Metrology concerns the science of measurement and is used in every branch of science and technology. High-level metrology is incredibly important for making high-accuracy measurements and manufacturing, where machinery must make precise movements.
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Even aircraft manufacturing now makes extensive use of metrological measurements for quality control – though making and verifying measurements at this large scale poses its own set of challenges.1
Metrological measurements provide verification of another measurement and provide a confidence level to any quoted values – for example, whether a translation stage moves within an accuracy of 0.1 or 0.01 mm.2 This is essential when working out whether a piece of equipment or a process will meet tolerance requirements, particularly for nanoscale fabrication techniques and high spatial resolution lithography methods that are particularly demanding in this area.
Optical Metrology
One of the most widely used metrological instruments has been optical laser systems combined with interferometer designs. Optical metrology is the science of measuring with light and covers a number of different measurement types, including time-of-flight measurements to measure distance, time domain reflectometers for evaluating fiber optics, and optical temperature sensors that analyze the thermal emission or energy level distribution in a target.3
An optical interferometer works on the principle of interference between two beams. In the simplest design, the incoming beam is split in two and sent along two different arms, usually described as the reference and variable arms. The reference arm has a fixed path length, but the path length can be varied along the variable arm to scan the interference pattern when the beams are recombined at the end for detection.
Changes in distance between the two arms correspond to a change in the interference patterns between the beams, making the interferometer highly sensitive to even small changes in distance, whether that is from the measurement system itself or external changes like small vibrations.
Many different interferometer designs can be used for metrology measurements. Computer-aided designing and manufacturing (CAD/CAM) methods like laser cutting or ion beam lithography incorporate laser-based interferometers in the equipment design to create feedback systems for sample or beam positioning. For microscale and below fabrication, there are also now a number of laser-based micrometer systems for high-precision gauge measurements.4,5
While optical metrology has undoubtedly been incredibly successful for many applications, there are still some challenges to overcome and some inherent limitations. Large-scale systems pose on set of challenges1, but the ever-decreasing size of devices, more nanoscale fabrication techniques and great demands on material qualities mean the advanced manufacturing market needs new metrological procedures.
The shot-noise limit of the light source used in an optical metrology instrument poses the ultimate limitation in phase-sensitive measurements, alongside the Rayleigh limit that limits the angular resolution.6 Designing metrological measurements that achieve close to these limits is very challenging, but a different approach than classical optical metrology is required to achieve the ultimate metrological precision.7
Quantum Metrology
Quantum metrology represents the ultimate metrological resolution, making it possible to surpass the shot-noise limit restricting classic measurements.6 Quantum metrology often serves two purposes – first, making higher resolution and accuracy measurements that would not be possible with classical techniques, but secondly, as a means of quantum hypothesis testing – verifying whether a process occurring is truly quantum or not.
Many quantum metrology instruments resemble their classical counterparts. Interferometers are commonly used in combination with laser light sources8, but the key difference is in the observables that are being measured.
Quantum metrological instruments often use entangled states or some squeezed states. One of the earliest and most famous examples of quantum metrology is the atomic clock, where the frequency of the vibrations in the ammonia molecule is used to set the international frequency standard. This was later replaced with the cesium atomic clock – where the frequency standard was set against a resonant frequency of the atom.
Squeezing light is a way of reducing the noise fluctuation in one parameter of the light. Most squeezed light is done by manipulating the position and momentum of the light. Heisenberg’s Uncertainty principle means that a precise knowledge of two conjugate variables is not possible.
By reducing the noise fluctuation by squeezing the light in the momentum domain, it increases the position. If the squeezed domain is used for the metrological measurements, this allows the instrument to surpass the classical shot-noise limit.
Many areas of optics and metrology research are making use of the noise reduction possible through the exploitation of quantum phenomena as this ultimately allows for more sensitive and greater precision measurements. For the biological and life sciences, the improved imaging resolution that can come from harnessing quantum metrology is highly appealing for imaging smaller and smaller biological structures.9 Entangled two-photon measurements are now being used in microscopy and super-resolution methods are being adapted to look at quantum correlations in systems.
References and Further Reading
Schmitt, R. H., et al. (2016). Advances in Large-Scale Metrology – Review and future trends. CIRP Annals - Manufacturing Technology, 65(2), pp.643–665. doi.org/10.1016/j.cirp.2016.05.002
Brown, R. J. C. (2021). Measuring measurement – What is metrology and why does it matter? Measurement, 168, pp.108408. doi.org/10.1016/j.physrep.2015.12.002
Gåsvik, K. J. (2003). Optical metrology. John Wiley & Sons. https://www.wiley.com//legacy/wileychi/opticalmetrology/
Stoup, J., & Doiron, T. (2021). A novel high accuracy micrometer for the measurement of diameter. Metrologia, 58, p.025002. https://iopscience.iop.org/article/10.1088/1681-7575/abd3b2
Valino, G., et al. (2017). Non-contact measurement of grinding pins laser micrometer laser micrometer. Procedia Manufacturing, 13, pp.534–541. doi.org/10.1016/j.promfg.2017.09.080
Cohen, L., et al. (2014). Super-resolved phase measurements at the shot noise limit by parity measurement. Optics Express, 22(10), pp.11945–11953. doi.org/10.1364/OE.22.011945
Zhu, J., et al. (2023). Achieving 1 . 2 fm / Hz 1 / 2 Displacement Sensitivity with Laser Interferometry in Two-Dimensional Nanomechanical Resonators : Pathways towards Quantum-Noise-Limited Measurement at Room Temperature. Chinese Physics Letters, 40, p.03102. doi.org/10.1088/0256-307X/40/3/038102
Liu, J., & Jing, X. (2013). Phase-matching condition for enhancement of phase sensitivity in quantum metrology. Physical Review A, 88, p.042316. doi.org/10.1103/PhysRevA.88.042316
Taylor, M. A., & Bowen, W. P. (2016). Quantum metrology and its application in biology. Physics Reports, 615, pp.1–59. doi.org/10.1016/j.physrep.2015.12.002
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