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A homodyne Michelson interferometer was developed to realize a dynamic vacuum standard. The interferometer measures variation in optical path due to refractive index changes related to the pressure of the gas. The measurement arm of the interferometer is formed by two quasi-parallel mirrors which act as a multiplication set-up to allow an increment...
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... [13][14][15][16][17] Since frequency is the entity that can be assessed with the highest accuracy in our society, [18][19][20] FPC-based refractometry has a great potential for accurate assessment of pressure. 11,[21][22][23][24] Several FP-based instrumentation are presently under development and a number of realizations with claimed expanded uncertainties (k = 2) in the mPa and parts-per-million (ppm) ranges have been reported, e.g., with [(2 mPa) 2 þ (8:8 Â 10 À6 P) 2 ] 1=2 by the National Institute of Standards and Technology, 21 [(10 mPa) 2 þ (10 Â 10 À6 P) 2 ] 1=2 by a collaboration between Umeå University (UmU) and RISE Research Institutes of Sweden (RISE), 25 and [(130 mPa) 2 þ (23 Â 10 À6 P) 2 ] 1=2 by the National Institute of Metrology. 26 Other systems, although not yet fully characterized, are under development by, e.g., Conservatoire National des Arts et Métiers, 27 Centro Español de Metrología, 28 and National Measurement Institute of India. ...
An updated version of an Invar-based dual Fabry–Perot cavity refractometer utilizing the gas modulation methodology has been characterized with regard to its ability to assess gas pressure in the low pressure regime, defined as the regime in which the instrumentation is mainly limited by the constant term a in the [(a)2+(b×P)2]1/2 expression for the uncertainty. It is first concluded that this ability is predominantly limited by three entities, viz., the empty cavity repeatability, the residual gas pressures in the evacuated (measurement) cavity, and the contamination of the gas residing in the measurement cavity that originates from leaks and outgassing. We then present and utilize methods to separately estimate the uncertainty of the updated refractometer from these entities. It was found that, when utilizing gas modulation cycles of 100 s and when addressing nitrogen, the system can assess pressure in the low pressure regime with an expanded uncertainty (k=2) of 0.75 mPa, mainly limited by the empty cavity repeatability and outgassing of hydrogen. This is more than 1 order of magnitude below the previously assessed low pressure performance of the instrumentation.
... Fabry-Pérot cavity (FPC) based refractometry is a sensitive laser-based methodology for the assessment of molar density and pressure [1][2][3][4][5][6][7]. By measuring the refractivity, n − 1, where n is the index of refraction, the density of a gas can be calculated using the Lorentz-Lorenz equation, and, if also its temperature is known, its pressure can be assessed by an equation of state [8][9][10][11][12][13]. ...
By measuring the refractivity and the temperature of a gas, its pressure can be assessed from fundamental principles. The highest performing instruments are based on Fabry-Perot cavities (FPC). Gas modulation refractometry (GAMOR)is a methodology that has the ability to reduce the influence of disturbances to such an extent that high-precision (sub-parts-per-million) assessments of pressure can be made by the use of FPCs of Invar. To allow for high accuracy assessments, it is of importance to assess the uncertainty contribution from the thermodynamic effects that are associated with the gas filling and emptying of the cavity (pV work). This paper presents a detailed scrutiny of the influence of the gas exchange process on the assessment of gas temperature on an Invar-based dual-FPC (DFPC) instrumentation. It is shown that by virtue of a combination of a number of carefully selected design entities (a small cavity volume with a bore radius of 3 mm, a spacer material with high heat capacitance, large thermal conductivity, and no regions that are connected with low thermal conductance, i.e. no heat islands, and a continuous assessment of temperature of the cavity spacer) the system is not significantly affected by pV work. Simulations show that 10 s after the filling all temperature gradients in the system are well into the sub-mK range. Experiments support that refractivity assessments initiated after 40 s are not significantly affected by the pV work. The analysis given in this work indicates that an upper limit for the influence of pV work on the Invar-based DFPC system using 100 s long gas modulation cycles is 0.5 mK/100 kPa (or 1.8ppm/100 kPa). Consequently, thermodynamic effects will not be a limiting factor when the Invar-based DFPC GAMOR system is used for assessments of pressure or as a primary pressure standard up to atmospheric pressures.
... Refractometry constitutes an optical technique for assessment of refractivity that, by use of the extended Lorentz-Lorenz equation, can assess gas (molar or number) density [1][2][3][4][5][6][7], and, by use of an equation of state, also pressure [8][9][10][11][12][13]. In addition, * Author to whom any correspondence should be addressed. ...
... Early demonstrations of its applicability were made in the second part of the twentieth century [1,2]. Despite this, it was not until the beginning of the second decade of this century that refractometer systems started to be realized for assessment of pressure or for realization of the pascal, e.g. by Egan et al and Mari et al [8,9]. However, not even since then has the development of the field been particularly rapid with only a limited number of works published during the subsequent years [10,22,47]. ...
By measuring the refractivity and the temperature of a gas, its pressure can be assessed from fundamental principles. The highest performing instruments are based on Fabry-Perot cavities where a laser is used to probe the frequency of a cavity mode, which is shifted in relation to the refractivity of the gas in the cavity. Recent activities have indicated that such systems can demonstrate an extended uncertainty in the 10 ppm (parts-per-million or 10-6) range. As a means to reduce the influence of various types of disturbances (primarily drifts and fluctuations) a methodology based on modulation, denoted Gas Modulation Refractometry (GAMOR), has recently been developed. Systems based on this methodology are in general high-performance, e.g. they have demonstrated precision in the sub-ppm range, and they are sturdy. They can also be made autonomous, allowing for automated and unattended operation for virtually infinite periods of time. To a large degree, the development of such instruments depends on the access to modern photonic components, e.g. narrow line-width lasers, electro- and acousto-optic components, and various types of fiber components. This work highlights the role of such modern devices in GAMOR-based instrumentation and provide a review on the recent development of such instruments in Sweden that has been carried out in a close collaboration between a research institute and the Academy. It is shown that the use of state-of-the-art photonic devices allows sturdy, automated and miniaturised instrumentation that, for the benefit of industry, can serve as standards for pressure and provide fast, unattended, and calibration-free pressure assessments at a fraction of the present cost.
... RIU, c = 2.8 · 10 −9 RIU/Pa, ppressure. There are optical methods for measuring pressurefor example, based on a change in the phase shift in interferometers due to a change in the refractive index [8,9]. A similar method of optical control was used in this work, but on the basis of the sensor under study. ...
Experimental study of the sensor in the Kretschmann optical scheme, in which the sensitive element is a reflection interferometer (RI) for the oblique incidence of light, is presented for the first time. A brief theory of RI is given. The experimental sample was used to measure the refractive index of the residual atmosphere in a vacuum chamber during its pumping. The high Q-factor of the RI resonator made it possible to obtain a fairly narrow spectral maximum with a width of 1.7 nm. The spectral sensitivity of the sensor was 1000 nm/RIU and the quality parameter was 529 RIU ⁻¹ , it was also demonstrated that resolution of 6.5·10 ⁻⁸ RIU can be achieved. Proposals for further improvement of the sensor characteristics are formulated. Keywords: reflection interferometer, total internal reflection, refractive index sensor.
... RIU, c = 2.8 · 10 −9 RIU/Pa, p -давление. Существуют оптические методы измерения давления -например, основанные на изменении набега фазы в интерферометрах из-за изменения коэффициента преломления [8,9]. Подобный метод оптического контроля был применен в данной работе, но на основе исследуемого сенсора. ...
Experimental study of the sensor in the Kretschmann optical scheme, in which the sensitive element is a reflection interferometer (RI) for the oblique incidence of light, is presented for the first time. A brief theory of RI is given. The experimental sample was used to measure the refractive index of the residual atmosphere in a vacuum chamber during its pumping. The high Q-factor of the RI resonator made it possible to obtain a fairly narrow spectral maximum with a width of 1.7 nm. The spectral sensitivity of the sensor was 1000 nm / RIU and the quality parameter was 529 RIU–1, it was also demonstrated that resolution of 6.5 10-8 RIU can be achieved. Proposals for further improvement of the sensor characteristics are formulated.
... ichelson interferometer (MI) has the advantages of high resolution and high precision, and is widely used in the fields of semiconductor [1], optics [2], and micro/nano technology [3], especially in the precision measurement of length [4], angle [5], refractive index [6], and thermal expansion coefficient [7]. A reconfigured polarizing Michelson interferometer (PMI) has also been developed by the author's group and used in micro/nano probes and coordinate measuring machines in recent years [8]. ...
Nonlinear errors, including direct current (DC) offset, lack of quadrature, and unstable amplitude, are inevitable in the sinusoidal waves of interferometry due to unsatisfactory detector system. Precision and possible measuring range of an interferometry are limited by the errors. An analog electronic method to solve the nonlinear errors is proposed in this paper. Preamplifier circuits, DC offset compensation circuits based on a low-pass filter, orthogonalized circuits based on vector operations, and regularized circuits based on automatic gain control (AGC) technology are analyzed, designed, and verified respectively. Using the designed circuits, a polarizing Michelson interferometer (PMI) system has been developed and used to measure a high-precision stage with a stroke of 15 mm and a maximum angular error of 35 arc-sec. Experimental results show that the errors of the sinusoidal waves between 20 Hz and 2 kHz in frequency and between 200 mV and 5 V in amplitude can be reduced effectively by the developed circuits. The expanded uncertainty of the developed PMI system is 47 nm. Further experiments have been carried out on a common guide rail with a length of 600 mm. Experimental results reveal that the tolerable angular error motion of the reflecting mirror of the PMI system is improved from ±68.5 arc-sec to ±274 arc-sec in a measuring distance of 500 mm. The proposed method can be used to reduce the nonlinear errors in sinusoidal wave signal processing fields.
... These exciting prospects have spurred a significant increase of interest within the field of refractometry. Work to explore and utilize the potential of optical methods for assessing the molar density and pressure of gas presently takes place at several national metrology institutes and universities [2][3][4][5][6][7][8][9]. ...
... As was alluded to above, to make viable assessments of large pressure shifts with short settling times, which is needed for a number of applications, it is of importance that the system has a fast response. Although several types of refractometers have been scrutinized over the years [3][4][5][6][7][8][10][11][12][13][14][15][16][17][18][19][24][25][26], virtually none of them has yet been assessed with respect to its short-term behavior. Access to two GAMOR-based refractometer systems allows for scrutiny of the short-term behavior of GAMOR-based refractometry in more detail. ...
Refractometry is a powerful technique for pressure assessments that, due to the recent redefinition of the SI system, also offers a new route to realizing the SI unit of pressure, the Pascal. Gas modulation refractometry (GAMOR) is a methodology that has demonstrated an outstanding ability to mitigate the influences of drifts and fluctuations, leading to long-term precision in the 10−7 region. However, its short-term performance, which is of importance for a variety of applications, has not yet been scrutinized. To assess this, we investigated the short-term performance (in terms of precision) of two similar, but independent, dual Fabry–Perot cavity refractometers utilizing the GAMOR methodology. Both systems assessed the same pressure produced by a dead weight piston gauge. That way, their short-term responses were assessed without being compromised by any pressure fluctuations produced by the piston gauge or the gas delivery system. We found that the two refractometer systems have a significantly higher degree of concordance (in the 10−8 range at 1 s) than what either of them has with the piston gauge. This shows that the refractometry systems under scrutiny are capable of assessing rapidly varying pressures (with bandwidths up to 2 Hz) with precision in the 10−8 range.
... By measuring the refractivity, n − 1, where n is the index of refraction, the density of the gas can be calculated by the use of the Lorentz-Lorenz equation, and, if its temperature is also measured, its pressure can be assessed by an equation of state [1]. The technique has demonstrated detection of gases with both high precision and good accuracy over a wide range of molar densities and pressures (for the latter, ranging from low millipascals to hundreds of kilopascals) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Recent works have indicated that the methodology also has the potential to replace current pressure standards, in particular in the 1 Pa to 100 kPa range [17]. ...
... Again, making use of Eqs. (8) and (12) implies that the leading term of the error (or uncertainty) in the assessment of the beat frequency in DFPC-based UMNI refractometry, δ[ f (t cmp )] DFPC UMNI , can be written as ...
Gas modulation refractometry (GAMOR) is a methodology for assessment of gas refractivity, molar density, and pressure that, by a rapid gas modulation, exhibits a reduced susceptibility to various types of disturbances. Although previously demonstrated experimentally, no detailed analysis of its ability to reduce the pickup of drifts has yet been given. This work provides an explication of to what extent modulated refractometry in general, and GAMOR in particular, can reduce drifts, predominantly those of the cavity lengths, gas leakages, and outgassing. It is indicated that the methodology is insensitive to the linear parts of so-called campaign-persistent drifts and that it has a significantly reduced susceptibility to others. This makes the methodology suitable for high-accuracy assessments and out-of-laboratory applications.
... Although there are a variety of means to assess refractivity [11][12][13][14][15], the most sensitive realizations are refractometry based on a Fabry-Pérot (FP) cavity [11,[16][17]. However, ordinary FP-based refractometers are often limited by the stability of the length of the cavity [5,18,19]. ...
A transportable refractometer for assessment of kPa pressures with ppm level precision is presented. It is based on the GAs MOdulation Refractometry (GAMOR) methodology, making it resistant to fluctuations and drifts. At the National Metrology Institute at RISE, Sweden, the system assessed pressures in the 4.3 - 8.7 kPa range with sub-ppm precision (0.5 - 0.9 ppm). The system was thereafter disassembled, packed, and transported 1040 km to Umea University, where it, after unpacking and reassembling, demonstrated a similar precision (0.8 - 2.1 ppm). This shows that the system can be disassembled, packed, transported, unpacked, and reassembled with virtually unchanged performance.
... Refractometry constitutes an optical technique for assessment of refractivity, gas density, and pressure that has demonstrated high precision and accuracy [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. It has been indicated that the technology can not only be used to assess pressure, but it also has the potential to replace current mechanical pressure standards, in particular in the 1-100 kPa range [17][18][19][20][21][22][23]. ...
... The averaging process will, though, not significantly affect the components of the fluctuations whose frequencies are lower than the inverse of (π times) the averaging time, i.e., for the case whenf D < 1/πt avg . For these components, it can be shown, by series expansion of Eq. (11), that the amount of the fluctuation picked up can be expressed as ...
Gas modulation refractometry is a technique for assessment of gas refractivity, density, and pressure that, by a rapid modulation of the gas, provides a means to significantly reduce the pickup of fluctuations. Although its unique feature has previously been demonstrated, no detailed explication or analysis of this ability has yet been given. This work provides a theoretical explanation, in terms of the length of the modulation cycle, of the extent to which gas modulation can reduce the pickup of fluctuations. It is indicated that a rapid modulation can significantly reduce the influence of fluctuations with Fourier frequencies lower than the inverse of the modulation cycle length, which often are those that dominate. The predictions are confirmed experimentally.
