Length measurement

Measurement techniques for three-dimensional structures very small in every dimension use specialized instruments such as ion microscopy coupled with intensive computer modeling.

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.

Transit-time measurement underlies most radio navigation systems for boats and aircraft, for example, radar and the nearly obsolete Long Range Aid to Navigation LORAN-C. For example, in one radar system, pulses of electromagnetic radiation are sent out by the vehicle (interrogating pulses) and trigger a response from a responder beacon.

In the top panel the path is such that the two beams reinforce each other after reassembly, leading to a strong light pattern (sun).

The result is the two beams are in opposition to each other at reassembly, and the recombined light intensity drops to zero (clouds).

Thus, as the spacing between the mirrors is adjusted, the observed light intensity cycles between reinforcement and cancellation as the number of wavelengths of path difference changes, and the observed intensity alternately peaks (bright sun) and dims (dark clouds).

By counting fringes it is found how many wavelengths long the measured path is compared to the fixed leg.

By using sources of several wavelengths to generate sum and difference beat frequencies, absolute distance measurements become possible.

This way non-ideal contributions to the refractive index can be measured and corrected for at another frequency using established theoretical models.

It may be noted again, by way of contrast, that the transit-time measurement of length is independent of any knowledge of the source frequency, except for a possible dependence of the correction relating the measurement medium to the reference medium of classical vacuum, which may indeed depend on the frequency of the source.

Similar techniques can provide the dimensions of small structures repeated in large periodic arrays like a diffraction grating.

Older methodologies that use a set of known information (usually distance or target sizes) to make the measurement, have been in regular use since the 18th century.

The time difference between several received signals is used to determine exact distances (upon multiplication by the speed of light).

Ranging methods without accurate time synchronization of the receiver are called pseudorange, used, for example, in GPS positioning.

Measuring dimensions of localized structures (as opposed to large arrays of atoms like a crystal), as in modern integrated circuits, is done using the scanning electron microscope.

These are not transit-time measurements, but are based upon comparison of Fourier transforms of images with theoretical results from computer modeling.

Such elaborate methods are required because the image depends on the three-dimensional geometry of the measured feature, for example, the contour of an edge, and not just upon one- or two-dimensional properties.

It is based on the effect where nuclear spin cross-relaxation after excitation by a radio pulse depends on the distance between the nuclei.

Unlike diffraction measurements, NOESY does not require a crystalline sample, but is done in solution state and can be applied to substances that are difficult to crystallize.