Handbook on Selection and use of precise frequency and time systems - Edition of 2026
Preface
Acknowledgements
CHAPTER 1 - Introduction and basic concepts
     1.1 A short note on terms and vocabulary
     1.2 Historical sketch
          1.2.1 Frequency standards
          1.2.2 Radio time dissemination
     1.3 Basic principles of frequency standards
          1.3.1 Quartz crystal frequency standards
          1.3.2 Microelectromechanical Systems (MEMS)
          1.3.3 Atomic frequency standards
               1.3.3.1 Spectroscopic properties of interest
               1.3.3.2 Passive and active atomic frequency standards
     1.4 Basic metrological concepts
          1.4.1 Frequency stability
               1.4.1.1 Definition
          1.4.2 Accuracy
               1.4.2.1 Residual frequency offsets
               1.4.2.2 Definition
     References
CHAPTER 2 - Characterisation: frequency domain, time domain
     2.1 Introduction
     2.2 Model of the oscillator
          2.2.1 The phasor model and the analytic signal
          2.2.2 The low-noise oscillator
          2.2.3 Spectrum of the low-noise oscillator
          2.2.4 The high-noise oscillator
          2.2.5 Spectrum of the high-noise oscillator
          2.2.6 Effect of frequency multiplication
          2.2.7 Demodulation of the noise processes
          2.2.8 Standard definition of noise processes
               2.2.8.1 Amplitude and phase noise processes
               2.2.8.2 Time error process
               2.2.8.3 Instantaneous frequency process
          2.2.9 Multiplicative and additive noise
               2.2.9.1 Multiplicative noise
               2.2.9.2 Additive noise
          2.2.10 Polynomial model
     2.3 Characterisation: definitions and methods
          2.3.1 Spectral domain
               2.3.1.1 Basic definitions
               2.3.1.2 Spectral purity concepts
          2.3.2 Time domain
               2.3.2.1 Introduction
               2.3.2.2 Basic concepts
                    2.3.2.2.1 Model of the frequency counter
                    2.3.2.2.2 Moving average operator
                    2.3.2.2.3 Increment operator
               2.3.2.3 Basic time domain measurements
                    2.3.2.3.1 The true variance
                    2.3.2.3.2 The Allan variance
                    2.3.2.3.3 The modified Allan variance
                    2.3.2.3.4 The time interval error
                    2.3.2.3.5 The time variance
                    2.3.2.3.6  The dynamic Allan variance
                    2.3.2.3.7  A long-term estimator TheoBR
                    2.3.2.3.8 Other time domain measurements
                    2.3.2.3.9 The multi-variance analysis
               2.3.2.4 Pitfalls
                    2.3.2.4.1 Effect of zero-crossing detection
                    2.3.2.4.2 Effect of dead-time
                    2.3.2.4.3 Effect of system bandwidth
                    2.3.2.4.4 Truncation effects
               2.3.2.5 Algorithms
                    2.3.2.5.1 Frequency averaging by phase sampling
                    2.3.2.5.2 Computation of classical Allan variance
                    2.3.2.5.3 Computation of modified Allan variance
                    2.3.2.5.4 Summary
               2.3.2.6 Applications
               2.3.2.7 Conversion between time and frequency domains
          2.3.3 Environmental
     2.4 A bridge to the next Chapter
     2.5 Appendix: Random processes
          2.5.1 Introduction
          2.5.2 Definition of a random process
          2.5.3 Stationary random processes
          2.5.4 Non-stationary random processes
          2.5.5 Auto-correlation function
          2.5.6 Power spectral density
          2.5.7 Linear filtering of random processes
     References
     ITU Texts
CHAPTER 3 - Local frequency and time sources
     3.1 Introduction
     3.2 Quartz crystal frequency standards
          3.2.1 The resonator
          3.2.2 The oscillator
          3.2.3 Frequency instability of quartz crystal oscillators
               3.2.3.1 Random frequency fluctuations
               3.2.3.2 Systematic effects
     3.3 General introduction to AFS
     3.4 Performance characteristics of traditional AFS
          3.4.1 Instability of atomic frequency standards
               3.4.1.1 Short-term frequency stability
               3.4.1.2 Medium-term frequency stability
                    3.4.1.2.1 Medium-term frequency stability in passive frequency standards
                    3.4.1.2.2 Medium-term frequency stability in active frequency standards
               3.4.1.3 Long-term frequency stability
          3.4.2 Accuracy of AFS
               3.4.2.1 Residual frequency offsets
               3.4.2.2 Definition
               3.4.2.3 Primary and secondary frequency standards
          3.4.3 Reproducibility, resettability
     3.5 The rubidium gas cell frequency standard
     3.6 The hydrogen maser
     3.7 The caesium beam AFS
     3.8 Miniaturized atomic frequency standards
          3.8.1 Getting rid of the discharge lamp
          3.8.2  Getting rid of the microwave resonator
          3.8.3 Getting rid of the issue of double-resonance excitation
     3.9 Advanced frequency standards based on laser-cooling and optical transitions
          3.9.1 Atomic fountains
          3.9.2 Other advanced AFS under development
          3.9.3 Optical frequency standards
          3.9.4 Applications of advanced frequency standards
     References
     ITU texts
CHAPTER 4 - Measurement techniques (Metrology)
     4.1 Frequency measurement techniques
          4.1.1 Direct measurement of time (phase)
               4.1.1.1 Estimating the frequency from the time data
          4.1.2 Direct measurement of frequency
          4.1.3 Heterodyne measurements
               4.1.3.1 Homodyne measurements
               4.1.3.2 The dual-mixer configuration
          4.1.4 Measurements of phase noise
               4.1.4.1 Basic measurement methods and techniques
               4.1.4.2 More about the architecture of commercial instruments
     4.2 Measurement techniques for transmission and reception links
          4.2.2 Optical fibre links: measurement methods
               4.2.2.1 Background
               4.2.2.2 Time-delay demodulation in fibre links
               4.2.2.3 Amplitude detection
               4.2.2.4 Coherent telecom techniques
               4.2.2.5 Heterodyne techniques
          4.2.1 Software-Defined Radio measurements in time metrology
               4.2.1.1 Software-defined radio principle
               4.2.1.2 Software-defined radio techniques applied to the TF field
               4.2.1.2 Use of SDR in TF applications
     ITU References
     References for § 4.2.1
     ITU texts
     References for § 4.2.2
CHAPTER 5 - Time Scales
     5.1 Introduction
          5.1.1 Universal Time
          5.1.2 Ephemeris Time
          5.1.3 International Atomic Time
          5.1.4 Coordinated Universal Time
          5.1.5 UTCr: the rapid realization of UTC
     5.2 Time scales in general relativity
          5.2.1 Coordinate systems in general relativity
          5.2.2 The 1991 IAU Resolution A4
               5.2.2.1 Recommendation I
               5.2.2.2 Recommendation II
               5.2.2.3 Recommendation III
               5.2.2.4 Recommendation IV
          5.2.3 The 2000 IAU Resolution B1.9
          5.2.4 International Atomic Time
          5.2.5 Other time scales
     5.3 Generation of time scales
          5.3.1 Expected qualities
               5.3.1.1 Reliability
               5.3.1.2 Stability
               5.3.1.3 Accuracy
               5.3.1.4 Delay of access
          5.3.2 Timing data
               5.3.2.1 General form of timing data
               5.3.2.2 Comparison of clocks located on the same site
               5.3.2.3 Comparison of clocks located on remote sites
          5.3.3 Time scale algorithms
               5.3.3.1 Definition of an average time scale
               5.3.3.2 Length of the basic interval of computation
               5.3.3.3 Weighting procedure
                    5.3.3.3.1 General ideas
                    5.3.3.3.2 Weighting procedure in UTC
                    5.3.3.3.3 Weighting procedure in UTCr
               5.3.3.4 Frequency prediction
                    5.3.3.4.1 General ideas
                    5.3.3.4.2 Frequency prediction in UTC and UTCr
          5.3.4 Accuracy of the scale interval of a time scale
          5.3.5 Examples
               5.3.5.1 Stability of UTC/TAI
               5.3.5.2 Stability of some independent time scales
               5.3.5.3 Steering of some local representations of UTC
     5.4 Dissemination of time scales
          5.4.1 Synchronizing the time scale of a laboratory
          5.4.2 Paper time scales
               5.4.2.1 The Kalman filter
     References
     ITU texts
CHAPTER 6 - Time and frequency dissemination
     6.1 Introduction
     6.2 Radiocommunication services
          6.2.1 VLF Services
          6.2.2 LF services
          6.2.3 HF broadcast
          6.2.4 Television broadcast
          6.2.5 GNSS (Broadcast)
          6.2.6 GNSS signals in high-accuracy applications
          6.2.7 Services based on other geostationary satellites
          6.2.8 Services based on meteorological satellites
          6.2.9 Commercial satellite services
          6.2.10 Two-way satellite time and frequency transfer
     6.3 Standardized wired services
          6.3.1 Services based on telephone
          6.3.2 Solutions and techniques used in computer and telecommunication networks
               6.3.2.1 Introduction
               6.3.2.2 Network Time Protocol (NTP)
               6.3.2.3 Precision Time Protocol (PTP)
               6.3.2.4 Distribution of time and frequency in telecommunication networks
               6.3.2.5 White Rabbit and High Accuracy PTP
               6.3.2.6 Other solutions
     6.4 Specialized high accuracy fibre-based services
          6.4.1 Modulation-based: ELSTAB
          6.4.2 Optical carrier-based
               6.4.2.1 Ultra-stable optical frequency transfer
               6.4.2.2 Delay and delay variations
               6.4.2.3 Free-running phase noise
               6.4.2.4 Stabilization techniques
                    Active noise cancellation
                    Two-way techniques
               6.4.2.5 Cascaded links
               6.4.2.6 Amplification techniques
               6.4.2.7 Compatibility with parallel data traffic
               6.4.2.8 Performances
               6.4.2.9 Fibre network for time and frequency dissemination
               6.4.2.10 Dedicated frequency channels
          6.4.3 Building scientific and societal infrastructure
          6.4.4 Implementation of optical fibre networks
          6.4.5 Outlook: fibre sensing
     References
     ITU Texts
CHAPTER 7 - Use of frequency sources
     7.1 Use of frequency sources in science and metrology
     7.2 Definition of the standard frequency
     7.3 Fundamental physics
     7.4 Applied physics
          7.4.1 Local measurement of g, the acceleration of gravity
          7.4.2 Global measurements of the gravitational constant G, and the gravitational potential g
          7.4.3 Very long baseline interferometry (VLBI)
     7.5 Positioning and navigation
          7.5.1 System design
          7.5.2 Doppler solutions
          7.5.3 Differential solutions
          7.5.4 Spherical solutions
               7.5.4.1 Timing applications based on spherical solutions
     7.6 Telecommunications
          7.6.1 Channel capacity
          7.6.2 Frequency division multiplexing
          7.6.3 Time division multiplexing
          7.6.4 The ITU-T standardization work
          7.6.5 Trellis coding
     7.7 Provision of electrical power
     7.8 Concluding comment
     References
     ITU texts
CHAPTER 8 - Time as a Service
     8.1 Overarching issues regarding the use of frequency sources
     8.2 Reliability, good practice of installation
     8.3 Resilience
     8.4 Traceability
CHAPTER 9 - Future prospects
     9.1 Introduction
     9.2 Optical frequency standards
          9.2.1 Single ion clocks
          9.2.2 Neutral atom clocks
          9.2.3 Specialized optical clocks
          9.2.4 Optical local oscillators and frequency combs
          9.2.5 Comparison of optical clocks
     9.3 Commercial optical clocks
          9.3.1 Optical atomic clocks based on the RB two-photon transition
          9.3.2 Optical frequency standards based on I₂ molecular transitions
          9.3.3 Optical clocks based on the laser-cooled single ions or atoms
     9.4 Applications
          9.4.1 Optically steered time scale
          9.4.2 Chronometric geodesy
          9.4.3 Information and communication systems
     9.5 The redefinition of the SI second
     References
CHAPTER 10 - Summary and conclusions
     10.1 Introduction
     10.2 Clocks and oscillators
          10.2.1 Devices based on a mechanical resonance
          10.2.2 Microwave atomic clocks
          10.2.3 Optical atomic clocks
          10.2.4 The future
     10.3 Clock ensembles
          10.3.1 Incorporating primary reference oscillators
          10.3.2 The Internet of Things (IoT)
     10.4 Networks of clocks
     References