)
Frequency stability of National Frequency Standard (NaFS) was determined as stability of the source oscillator of the atomic clock Cesium HP5071A. NaFS in SNSU-BSN is maintained by Sub Directorate of National Measurement Standards for Electricity and Time. Stability of NaFS 5.9×10-14 (@ 1 day) calculated taken from Circular T (July 2019 – March 2020). The identified uncertainties to analyze uNaFS based on Eq. (8) are tabulated in Table 2.
Table 2. The Identified Uncertainties in uNaFS Calculation
Uncertainty Value (relative)
u(xi) Xi
uUTC 7.0×10-16
uLink 2.3×10-15
( )
UTC IDN
u 3.5×10-14
Stability
u 5.9×10-14
uNaFS 5.9×10-14
Based on the evaluation of theuNaFS, stability of NaFS is the source uncertainty that significantly contributes to the NaFS uncertainty compare to the others.
Universal Counter Agilent 53132A was used for measuring beat frequency signal of KIM-1 and UUC laser. The uncertainty calculation of 0.01 – 225 MHz frequency measurement was determined by formula in Eq. (12) (Agilent, 1999):
2 2
time base error
gate time 4 (2 trigger error ) gate time number of samples 2
gate time
acc
res ctr
jitter
t
u t f
t
(12)
Since 10 MHz of NaFS used as a frequency reference of the universal counter, time base error taken from uncertainty of NaFS (5.9×10-14, relative).
The operation manual of Agilent 53132A mentions tacc = 100 ps (worst case), tres= 225 ps (typical), and tjitter= 3 ps. Number of samples was calculated following the method in the manual, which specifies multiplying the gate time setting by the
frequency to be calibrated for the frequency less than 200 kHz and by 2×105 for frequency greater than 200 kHz. Trigger error of the counter is 7.1×10-13 (Agilent, 1999). The calculation result of the counter uncertainty based on Eq. (12) is 1.3×10-11 (relative).
Reference frequency 10 MHz of NaFS is distributed by mean of frequency distribution amplifier (FDA). Therefore, it is necessary to consider incremental uncertainty derived from the insertion of FDA (Microsemi 4036B S/N: He-96011-02) with temperature coefficient 10 ps/degree and placed in room with maximum of variation temperature 6 C for half day of
variation time. Thus, uncertainty of FDA (uFDA) is 1.4×10-15 (relative) was obtained by formula in Eq. (13) (APMP Guideline, 2013):
Temp CoeffTemp Variation 2
FDA Variation Time
u
(13) NaFS realized in Atomic Clock Ensemble (Cesium atomic clock and FDA) is provided to the calibration room through 25 m coaxial cable with temperature coefficient 0.3 ps/m/degree. Uncertainty of coaxial cable is 1.0×10-15 (relative) that calculated by Eq. (14) (APMP Guideline, 2013):
Time Variation
Length Cable ( Variation Temp
Coeff uCx Temp
(14) Table 3. The Identified Uncertainty Sources of the Beat Frequency Measurement Uncertainty
u(xi)
Standard Uncertainty
ui (relative) Type Sensitivity Coefficient (ci)
Probability Distribution
Uncertainty Contribution (ui.ci)
urep 0 Type A 1 Normal 0
ustd 6.3×10-11 Type B 1 Normal 6.3×10-11
uCtr 1.3×10-11 Type B 1 Rectangular 1.3×10-11
uNaFS 5.9×10-14 Type B 1 Normal 5.9×10-14
uFDA 1.4×10-15 Type B 1 Normal 1.4×10-15
uCx 1.0×10-15 Type B 1 Normal 1.0×10-15
Combine 6.4×10-11 Expanded 1.3×10-10
The identified uncertainties to determine ( )
u f of the beat frequency of KIM-1 and UUC laser are tabulated in Table 3.
Based on uncertainty tabulation shown in Table 3, the best measurement capability of optical wavelength (633 nm) using beat
frequency measurement in SNSU-BSN, declares relative uncertainty of ± 1.3×10-10 shows in Table 3, by excluding UUC effect.
In case of the calibration replica with laser head Agilent 5519B, f = 122.931 MHz and the identified uncertainties shows in
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Table 4. The combine uncertainty of the six uncertainties sources is 3.0×10-2 MHz. The major and significant uncertainty contribution in the beat frequency measurement came from the standard uncertainty (KIM-1). The uncertainty of the beat frequency (u(f)) is 6.0×10-2 MHz which expressed at 95% confidence level with coverage factor k = 2. KIM-1 as reference frequency has nominal value, taken from CCL-K11 comparison result, fKIM-1 = 473 612 353.613 MHz (Matus M., V. Gavalyugov, D. Tamakyarska, M.
Ranusawud, A. Tonmueanwai, F. L. Hong, J. Ishikawa, G. Moona, R. Sharma, A.
Hapiddin, A. M. Boynawan, N. Alqahtani, M. Alfohaid, L. Robertsson, 2017) with uncertainty 0.030 MHz as shown in Table 4.
Therefore, the optical frequency of UUC laser equal to 473 612 230.681 MHz obtained by formula in Eq. (1) with uncertainty u f
UUC
0.090 MHz calculated by using Eq. (5).Table 4. Result of the Identified Uncertainties Calculation for f = 122.931 MHz
Uncertainty Uncertainty Value, absolute
u(xi) (MHz)
urep 3.1×10-3
ustd 3.0×10-2
uCtr 1.6×10-9
uNaFS 7.3×10-12
uFDA 1.7×10-13
uCx 1.2×10-13
We calculated for the optical wavelength of UUC Laser using Eq. (2) with it uncertainty using Eq. (6).
The result was (632.991 376 86 ± 8.0×10-8) nm, correction value -0.000 164 30 nm.
Through this uncertainty analysis, the optical wavelength 633 nm calibration system can be validated and trace back with documented unbroken calibration chain to the primary standard of length, KIM-1 where established in SNSU-BSN.
4. CONCLUSION
The optical wavelength calibration of stabilized He-Ne laser has been evaluated based on the contribution of the uncertainty sources in the measurement system. Beat frequency measurement is applied as a method in calibration system using reference standard of KIM-1. From the uncertainty analysis result, the best measurement capability of the optical wavelength calibration system for stabilized He-Ne laser declares by a relative uncertainty ± 1.3×10-10. Standard uncer-tainty of KIM-1 significantly contributes to the uncertainty of the beat frequency and the optical wavelength of UUC laser. Result of the uncertainty evaluation managed to ensure the calibration capability can be traced back with documented unbroken calibration
chain to the primary standard of KIM-1 in SNSU-BSN.
ACKNOWLEDGMENTS
This research work was supported by the National Measurement Standard Laboratory – National Standardization Agency related to the experiment facilities.
Support from the colleagues in the Length Metrology Laboratory who maintain Agilent 5519B is also acknowledged.
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