time & frequency metrology an introduction€¦ · 1 tropical year = 365,2422 solar days = 366,2422...
TRANSCRIPT
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Time & Frequency MetrologyAn introduction
Cold Atoms and Molecules & Applications in Metrolog y
16-21 March 2015, Carthage, Tunisia
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 1
Noël DimarcqSYRTE – Systèmes de Référence Temps-Espace, Paris
An introduction
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Contents
� Measurement of time with a linear process – Earth rotation
� Measurement of time with a periodic process – The oscillators and their defaults
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 2
� Time, frequency and phase – Relations and noise characterization
� Conclusion
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Contents
� Measurement of time with a linear process – Earth rotation
� Measurement of time with a periodic process – The oscillators and their defaults
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 3
� Time, frequency and phase – Relations and noise characterization
� Conclusion
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Flows : Water clock Sand clock
Measuring time with a « linear » process
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 4
Combustion : Candles
Rotation : Earth rotation angle
Oil lamp
Measured time = K x measured parameter = Real time?
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Gnomons, sundials and meridian telescopes
Measuring time with Earth rotation
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 5
Measuring time = Knowledge ot he Earth orientation
���� Measured time = K x θθθθEarth
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The SI unit of time – the second – is defined as :
���� until 1956 : the fraction 1/86 400 of the mean solar day
Definitions of the unit of time
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 6
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The length of the solar day fluctuates due to :
- Tilt of the Earth rotation axis and the ellipticit y of the Earth orbit around the Sun
- Precession of the equinoxes
Irregularities of the solar day
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 7
in minutes
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The SI unit of time – the second – is defined as :
���� until 1956 : the fraction 1/86 400 of the mean solar day
���� 1956 to 1967 : the fraction 1/31,556,925.9747 of the tropical year 1900 1 tropical year = 365,2422 solar days = 366,2422 sideral days
Definitions of the unit of time
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 8
1 tropical year = 365,2422 solar days = 366,2422 sideral days
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The earth rotation rate fluctuates due to :
- tides (Moon, Sun)
- inner effects (core – mantle interface)
- atmosphere and meteorological effects
- hydrological effects
- seisms (earthquakes, tsunamis, …)
Fluctuations of Earth rotation
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 9
seisms (earthquakes, tsunamis, …)
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Fluctuations of Earth rotation
0
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 10
Leap seconds
���� Next leap second on 30 June 2015
23:59:5823:59:5923:59:6000:00:0000:00:01
(in UTC)
1900Leap seconds
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Contents
� Measurement of time with a linear process – Earth rotation
� Measurement of time with a periodic process – The oscillators and their defaults
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 11
� Time, frequency and phase – Relations and noise characterization
� Conclusion
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���� Analogy with the measurement of a length with a rul er : count the graduations between the start and the end
Measuring time with a periodic process
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 12
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Physical signal
Oscillator = temporal ruler
Period = elementary temporal graduation
���� Measuring time with an oscillator : count the oscil lations between the start and the end
Measuring time with a periodic process
T : period
ν = 1/T : frequencyT
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 13
signal
Counter
1234
t
t
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���� The thinner the graduations, the better the measure ment precision
Importance of the size of the graduations
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 14
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t
t
���� The smaller the period ( = the higher the frequency), the better the measurement precision
Importance of the oscillator frequency
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 15
t
νννν [Hz]1 103 106 109 1012 1015
mechanicalOscillator ���� quartz microwave laser
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kHz – MHz : BAW quartz oscillators (Bulk Acoustic Waves), MEMS Si
MHz – GHz : SAW quartz oscillators (Surface Acoustic Waves), FB AR (Film Bulk-Acoustic wawe Resonator), …
10 GHz : DRO (Dielectric Resonator Oscillators), cryogenic o scillators (whispering modes), OEO-Optoelectronic oscillators…
THz – 1000 THz : Laser
Oscillators families
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 16
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Which confidence in a measurement ?
Measurement at another moment or with another ruler
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 17
Quality of the measurement =
Evaluation of the uncertainty (fluctuations, biases ) +
Necessary comparisons between various standards
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t
Which confidence in time measurement ?
Variations of the oscillation frequency during the measurement or oscillators with
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 18
Quality of time measurement =
Evaluation of the frequency fluctuations and freque ncy biases +
Necessary comparisons between various standards
oscillators with unequal frequencies
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Defaults of oscillators
� The frequency depends on the oscillator dimensions :L
dLd ∝νν
1610−=ννd
If L = 10 cm dL ~ 0.01 fm
� The frequency depends on the environment (temperatu re, pressure, hygrometry, gravity, vibrations, electromagnetic fi elds, radiations, …)
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 19
Shielding, fine control, stabilization of the environment (T°, P, vibrations, e.m. fields, …)
Use of materials with low thermal expansion coeffcients (Invar, Zerodur, ULE, …)
Search for an inversion point to cancel the first order temperature dependence
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Thermal sensitivity of quartz oscillators
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 20
+g-sensitivity
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Gravimetric sensitivity of a mechanical pendulum
« En 1672, M. Richer étant allé à l'isle de Cayenne, environ à 5d de l'équateur, pour y faire des observations astronomiques, trouva que son horloge à pendule qu'il avoit reglée à Paris, retardoit de 2' 28''par jour »
l
g
πν
2
1≈
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 21
lπ2
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Gravimetric sensitivity of a mechanical pendulum
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 22
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CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 23
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−≈ 20161
12
1 θπ
νl
gPendulum frequency
Other defaults of oscillators
� The frequency depends on the oscillation amplitude (isochronism default)
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 24
� Ageing effects
Frequency drifts
Frequency jumps
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OSCILLATOR
(quartz, µw, laser, …)
frequency νννν :
Unstable
Inaccurate
νννν
ATOM / ION
SERVO LOOP
correctionfrequency νννν :
Stable
Accurate
= νννν0
Basic principle of atomic clocks / atomic frequency standards
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 25
νννννννν0000
E2
E1h νννν0 = E2 –E1
ATOM / ION REFERENCE
νννν0 νννν
CLOCK SIGNAL
2
1
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The SI unit of time – the second – is defined as :
���� until 1956 : the fraction 1/86 400 of the mean solar day
���� 1956 to 1967 : the fraction 1/31,556,925.9747 of the tropical year 1900 1 tropical year = 365,2422 solar days = 366,2422 sideral days
Definitions of the unit of time
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 26
1 tropical year = 365,2422 solar days = 366,2422 sideral days
���� since 1967 : the duration of 9 192 631 770 periods of the radi ation corresponding to the transition between the two hyp erfine levels of the ground state of the cesium 133 atom ( Added in 1999 ���� This definition refers to a cesium atom at rest at a temperature of 0 K)
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Contents
� Measurement of time with a linear process – Earth rotation
� Measurement of time with a periodic process – The oscillators and their defaults
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 27
� Time, frequency and phase – Relations and noise characterization
� Conclusion
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An oscillator is never perfect…
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 28
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( )y(t)ευυ(t) ++×= 100
)()(
νδν t
ty =
Real Ideal Frequency Frequency
( )ttA ).(.2cos. υπSignal delivered by a frequency standards :
Frequency uncertainties
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 29
frequency frequency bias fluctuations
Instability : « amplitude » of frequency fluctuations (« type A » uncertainty uA)
Inaccuracy : uncertainty δεδεδεδε on the frequency bias due to systematic effects (« type B » uncertainty uB)
Total frequency uncertainty u total : 222
BAtotal uuu +=
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Stability and accuracy
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 30
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0υυ(t) =Frequency :
tdttυ(t)t
..2')'(2 0νππϕ == ∫Phase :
( )ttASignal ).(.2cos. υπ= ( ) ( ))(cos.).(.2cos. tAttASignal ϕυπ == ( ) ( ) ( ))(..2cos.)(cos.).(.2cos. 0 tTAtAttASignal υπϕυπ ===Frequency, phase and time
Linear evolution of the phase
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 31
ttt
tT ===00
1.
2
)(
.2
)()(
υπϕ
υπϕ
Time :
0
0∫
PeriodNumber of counted oscillations
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( )ευυ(t) +×= 10Frequency :
( )tdttυ(t)t
.1..2')'(2 0 ενππϕ +== ∫Phase :
Frequency, phase and time
( ) ( ) ( ))(..2cos.)(cos.).(.2cos. 0 tTAtAttASignal υπϕυπ ===
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 32
( )ttttT .11.2
)(
.2
)()(
00
ευπ
ϕυπ
ϕ +===Time :
0
0∫
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( )y(t)ευυ(t) ++×= 10Frequency :
( )
++== ∫∫ ')'(.1.2')'(2 0 dttytdttυ(t)
tt
ενππϕPhase :
Frequency, phase and time
( ) ( ) ( ))(..2cos.)(cos.).(.2cos. 0 tTAtAttASignal υπϕυπ ===
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 33
( ) )(.11.2
)(
.2
)()(
00
txttt
tT ++=== ευπ
ϕυπ
ϕTime :
∫=⇔=t
dttytxdt
tdxty
0
')'()()(
)(
∫∫0
0
0
with
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Sy(f)
Sνννν(f) [Hz2.Hz-1]
[Hz-1] σσσσy(ττττ)[dimensionless]
Depending on the applications, the measurement will be sensitive to frequency and/or phase and/or time fluctuations
Characterization of frequency, phase and time noises
Frequency
noise / uncertainty
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 34
Phase
noise / uncertainty
Time
noise / uncertainty
Sφφφφ(f) [rad2.Hz-1] σσσσx(ττττ) [s]
Variances and deviations
Characterization on long term (« low » Fourier frequency)
Power Spectral Densities
Characterization on short term (« high » Fourier frequency)
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Total measurement noise with a bandpass [f0-∆f/2 , f0+∆f/2] :
dffSff
ff).(noise Total
2/
2/
0
0∫
∆+
∆−= υ
Sν(f) : Power Spectral Density (PSD) of the frequency noise [in Hz2 /Hz]
Spectral description of noise (ex.: frequency noise)
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 35
Fourier frequency ff0
∆∆∆∆f
Sν(f)
τ1∝∆f
Averaging over a duration ττττ
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PSD for different noise types
∑== αανν fh
fSfSy )(1
)(20
Relative frequency noise
(independent of νννν0)Absolute frequency noise
(dependent on νννν0)
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 36
f
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Time description of noise
νδν=)(ty
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 37
( ) ( )212 21 τττσ kky yy −= +
( ) ( )212 τττσ kky yy −= +
Allan deviation:
Classical variance:
Average over all the
τky
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Allan variance and filtering
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 38
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Relation between PSD and Allan deviation
τ τ τ τ : integration time
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 39
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Allan deviation behaviour
White frequency noise: the frequency stability (Allan deviation) improves as
τ1
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 40
σσσσy(ττττ)
τ τ τ τ [s]
deviation) improves asτ
1
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White frequency noise: the frequency stability (Allan deviation) improves as 1
Allan deviation behaviour
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 41
Frequency flicker noise:
Stability floor
σσσσy(ττττ)
τ τ τ τ [s]
deviation) improves asτ
1
-
10-13
100
τ τ τ τ -1/2 τ τ τ τ +1/2
∫=⇔=t
dttytxdt
tdxty
0
')'()()(
)(
Allan deviation (in frequency) and time deviation
���� Case of white frequency noise
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 42
10-1 100 101 102 103 104 105 106 107
10-16
10-15
10-14
10
σσ σσ y( ττ ττ
)
ττττ [s]
10-1 100 101 102 103 104 105 106 107
0,1
1
10
σσ σσ x( ττ ττ
) [p
s]ττττ [s]
τ τ τ τ -1/2 τ τ τ τ +1/2
σσσσy(ττττ)σσσσX(ττττ)
ττττ ττττ
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[ ]( )ttt .)()(.2cos 21 υυπ −
21 υυ −22
21 σσ +
Mean frequency difference :(for Tuning / Syntonisation)
Total noise :
Comparisons – Beatnote technique
)T-T( 2121 ϕϕ −
If equal frequencies, mean phase (or time) difference (for Synchronization) :
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 43
FrequencyStandard
1
Frequency Standard
2
)).(.2cos(. 11 ttA υπ )).(.2cos(. 22 ttA υπ
)).(.2cos().).(.2cos( 2121 ttttAKA υπυπ
Low pass filter
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At the beatnote output:
o mean value of the frequency difference ���� validation of the frequency accuracy budget
o total noise of the frequency difference ���� access to the frequency (or phase) stability
( ) ( ) ( )222 σσσ +=
Comparisons – Beatnote technique
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 44
- if standard 1 is much better than standard 2:
- if the two standards are identical:
( ) ( ) ( )22 standard21 standard2notebeat σσσ +=
notebeat 2 standard σσ =
2notebeat
2 standard1 standard
σσσ ==
-
[ ]( )ttt .)()(.2cos 21 υυπ −
Frequency / Phase locking of a slave oscillator
to a master oscillator
Frequency or Phase Lock Loop (PLL)
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 45
Master oscillator
Slaveoscillator
)).(.2cos(. 11 ttA υπ )).(.2cos(. 22 ttA υπ
Low Pass Filter
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Contents
� Measurement of time with a linear process – Earth rotation
� Measurement of time with a periodic process – The oscillators and their defaults
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 46
� Time, frequency and phase – Relations and noise characterization
� Conclusion
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1000 yrs
1 million yrs
1 billion yrs
1 second
error after:
Industrial Cs beam clocks
Cold atom fountain
Optical clocks
Precision of time measurement
Age of universe
10-16
10-18
δν/νδν/νδν/νδν/ν
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 47
1000 yrs
1 year
1 hour
1600 1700 1800 1900 2000
1 second
error after:
Harrison clock
Shortt clock
Quartz oscillator
First Cs beam clock
Astronomical, mechanical and electrical era Atomic era
Huygens pendulum
1 day
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� Local oscillators in any electronic devices, PLL, f ilters, sensors, …
� Fundamental metrology (SI units), time scales(TAI, UTC, UTC(k), )
� Ranging, positioning, navigation, GNSS
� Network synchronisation, telecom, smart grids, DSN, VLBI, …
Wide spectrum of T/F metrology applications
CAMAM 2015, N. Dimarcq, « T/F metrology – An introduction » 48
� Fundamental physics (drift of fundamental constants , gravitational shift, high precision spectroscopy, …)
� Detection of gravitation waves, relativistic geodes y
� Astronomy (pulsars time tagging)
� RADAR, LIDAR, atmosphere analysis, …
� Etc, etc, etc …