**1. Introduction**

50 Modern Metrology Concerns

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Absolute distance metrology is needed for a wide gamut of applications with different ranges and resolutions. One good example is space missions requiring independent satellites working cooperatively: the management of such formations requires several levels of metrology to keep the formation coherent and to enable guidance and navigation of the complete formation (Calvel et al., 2004). Beyond a certain level of accuracy, at the end of the metrology chain, optical metrology becomes mandatory to achieve the required high accuracy.

Optical metrology is normally used to describe the measurement of some physical parameter using optical methods. Almost all of the technical fields we can think of make use of optical metrology. A good example is the use of interferometry to achieve high accuracy in length measurements. Optical interferometry relies on the phenomenon of interference between light waves to make extremely accurate measurements. In 1887, Michelson, along with physicist Edward W. Morley, set up an experiment to determine if the speed of light was dependent on the speed of the observer. According to the accepted theory of that time, light had to propagate in a medium called the ether. The motion of Earth travelling through the ether would affect the fringe pattern on Michelson's interferometer, because it would take the light longer to travel over one arm than the other arm. When the interferometer was rotated through 90°, the fringes would shift if the speed of light was not constant. In this most celebrated null experiment in the history of science, Michelson and Morley observed no changes in the fringes after many repetitions. The speed of light appeared to be constant, regardless of the speed of its source, a fact that was later explained by Einstein's theory of relativity.

The "failure" of the Michelson-Morley experiment was the seed of the new science of interferometry. The improved device used in the Michelson-Morley experiment was one of the first interferometers, and Michelson, who had always an intense passion for accuracy in measurement, quickly recognized his invention's potential for highly accurate instrumentation.

Since its debut, the interferometer (Fig. 1) has undergone a number of modifications and has been specialized for use in a variety of fields. In 1895, Michelson used it to measure the International Prototype Metre in Paris in units of wavelength (Michelson & Benoit, 1985).

Fig. 1. Setup of a Michelson interferometer.

Michelson's contributions to interferometry, from 1880 to 1930, dominated the field to such extent that optical Interferometry was regarded for many years as a closed chapter. However, the last few decades have seen an explosive growth of interest in interferometry due to several new developments, mainly associated to the light source. The improvement of frequency stabilised lasers, of frequency tunable lasers and, lately, the appearance of femtosecond lasers have encouraged the use of the interferometer in dimensional metrology. In addition, nanometre-level interferometry with low-coherence sources has also created a plethora of additional metrological applications and technological developments. Interferometry is still alive in the XXI century.

Coherent absolute distance metrology is one of the most interesting techniques for dimensional metrology. Without movement of the mirror that define the Optical Path Difference (OPD) in the interferometer, measurements are made without ambiguity, by using either one or several synthetic wavelengths resulting from the beating of two or more wavelengths (multiple wavelength interferometry) or, in the case of frequency sweeping interferometry, from an optical frequency sweep.

Frequency Sweeping Interferometry (FSI) based sensors are relatively simple devices and can fulfil an important role in dimensional metrology. In addition, their parameterisation flexibility allows various tradeoffs to be performed, either technology driven or application related.

The generation of the synthetic wavelength in FSI is based on optical frequency sweeping the laser source within a given sweep range. As frequency sweeps, detection electronics counts synthetic wavelength maxima (temporal "synthetic fringes") without ambiguity. Its sensitivity to variations of distance (drift) during the sweep limits the maximum resolution to a few micrometres. FSI does not require stabilised or well known laser sources and relies only on a tunable laser and a frequency sweep range measurement subsystem (for example, based on a Fabry-Pérot interferometer). FSI sensor complexity can be tuned to system specifications – when requirements are modest, FSI complexity is reduced accordingly.

In the last years, FSI has seen a considerable development and several solutions have been presented. The most important are based only upon a tunable laser and a frequency measurement sub-system, systems built around both a reference and a measurement interferometer, or based on the use of an additional stabilized laser, some developed for high accuracy under special controlled laboratory conditions, others driven by robustness in

Michelson's contributions to interferometry, from 1880 to 1930, dominated the field to such extent that optical Interferometry was regarded for many years as a closed chapter. However, the last few decades have seen an explosive growth of interest in interferometry due to several new developments, mainly associated to the light source. The improvement of frequency stabilised lasers, of frequency tunable lasers and, lately, the appearance of femtosecond lasers have encouraged the use of the interferometer in dimensional metrology. In addition, nanometre-level interferometry with low-coherence sources has also created a plethora of additional metrological applications and technological developments.

Coherent absolute distance metrology is one of the most interesting techniques for dimensional metrology. Without movement of the mirror that define the Optical Path Difference (OPD) in the interferometer, measurements are made without ambiguity, by using either one or several synthetic wavelengths resulting from the beating of two or more wavelengths (multiple wavelength interferometry) or, in the case of frequency sweeping

Frequency Sweeping Interferometry (FSI) based sensors are relatively simple devices and can fulfil an important role in dimensional metrology. In addition, their parameterisation flexibility allows various tradeoffs to be performed, either technology driven or application

The generation of the synthetic wavelength in FSI is based on optical frequency sweeping the laser source within a given sweep range. As frequency sweeps, detection electronics counts synthetic wavelength maxima (temporal "synthetic fringes") without ambiguity. Its sensitivity to variations of distance (drift) during the sweep limits the maximum resolution to a few micrometres. FSI does not require stabilised or well known laser sources and relies only on a tunable laser and a frequency sweep range measurement subsystem (for example, based on a Fabry-Pérot interferometer). FSI sensor complexity can be tuned to system specifications – when requirements are modest, FSI complexity is reduced accordingly.

In the last years, FSI has seen a considerable development and several solutions have been presented. The most important are based only upon a tunable laser and a frequency measurement sub-system, systems built around both a reference and a measurement interferometer, or based on the use of an additional stabilized laser, some developed for high accuracy under special controlled laboratory conditions, others driven by robustness in

Fig. 1. Setup of a Michelson interferometer.

Interferometry is still alive in the XXI century.

interferometry, from an optical frequency sweep.

related.

uncontrolled environments (Kinder & Salewski, 2002; Cabral & Rebordão, 2005; Swinkels et al., 2005; Yang et al., 2005). An example is the Dual FSI concept, conceived to overcome the decrease in accuracy as the measurement range increases, as a consequence of the uncertainty propagation in the synthetic wavelength measurement. To overcome this problem, in order to maintain the low complexity associated to short distances, in Dual FSI the measurement process for larger ranges is reduced to the close range case, by increasing the reference arm with a long reference fibre and using an ancillary interferometer to measure (calibrate) continuously the fibre length.
