Metrology and SI

…statistical analysis of repeating measurements

… information from other sources (calibration data, literature, manufacturer specs)

Time-of-flight

1. Counting atoms in a silicon sphere

2. Gravimetric methods

3. Gas methods – using the ideal gas law

4. Electrochemical methods

Law of propagation of uncertainty

1. f: Function that defines how yy depends on the input quantities xixi​

2. xi: Input quantities

3. u(xi): Standard uncertainty of each input quantity xi

• The function f(x1,x2,...,xn) that relates inputs to the output must be differentiable.

• Input quantities must be uncorrelated — unless covariances are included.

Precision is the closeness of agreement between repeated measurements under the same conditions.

It tells you how consistent the results are — not how close they are to the true value.

Nonlinearity is the deviation of a measuring system's output from a straight-line (linear) relationship between input and output.

Bundesamt für Eich- und Vermessungswesen (BEV)

• h: Planck constant

• NA​: Avogadro constant

• Kcd​: Luminous efficacy constant

c = speed of light in vacuum

• ⟨V2⟩: Mean-square noise voltage

• k: Boltzmann constant

• T: Absolute temperature (in kelvin)

• R: Electrical resistance (in ohms)

• Δf: Bandwidth over which the noise is measured (in hertz)

Accuracy is the closeness of agreement between a measured value and the true value of the measurand.

It combines both:

• Precision (repeatability)

• Trueness (closeness to the reference value).

Slew rate is the maximum rate of change of the output signal of a measuring system.

It shows how fast the system can respond to a changing input over time.

In metrology, a standard is a realization of a quantity with a known value and associated uncertainty, used as a reference for calibration.

• ΔvCs​: Hyperfine transition frequency of Caesium-133

• c: Speed of light in vacuum

• kB​: Boltzmann constant

• e: Elementary charge

Kcd = luminous efficacy of monochromatic radiation

An optical interferometer is a device that splits a beam of light, sends the parts along different paths, and then recombines them to measure the difference in path length based on interference patterns.

It’s used for precise distance measurements, especially in metrology

1. Length – unit: meter (m)

2. Mass – unit: kilogram (kg)

3. Time – unit: second (s)

4. Electric current – unit: ampere (A)

5. Thermodynamic temperature – unit: kelvin (K)

6. Amount of substance – unit: mole (mol)

7. Luminous intensity – unit: candela (cd).

The 7 base units of the SI (International System of Units) are:

1. Meter (m) – for length

2. Kilogram (kg) – for mass

3. Second (s) – for time

4. Ampere (A) – for electric current

5. Kelvin (K) – for thermodynamic temperature

6. Mole (mol) – for amount of substance

7. Candela (cd) – for luminous intensity

Trueness is the closeness of agreement between the average of many measured values and a reference (true) value of the measurand.

It reflects how unbiased the measurements are

An atom clock uses the fixed frequency of an atomic transition as a reference to keep time. A feedback loop adjusts a microwave oscillator to stay in resonance with this atomic frequency, ensuring extremely precise timekeeping.

The operation that, under specified conditions, establishes a relation between the quantity values and uncertaintiesprovided by measurement standards and the corresponding indications of a measuring instrument, and uses this information to produce a measurement result.

1. Acoustic Gas Thermometry

2. Radiometric Thermometry

3. Johnson Noise Thermometry

4. Fixed-point Thermometry

Johnson noise thermometry is especially suited for very low temperatures (below 4 K), due to its high sensitivity in that range.

Radiometric thermometry is a method to determine temperature by measuring the thermal radiation emitted by an object and applying Planck’s law of blackbody radiation.

It is especially useful at high temperatures (e.g. >1000 K).

Radiant intensity measures physical power per solid angle (W/sr), while luminous intensity (cd) is weighted by human eye sensitivity to different wavelengths — it reflects perceived brightness.