Open Access
Add to BibSonomy
Abstract
Mass sensing offering both a broad detection range and a high resolving power is essential for quantitative precision content analysis and high-yield mass production of various kinds of materials. Here, we propose and successfully demonstrate a novel type of simple low-cost optomechanical mass sensing employing an optical displacement detector that consists of a free-space Fabry-Pérot optical cavity and an intra-cavity wedge prism pair, which provides an enhanced resolution and an extended capacity simultaneously. By implementing the null-method-based scheme of mass measurement, we achieve a resolution higher than 5000:1 (mass range from <200 mg to >1 kg) and an excellent linearity of R2>0.99998 in the prototype demonstration.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-resolution mass sensing offering a large capacity and a high sensitivity simultaneously is important in a wide variety of quantitative content analyses and precision manufacturing processes of chemicals, biomedicines, and semiconductors, as their high-yield mass production requires precise mass measurement of raw materials in large quantities. Several recent works have focused particularly on enhancing the sensitivity of mass detection by incorporating micro/nano-scaled mechanical resonators, such as micro-cantilevers [1], micro-disks [2], carbon nanotubes [3], and graphene membranes [4]. Their properties of small masses, high mechanical quality factors, high mechanical resonant frequencies, compactness, and robustness against environmental perturbations have reportedly yielded remarkable sensitivities, which in some cases reached even a yoctogram (10−24 g) scale that is comparable to the single proton mass [5]. However, while these mass sensors are suitable especially for single-molecule detection and ultrasensitive mass spectroscopy [6–10], they have certain upper limits in measurable masses (typically below microgram) owing to their tiny sizes. On the contrary, mass sensors based on macro-scale transducers (e.g., load cells) provide wide detection ranges beyond microgram [11–13] but reduced sensitivities compared to the micro/nano-scaled counterparts. In order to achieve a high sensitivity and a large capacity at the same time, much effort has been made to develop highly efficient precision deformation sensors based on thin film strain gauges [14], piezoelectric force sensors [15], and dual-photodiode displacement sensors [16]. The most sensitive mass sensor up to date shows a 0.1 μg readability using a strain gauge [17], but still a relatively narrow detection range (from 0.3 mg to 6 g).
In this paper, we propose and experimentally demonstrate, to the best of our knowledge, the first optical-cavity-based mass detector, where we employ as a displacement sensor a low-cost simple free-space Fabry-Pérot optical cavity combined with an intra-cavity wedge prism pair (WPP), which can provide a high sensitivity and a large capacity simultaneously. The use of an optical cavity in sensing in general permits high-sensitivity detection, which enables potentially the measurement of a tiny displacement of even picometers or below [18–20]. The displacement sensor is connected to a load cell that can produce a displacement up to a few millimeters when loaded with a mass of a couple of kilograms. We successfully achieve a readability below 200 mg and a capacity larger than 1 kg at the same time (>5000:1 resolution), together with an excellent linearity of R2>0.99998 over the entire range of measurable mass.
2. Optical-cavity-based displacement sensor
Our displacement sensor is composed of a free-space Fabry-Pérot optical cavity and an intra-cavity WPP, as described in Fig. 1(a). We detect the displacement of WPP produced along the direction perpendicular to the optical beam axis by monitoring the resulting change of cavity transmission, while both the cavity length and the laser frequency are fixed. One might think of a simpler scheme depicted in Fig. 1(b) as an alternative, where the displacement of one of the two cavity mirrors along the direction of optical beam axis is detected. This type of configuration, however, has an intrinsic upper bound in measurable displacement, the half of the laser wavelength (e.g., 775 nm for the laser wavelength of 1550 nm), due to the 2π ambiguity. On the other hand, large-capacity mass detection requires the displacement measurement over the range that far exceeds this upper limit. For instance, typical load cells generate displacements up to several millimeters. One might consider counting the number of cavity resonance peaks [21] to solve this issue. This method, however, requires a complicated and expensive electronic equipment together with a sophisticated data processing algorithm to count every cavity resonance peak that quickly passes back and forth, in particular when a heavy displacement oscillation is created during the settling time right after a mass is placed on the sensor. Our scheme employing an intra-cavity WPP solves these issues, greatly enhancing the range of measurable displacement, while keeping the high sensitivity provided by the use of an optical cavity. As shown in Fig. 1(c), the cavity response to the WPP displacement exhibits the well-known resonance behavior (dark blue curve), similar to what the cold cavity shows with respect to the cavity length variation (light blue curve). In contrast to the cold cavity case, however, the change of optical path length inside the WPP can be made much smaller than the WPP displacement, which dramatically widens the displacement range that can be measured without the 2π ambiguity. Furthermore, it is also economical and highly efficient because it has a simple structure consisting of low-cost commercially available optical components and excludes the need of complicated and expensive electronics for counting the large number of resonance peaks.
Fig. 1 Operating principle of the optical-cavity-based displacement sensor. (a) Schematic diagram of our displacement sensor, which consists of a free-space Fabry-Pérot optical cavity and an intra-cavity wedge prism pair (WPP). The WPP displacement along the direction perpendicular to the laser beam gives rise to the change of cavity transmission, whereas the two cavity mirrors and the laser frequency are fixed. (b) Scheme of a simpler optical-cavity-based displacement sensor that one might imagine as an alternative, where the displacement of a cavity mirror along the laser beam direction is detected. (c) Cavity transmission as a function of the position of WPP (for (a), dark blue curve) or cavity mirror (for (b), light blue curve), where the laser frequency is fixed. Compared to the case of (b) in which the range of measurable displacement is limited to the half of the laser wavelength due to the 2π ambiguity, the use of a WPP in (a) provides a much broader range of measurable displacement. The variation of cavity transmission with the change of WPP displacement (green curve) for the case of (a) is also displayed as a red curve. (d) Structure of the WPP together with a transmitting laser beam that is displaced with respect to the zero point by a distance of x. n1 and n2 are the refractive indices of the two wedge prisms, and α is the common wedge angle. (e) Measured cavity transmission over a range of position of a fabricated WPP. A resonance peak is clearly seen with the full width at half maximum of 180 μm, which is much larger than the half of the laser wavelength (775 nm) used in the measurement.
The WPP is composed of two wedge prisms having an equal wedge angle but slightly different refractive indices, which are attached to each other as described in Fig. 1(d). In this work, we develop a WPP (with Tempotec Optics Co., Ltd.) that is comprised of two wedge prisms made out of BK7 (n1 = 1.50065 @ λ = 1550 nm) and H-K9L (n2 = 1.50084 @ λ = 1550 nm), respectively, which we carefully select in such a way that their refractive indices are as close as possible to each other. They have a wedge angle of α = 0.5°, which is the smallest angle that we can produce, and are glued together by a thin layer of transparent adhesive (Norland NOA 61) to form a WPP. As the WPP is displaced along the direction orthogonal to the laser beam, the optical path length inside the WPP is changed, which in turn alters the cavity transmission. When the WPP moves by a distance of x, the round-trip optical phase of the transmitting laser beam is changed by an amount of
where k0 is the propagation constant in vacuum. Here, we assume that the difference of the two refractive indices is so tiny (n2 – n1 = 1.9 × 10−4 in our case) that the refraction at the interface between the two prisms is negligible. Equation (1) indicates that the use of an intra-cavity WPP can enhance dramatically the range of measurable displacement without the 2π ambiguity by a factor of (i.e., 0.47 m at 1550 nm wavelength), compared to the case of Fig. 1(b) (775 nm at 1550 nm wavelength). A practical issue in the fabrication of WPPs, however, is that it is very difficult to make the wedge angles of the two wedge prisms match exactly. A slight difference between the two wedge angles yields non-uniformity of the thickness of WPP over its surface, which can degrade the enhancement factor of the range of measurable displacement. In this case, the enhancement factor is limited to , where , is the refractive index of the surrounding air, and α1 and α2 are the two wedge angles. We measure the cavity transmission while varying the displacement of a fabricated WPP, which reveals that the measurable displacement without the 2π ambiguity is limited to 7.0 mm, with the cavity finesse of 41.7 and the FWHM of 180 μm as shown in Fig. 1(e). This reduction of enhancement factor down to 9000 could take place by even a tiny wedge angle difference of α2–α1 = 0.013°. Nevertheless, the load cell that we use in this work can produce a WPP displacement up to only 2.75 mm, which we can fully determine without the 2π ambiguity. Precise control of the wedge angle via careful polishing in the fabrication of individual wedge prisms would improve the range of measurable displacement.3. Null-method-based optomechanical mass sensing system
To further increase the precision of mass detection, we adopt the null method [22] by implementing a negative feedback system as described in Fig. 2. First, before placing a mass on the load cell, we set the zero point of the WPP position by adjusting the electromagnet voltage to fix the cavity transmission at its midpoint (cavity side-fringe locking) [Fig. 2(a)]. Right after a mass is put on the load cell, the WPP starts to move and the resulting change of cavity transmission produces a non-zero error signal [Fig. 2(b)]. A PID controller in the negative feedback system receives the error signal and then generates a voltage that is applied to the electromagnet, which tends to move the WPP back to its original zero point. The magnitude of the electromagnet voltage at which the WPP is at rest at its original zero point (i.e., the error signal at the PID controller stays at zero) determines the value of mass [Fig. 2(c)]. This null-method-based scheme, in particular, makes the mass measurement much less affected by the non-uniformity of WPP thickness over the surface that can arise from the above-mentioned wedge angle mismatch or imperfect surface polishing. We confirm experimentally that the WPP displacement has an excellent linear relationship with the electromagnet voltage as shown in Fig. 2(d).
Fig. 2 Operating principle of the null-method-based mass measurement using the optical-cavity-based displacement sensor. The WPP is inside an optical cavity as described in Fig. 1(a). We use a negative feedback system employing an electromagnet. (a) The WPP that is connected to the load cell through a bar is located at the zero point when there is no mass on the load cell. (b) When the mass is put on the load cell, the hinge inside the load cell moves up, which in turn gives rise to an upward displacement of the WPP and subsequently a change of cavity transmission. (c) The change of cavity transmission generates a voltage from a PID controller in the negative feedback system, which is then applied to the electromagnet to pull down the WPP back to its original zero point. This electromagnet voltage determines the value of mass. (d) Measured displacement of the WPP over a range of voltage applied to the electromagnet. The blue open circles are experimental results, whereas the red line is a linear fit. An excellent linear relationship is clearly seen over the entire range of WPP displacement (2.75 mm). Here, positive values of displacement correspond to upward shifts.
Figure 3 shows the overall schematic diagram of our optomechanical mass sensing system. A single-mode laser oscillating at 1550 nm wavelength is used as a light source, and its output is sent to a confocal Fabry-Pérot optical cavity, which is composed of two concave mirrors of 97% reflectivity and a WPP of thickness of 4.84 mm in the middle. The cavity quality factor and the free spectral range are measured as 1.46 × 106 (cavity finesse: 41.7) and 5.55 GHz, respectively. On the other hand, the cold cavity is characterized to have the quality factor of 1.25 × 106 (cavity finesse: 39.4) and the free spectral range of 6.11 GHz that corresponds to the cavity length of 24.5 mm. The slight increase of the cavity finesse by the insertion of the WPP is mainly due to the fact that the monolithic cavity mount is designed in such a way that the cavity is better mode-matched in the presence of the WPP. We note that the imperfect optical alignment of the two cavity mirrors inside the non-adjustable monolithic mount lowers the cavity finesse compared to the predicted value (~100), while the transmission loss of the WPP measured as 0.6% does not cause any significant influence on the cavity finesse. A photodetector is used to receive the laser light transmitted through the cavity. The photodetector signal is fed into a PID controller, which generates a voltage that is applied to the electromagnet for the null-method-based mass measurement. We integrate the load cell, the electromagnet, and all the optics components including the cavity mirrors together into a carefully designed monolithic base plate to maximize the stability of the overall system.
Fig. 3 Schematic diagram of the optomechanical mass sensing system, where the optical-cavity-based displacement sensor in Fig. 1(a) and the load cell are combined together with an electromagnet and a PID controller to implement the negative feedback system and the null-method-based mass measurement. A single-mode laser beam at 1550 nm wavelength is sent to the free-space Fabry-Pérot optical cavity to detect the displacement of the WPP, which is allowed to change by the mass on the load cell and/or the voltage applied to the electromagnet. Note that the two WPPs displayed in the diagram actually correspond to a single device. CM, cavity mirror.
4. Characterization of mass sensing system
First, we examine the linearity and repeatability of our system over the entire range of detectable mass. To determine the repeatability, we repeat the entire measurement procedure described in Figs. 2(a-c) 20 times for each mass. Here, the value of each mass is also carefully determined by using a high-precision balance, prior to the test of our system. As shown in Fig. 4, our system shows an excellent linearity (R2 > 0.99998) over the entire range of detectable mass from <200 mg to >1 kg (resolution >5000:1). The upper bound of measurable mass (about 1 kg) is limited by the fact that when the mass of over 1 kg is put on the load cell, the WPP displacement fluctuates so heavily that the negative feedback system gets disabled, which is in our case due to the small bandwidth (i.e., slow response) and insufficient magnetic force of the electromagnet. In order to make the mass sensing work at larger masses beyond 1 kg, it would be required to develop a high-speed negative feedback system that incorporates an improved electromagnet generating larger magnetic forces. On the other hand, the lower limit of detectable mass (about 200 mg) is determined primarily by the repeatability (i.e., uncertainly of 200 mg) and attributed to the residual long-term drift of the zero-point electromagnet voltage. We investigate the origin of the long-term drift systematically by monitoring the temporal variation of the output signal from each component in the mass sensing system. During about 10 seconds, a typical time required for single mass measurement, the transmission of the free-running optical cavity drifts by an amount that is equivalent to typically a few hundreds of milligrams [Fig. 5(b)]. This is very similar to the variation of the zero-point mass in the overall system [Fig. 5(a)], which indicates that the repeatability of our mass sensing system (200 mg) is governed mainly by the long-term drift of the free-running optical-cavity-based displacement sensor. The variation of ambient temperature, for instance, gives rise to the thermal change of WPP thickness. The linear thermal expansion coefficient of the WPP materials (BK7 and H-K9L) is 7.1 × 10−6 K−1 [23], which yields a thermal thickness change of 34 nm/K for the 4.84-mm-thick WPP. This in turn changes the cavity resonance frequency by 370 MHz/K, which contributes significantly to the long-term drift of our system. On the other hand, the frequency variation of the free-running laser by temperature change is about 0.25 MHz/K. It is checked that the speed of the resulting laser frequency drift is kept well below 0.1 MHz/second in our experimental environment, which is sufficiently slow for a reliable mass measurement within 10 seconds. We expect that the repeatability could be improved by using materials exhibiting low thermal expansion for the WPP and the cavity mount, actively stabilizing the laser frequency, and carrying out the mass measurement in a calmer and dry environment without airflow at a constant ambient temperature.
Fig. 4 Linearity and repeatability of the mass sensing system. The change of electromagnet voltage is measured for different values of mass on the load cell. The blue open circles are the experimental measurements and the red line is a linear fit. The error bars represent the expanded uncertainties (k = 2) in repeated measurements 20 times for each mass.
Fig. 5 (a) Typical long-term drift of the zero-point mass determined from the variation of the electromagnet voltage when the negative feedback is turned on. (b) Typical long-term drift of the zero-point mass determined from the variation of the cavity transmission when the negative feedback is switched off. The similarity between the amounts of the two long-term drifts indicates that the repeatability of the overall mass sensing system is governed mainly by the slow environmental perturbation of the optical cavity and/or laser frequency. Both measurements in (a) and (b) are carried out without a mass on the load cell.
We also examine the transient response characteristics of the mass sensing system. First, to investigate the speed of the negative feedback system, which can affect significantly the capacity of the system as above-mentioned, we measure the response function of the system by sending the sinusoidally frequency-modulated laser light to the optical cavity and detecting the resulting fluctuation of the cavity transmission. When the negative feedback is turned off and the WPP position is consequently fixed, the cavity transmission is modulated, as shown in Fig. 6(a). The laser frequency modulation in this case corresponds to the oscillation of the WPP position with an amplitude of 9.2 μm under the fixed laser frequency. We then switch on the negative feedback to suppress the cavity transmission oscillation, and measure the dependence of cavity transmission oscillation on the modulation frequency. If the negative feedback is fast enough to track the laser frequency modulation, the cavity transmission modulation would be almost eliminated. As shown in Fig. 6(b), at very low modulation frequencies, the negative feedback works so properly that the cavity transmission modulation is highly suppressed, the suppression ratio reaching almost 40 dB. The suppression ratio, however, decreases monotonically as the modulation frequency rises, its 3 dB cut-off frequency being determined as 20 Hz, which is mostly limited by the slow mechanical response of the electromagnet.
Fig. 6 Measurement of the speed of the negative feedback system using a sinusoidally frequency-modulated laser light. (a) Trace of the cavity transmission of a 1 Hz frequency-modulated laser light, which is obtained with the negative feedback switched off. In this case, the laser frequency modulation is equivalent to the modulation of WPP displacement with the amplitude of 9.2 μm. (b) Suppression of the modulation of cavity transmission of the frequency-modulated laser light by the negative feedback, which is measured over a range of the laser modulation frequency. The 3 dB cutoff frequency of the negative feedback system is determined as 20 Hz.
Finally, we investigate the impulse response characteristics of our mass sensing system, which is an important property determining the settling time of the system. The transient behavior of the WPP displacement is obtained immediately after the mass of 100 g is placed on the load cell. As shown in Fig. 7(a), the oscillation amplitude is exponentially damped with a 1/e decay time of about 2 seconds. Figure 7(b) shows the Fourier transform of the transient displacement trace in Fig. 7(a), which reveals the primary resonances of the system at 88 Hz and 641 Hz. Due to the above-mentioned slow response characteristics of the system (3 dB bandwidth of 20 Hz), the vibration of WPP position is hardly suppressed by the negative feedback and appears as the cavity transmission modulation, while the electromagnet voltage does not show significant modulation at the resonant frequencies. We note that these resonant frequencies slightly decrease as the mass placed on the load cell increases, which is a typical behavior of mechanical damped harmonic oscillators. Installation of mechanical dampers working for the two main resonances would reduce the settling time, which could also help improve the drift-limited repeatability.
Fig. 7 Measurement of the settling time of the mass sensing system. (a) Transient trace of the WPP displacement obtained right after a 100 g mass is placed on the load cell. (b) Fourier transform of the displacement trace in (a). The most significant mechanical resonances appear at 88 Hz and 641 Hz.
5. Conclusion
We have proposed and successfully demonstrated an optical-cavity-based optomechanical mass sensing system that offers a large capacity and a high resolving power simultaneously. This novel type of mass detector employs a free-space Fabry-Pérot optical cavity with an intra-cavity WPP as a displacement sensor. The use of an optical cavity provides a high sensitivity of mass detection, whereas the WPP enlarges the measurable range remarkably, by a factor of 9000 in our case, which could be hardly achieved with the previously reported micro/nano-scaled mass detectors. In addition, the simple economical configuration of our system can be implemented with low-cost commercially available components and excludes the need of expensive and complicated electronics to count a large number of resonance peaks at large displacements. We have achieved with the prototype demonstration a capacity larger than 1 kg and a readability below 200 mg (resolution of >5000:1) at the same time, together with an excellent linearity of R2>0.99998 over the entire range of measurable mass.
We believe that the simple structure of our system readily allows for further size minimization, which would yield a higher repeatability via improvement of the robustness of the system against external thermal and mechanical perturbations. Furthermore, the use of a higher-quality-factor optical cavity made out of low-thermal-expansion materials and a faster negative feedback system that incorporates an improved electromagnet generating larger magnetic forces would further enhance both the sensitivity and capacity. For instance, it has been reported that a thermally controlled high-quality-factor Fabry-Pérot optical cavity fixed on a carefully designed mount in combination with active frequency stabilization can yield fractional frequency instabilities below 10−16 at room temperature [24]. By incorporating such the ultra-stable optical cavity having a high finesse (on the order of 1,000 that would be limited by the transmission loss of the WPP), it would be possible to achieve ultrahigh sensitivities in the microgram regime, while keeping the capacity at several kilograms, which then yields unprecedentedly ultrahigh resolution (108:1 or beyond) that has not been achieved so far with any types of mass sensors.
Funding
National Research Foundation of Korea (NRF) by the Korea government (MSIT) (NRF-2013R1A1A1007933, NRF-2016R1A2B4011862).
References
1. R. Raiteri, M. Grattarola, H.-J. Butt, and P. Skládal, “Micromechanical cantilever-based biosensors,” Sens. Actuators B Chem. 79(2–3), 115–126 (2001). [CrossRef]
2. F. Liu, S. Alaie, Z. C. Leseman, and M. Hossein-Zadeh, “Sub-pg mass sensing and measurement with an optomechanical oscillator,” Opt. Express 21(17), 19555–19567 (2013). [CrossRef] [PubMed]
3. B. Lassagne, D. Garcia-Sanchez, A. Aguasca, and A. Bachtold, “Ultrasensitive mass sensing with a nanotube electromechanical resonator,” Nano Lett. 8(11), 3735–3738 (2008). [CrossRef] [PubMed]
4. J. Atalaya, J. M. Kinaret, and A. Isacsson, “Nanomechanical mass measurement using nonlinear response of a graphene membrane,” Europhys. Lett. 91(4), 48001 (2010). [CrossRef]
5. J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, “A nanomechanical mass sensor with yoctogram resolution,” Nat. Nanotechnol. 7(5), 301–304 (2012). [CrossRef] [PubMed]
6. N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng. 20(4), 045023 (2010). [CrossRef]
7. Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, “Zeptogram-scale nanomechanical mass sensing,” Nano Lett. 6(4), 583–586 (2006). [CrossRef] [PubMed]
8. F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. U.S.A. 105(52), 20701–20704 (2008). [CrossRef] [PubMed]
9. F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002). [CrossRef]
10. T. P. Burg, M. Godin, S. M. Knudsen, W. Shen, G. Carlson, J. S. Foster, K. Babcock, and S. R. Manalis, “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature 446(7139), 1066–1069 (2007). [CrossRef] [PubMed]
11. A. N. Ormond, “Platform load cell,” U.S. Patent No. 3,960,013 (1976).
12. S. Suzuki, K. Sakamoto, and T. Kitagawa, “Load-cell balance,” U.S. Patent No. 4,332,174 (1982).
13. J. A. Pugnaire, “Shear strain load cell,” U.S. Patent No. 3,376,537 (1968).
14. G. R. Witt, “The electromechanical properties of thin films and the thin film strain gauge,” Thin Solid Films 22(2), 133–156 (1974). [CrossRef]
15. S. Tadigadapa and K. Mateti, “Piezoelectric MEMS sensors: state-of-the-art and perspectives,” Meas. Sci. Technol. 20(9), 092001 (2009). [CrossRef]
16. D. A. Shaddock, M. B. Gray, and D. E. McClelland, “Frequency locking a laser to an optical cavity by use of spatial mode interference,” Opt. Lett. 24(21), 1499–1501 (1999). [CrossRef] [PubMed]
18. T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, “A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity,” Nat. Photonics 6(10), 687–692 (2012). [CrossRef]
19. C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nat. Phys. 4(7), 555–560 (2008). [CrossRef]
20. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011). [CrossRef] [PubMed]
21. F. Barone, E. Calloni, R. D. Rosa, L. D. Fiore, F. Fusco, L. Milano, and G. Russo, “Fringe-counting technique used to lock a suspended interferometer,” Appl. Opt. 33(7), 1194–1197 (1994). [CrossRef] [PubMed]
22. J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77(5), 053809 (2008). [CrossRef]
24. S. Häfner, S. Falke, C. Grebing, S. Vogt, T. Legero, M. Merimaa, C. Lisdat, and U. Sterr, “8 × 10−17 fractional laser frequency instability with a long room-temperature cavity,” Opt. Lett. 40(9), 2112–2115 (2015). [CrossRef] [PubMed]
