Length measurement

Length measurement is implemented in practice in many ways. The most commonly used approaches are the transit-time methods and the interferometer methods based upon the speed of light. For objects such as crystals and diffraction gratings, diffraction is used with X-rays and electron beams. Measurement techniques for three-dimensional structures very small in every dimension use specialized instruments such as ion microscopy coupled with intensive computer modeling.

For a discussion of astronomical methods for determining cosmological distances, see the article Cosmic distance ladder.

The ruler the simplest kind of length measurement tool: lengths are defined by printed marks or engravings on a stick. The meter was initially defined using a ruler before more accurate methods became available.

Gauge blocks are a common method for precise measurement or calibration of measurement tools.

For small or microscopic objects, microphotography where the length is calibrated using a graticule can be used. A graticule is a piece that has lines for precise lengths etched into it. Graticules may be fitted into the eyepiece or they may be used on the measurement plane.

The basic idea behind a transit-time measurement of length is to send a signal from one end of the length to be measured to the other, and back again. The time for the round trip is the transit time Δt, and the length ℓ is then 2ℓ = Δt*"v",with v the speed of propagation of the signal, assuming that is the same in both directions. If light is used for the signal, its speed depends upon the medium in which it propagates; in SI units the speed is a defined value c₀ in the reference medium of classical vacuum. Thus, when light is used in a transit-time approach, length measurements are not subject to knowledge of the source frequency (apart from possible frequency dependence of the correction to relate the medium to classical vacuum), but are subject to the error in measuring transit times, in particular, errors introduced by the response times of the pulse emission and detection instrumentation. An additional uncertainty is the refractive index correction relating the medium used to the reference vacuum, taken in SI units to be the classical vacuum. A refractive index of the medium larger than one slows the light.

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