Absolute refractometry of dry gas to ±3 parts in 10⁹

The enhancement detection method based on the Fabry-Pérot cavity using terahertz frequency-domain spectroscopy

This article demonstrates a simple, efficient, and low-cost gas detection method for gases with absorption peaks in the terahertz range. A modes-adjustable Fabry-Pérot cavity is designed. By adjusting the length of the cavity, the center resonant frequency of the cavity can be coupled to the gas absorption peak. This kind of coupling can greatly enhance gas detection. To detect gas absorption peaks, we choose terahertz frequency domain spectroscopy (THz-FDS), whose frequency resolution can be up to the MHz level. Vapor is selected to verify the coupling phenomenon. The resonant frequency of the cavity is modified to couple to 0.56 THz, the absorption peak of vapor. Experiments are conducted at different humidity levels, the humidity is controlled by the supersaturated salt solution. Results indicate that at a humidity level of 15 %, the coupling effect can enhance the detectability of vapor by approximately 167 %, and this enhancement effect diminishes as humidity increases. We analyze the effect of different modes on the coupling and find that the high modes can make the coupling easier, but have little effect on the enhancement. Furthermore, the method is used to detect biomolecule-α-tyrosine to ensure it has wide applicability. This method can be used to detect substances with absorption peaks in the THz regime, especially for low-concentration gas.

Procedure for automated low uncertainty assessment of empty cavity mode frequencies in Fabry-Pérot cavity based refractometry

A procedure for automated low uncertainty assessment of empty cavity mode frequencies in Fabry-Pérot cavity based refractometry that does not require access to laser frequency measuring instrumentation is presented. It requires a previously well-characterized system regarding mirror phase shifts, Gouy phase, and mode number, and is based on the fact that the assessed refractivity should not change when mode jumps take place. It is demonstrated that the procedure is capable of assessing mode frequencies with an uncertainty of 30 MHz, which, when assessing pressure of nitrogen, corresponds to an uncertainty of 0.3 mPa.

Expansivity of Fused Quartz Glass Measured Within 6 × 10-10 K-1

A method is described to measure the thermal expansion coefficient of fused quartz glass. The measurement principle is to monitor the change in resonance frequency of a Fabry-Perot cavity as its temperature changes; the Fabry-Perot cavity is made from fused quartz glass. The standard uncertainty in the measurement was less than 0.6 (nm·m-1)·K-1, or 0.15 %. The limit on performance is arguably uncertainty in the reflection phase-shift temperature dependence, because neither thermooptic nor thermal expansion coefficients of thin-film coatings are reliably known. However, several other uncertainty contributors are at the same level of magnitude, and so any improvement in performance would entail significant effort. Furthermore, measurements of three different samples revealed that material inhomogeneity leads to differences in the effective thermal expansion coefficient of fused quartz; inhomogeneity in thermal expansion among samples is 24 times larger than the measurement uncertainty in a single sample.

In situ determination of the penetration depth of mirrors in Fabry-Perot refractometers and its influence on assessment of refractivity and pressure

A procedure is presented for in situ determination of the frequency penetration depth of coated mirrors in Fabry-Perot (FP) based refractometers and its influence on the assessment of refractivity and pressure. It is based on assessments of the absolute frequency of the laser and the free spectral range of the cavity. The procedure is demonstrated on an Invar-based FP cavity system with high-reflection mirrors working at 1.55 μm. The influence was assessed with such a low uncertainty that it does not significantly contribute to the uncertainties (k = 2) in the assessment of refractivity (<8 × 10^-13) or pressure of nitrogen (<0.3 mPa).

New method for residual amplitude modulation control in fibered optical experiments

When locking the frequency of a laser to an optical cavity resonance, the residual amplitude modulation (RAM), which accompanies the phase modulation necessary to build the error signal, is a major limitation to the frequency stability. We show that the popular method demonstrated by Wong and Hall to cancel this effect, based on the measurement of the RAM using an auxiliary detector, is limited in the case of optical setups exhibiting polarization dependent losses and an imperfect polarizer at the modulator output, such as guided-wave optical systems.We propose and demonstrate a new method, using a single photodetector, to generate the two error signals and demonstrate its usefulness in the case of fibered systems.

The Short-Term Performances of Two Independent Gas Modulated Refractometers for Pressure Assessments

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.

High-accuracy measurement system for the refractive index of air based on a simple double-beam interferometry

A measurement system based on a simple double-beam interferometry is built to realize the measurement of air refractive index with high accuracy. The basic principle of the system is that, through measuring the change of optical path difference caused by rapid and smooth vacuumization, measurement of refractive index of air is converted to length measurement. Error correction and signal processing are studied to ensure high-accuracy measurement of the refractive index of air. Three applicable methods are used in system. The system based on the methods realize the subdivision and counting of interference fringe by software with three-error correction, error compensation for the end-window plates' thickness change caused by vacuumization, steady realization of high vacuum conditions. To verify the accuracy and reliability of the system, the measurement results are compared with that obtained from the method based on empirical Edlén's formula. Analysis result shows that the expanded measurement uncertainty of the system is U = 5×10^-9, with k = 2. The system can be used to compensate the laser wavelength error caused by the refractive index of air with high accuracy.

Transient heating in fixed length optical cavities for use as temperature and pressure standards

Optical refractometry techniques enable realization of both pressure and temperature directly from properties of the gas. The NIST refractometer, a fixed length optical cavity (FLOC) has previously been evaluated for operation as pressure standard, and now in this paper, is evaluated for the feasibility of operation as a primary temperature standard as well. The challenge is that during operation, one cavity is filled with gas. Gas dynamics predicts that this will result in heating which in turn will affect the cavity temperature uniformity, impeding the ability to measure the gas temperature with sufficient accuracy to make the standard useful as a primary standard for temperature or pressure. Temperature uniformity across the refractometer must be less than 0.5 mK for measurements of the refractivity to be sufficiently accurate for the FLOC. This paper compares computer modeling to laboratory measurements, enabling us to validate the model to predict thermal behavior and to accurately determine the measurement uncertainty of the technique. The results presented in this paper show that temperature of the glass elements of the refractometer and 'thermal-shell' copper chamber are equivalent to within 0.5 mK after an equilibration time of 3000 s (when going from 1 kPa to 100 kPa). This finding enables measurements of the copper chamber to determine the gas temperature to within an uncertainty (k = 1) of 0.5 mK. Additionally, the NIST refractometer is evaluated for feasibility of operation as temperature standard.

Precision spectroscopy of atomic helium

Helium is a prototype three-body system and has long been a model system for developing quantum mechanics theory and computational methods. The fine-structure splitting in the 23P state of helium is considered to be the most suitable for determining the fine-structure constant α in atoms. After more than 50 years of efforts by many theorists and experimentalists, we are now working toward a determination of α with an accuracy of a few parts per billion, which can be compared to the results obtained by entirely different methods to verify the self-consistency of quantum electrodynamics. Moreover, the precision spectroscopy of helium allows determination of the nuclear charge radius, and it is expected to help resolve the 'proton radius puzzle'. In this review, we introduce the latest developments in the precision spectroscopy of the helium atom, especially the discrepancies among theoretical and experimental results, and give an outlook on future progress.

Invar-based refractometer for pressure assessments

Gas modulation refractometry (GAMOR) is a methodology that can mitigate fluctuations and drifts in refractometry. This can open up for the use of non-conventional cavity spacer materials. In this paper, we report a dual-cavity system based on Invar that shows better precision for assessment of pressure than a similar system based on Zerodur. This refractometer shows for empty cavity measurements, up to 10⁴ s, a white noise response (for N₂) of 3 mPa s^1/2. At 4303 Pa, the system has a minimum Allan deviation of 0.34 mPa (0.08 ppm) and a long-term stability (24 h) of 0.7 mPa. This shows that the GAMOR methodology allows for the use of alternative cavity materials.

High-precision gas refractometer by comb-mode-resolved spectral interferometry

High-accuracy knowledge of gas refractivity is typically crucial for optical interferometry, precise optical systems, and calculable pressure standard development. Here, we demonstrate an absolute gas refractometer by spectral interferometry and a high-resolution spectrometer. The spectral interferometry relies on a comb with fiber Fabry-Pérot filtering cavity, and a double-spaced vacuum cell. The spectrometer employs a virtually imaged phased array, diffraction grating and near-infrared camera to fully resolve the comb modes. Finally, by means of fast-Fourier-transform, the group refractivity can be derived from the spectrally resolved interferograms of the two beams propagating in the inside and outside of the vacuum cell. To confirm the feasibility and performance of the gas refractometer, the measurement of ambient air was conducted. The proposed scheme has a combined uncertainty of 1.3 × 10^-9 for air and a single measurement only takes 10 ms, which is applicable for gas refractivity monitoring and compensating in real time.

Frequency comb calibrated frequency-sweeping interferometry for absolute group refractive index measurement of air

The absolute group refractive index of air at 194061.02 GHz is measured in real time using frequency-sweeping interferometry calibrated by an optical frequency comb. The group refractive index of air is calculated from the calibration peaks of the laser frequency variation and the interference signal of the two beams passing through the inner and outer regions of a vacuum cell when the frequency of a tunable external cavity diode laser is scanned. We continuously measure the refractive index of air for 2 h, which shows that the difference between measured results and Ciddor's equation is less than 9.6×10^-8, and the standard deviation of that difference is 5.9×10^-8. The relative uncertainty of the measured refractive index of air is estimated to be 8.6×10^-8. The data update rate is 0.2 Hz, making it applicable under conditions in which air refractive index fluctuates fast.

Modified Sagnac interferometer for contact-free length measurement of a direct absorption cell

Accurate path length measurements in absorption cells are recurrent requirements in quantitative molecular absorption spectroscopy. A new twin path laser interferometer for length measurements in a simple direct path absorption geometry is presented, along with a full uncertainty budget. The path in an absorption cell is determined by measuring the optical path length change due to the diminution of the refractive index when the cell originally filled with nitrogen gas is evacuated. The performance of the instrument based on a stabilized HeNe laser is verified by comparison with the results of direct mechanical length measurements of a roughly 45 mm long, specially designed absorption cell. Due to a resolution of about 1/300 of a HeNe fringe, an expanded (coverage factor k=2) uncertainty of 16 μm in the length measurement is achieved, providing an expanded relative uncertainty of 3.6·10⁻⁴ for the length of our test absorption cell. This value is about 8 times lower than what has been reported previously. The instrument will be useful for precision measurements of absorption cross sections of strong absorbers which require short light paths, such as ozone, halogen oxides, sulfur dioxide, and volatile organic compounds in the UV.

Active cancellation of residual amplitude modulation in a frequency-modulation based Fabry-Perot interferometer

Residual amplitude modulation (RAM) is one of the most common noise sources known to degrade the sensitivity of frequency modulation spectroscopy. RAM can arise as a result of the temperature dependent birefringence of the modulator crystal, which causes the orientation of the crystal's optical axis to shift with respect to the polarization of the incident light with temperature. In the fiber-based optical interferometer used on the National Institute of Standards and Technology calculable capacitor, RAM degrades the measured laser frequency stability and correlates with the environmental temperature fluctuations. We have demonstrated a simple approach that cancels out excessive RAM due to polarization mismatch between the light and the optical axis of the crystal. The approach allows us to measure the frequency noise of a heterodyne beat between two lasers individually locked to different resonant modes of a cavity with an accuracy better than 0.5 ppm, which meets the requirement to further determine the longitudinal mode number of the cavity length. Also, this approach has substantially mitigated the temperature dependency of the measurements of the cavity length and consequently the capacitance.

Absolute group refractive index measurement of air by dispersive interferometry using frequency comb

The absolute group refractive index of air at 1563 nm is measured by dispersive interferometry, and a combined uncertainty of 1.2 × 10(-8) is achieved. The group refractive index of air is calculated from the dispersive interferograms of the two beams passing through the inner and outer regions of a vacuum cell by fast-Fourier-transform. Experimental results show that the discrepancies between our method and modified Edlén equation are less than 3.43 × 10(-8) and 4.4 × 10(-8) for short-term and long-term experiments, respectively. The interferogram update rate is 15 ms, which makes it suitable for application of real-time monitoring. Furthermore, it is promising to improve the measurement uncertainty to 3.0 × 10(-9) by changing the material of the vacuum cell and measuring its length more accurately through optical interferometry.

Real-time compensation of the refractive index of air in distance measurement

A two-color scheme of heterodyne laser interferometer is devised for distance measurements with the capability of real-time compensation of the refractive index of the ambient air. A fundamental wavelength of 1555 nm and its second harmonic wavelength of 777.5 nm are generated, with stabilization to the frequency comb of a femtosecond laser, to provide fractional stability of the order of 3.0 × 10(-12) at 1 s averaging. Achieved uncertainty is of the order of 10(-8) in measuring distances of 2.5 m without sensing the refractive index of air in adverse environmental conditions.

Performance of a dual Fabry-Perot cavity refractometer

We have built and characterized a refractometer that utilizes two Fabry-Perot cavities formed on a dimensionally stable spacer. In the typical mode of operation, one cavity is held at vacuum, and the other cavity is filled with nitrogen gas. The differential change in length between the cavities is measured as the difference in frequency between two helium-neon lasers, one locked to the resonance of each cavity. This differential change in optical length is a measure of the gas refractivity. Using the known values for the molar refractivity and virial coefficients of nitrogen, and accounting for cavity length distortions, the device can be used as a high-resolution, multi-decade pressure sensor. We define a reference value for nitrogen refractivity as n-1=(26485.28±0.3)×10(-8) at p=100.0000  kPa, T=302.9190  K, and λ(vac)=632.9908  nm. We compare pressure determinations via the refractometer and the reference value to a mercury manometer.

Air refractive index measurement using low-coherence interferometry

This paper presents a theoretical analysis and an experimental verification of a direct method for a refractive index of air measurement combining low-coherence interferometry and laser interferometry. The method is based on monitoring optical path changes in a measuring arm of the Michelson interferometer caused by the different optical environment in a double-spaced glass cell. This article presents a set of experimental results in comparison with the results obtained by a couple of reference techniques and proves the ability of the designed method to measure the refractive index of air with accuracy in the order of 10^-8.

Note: Real-time absolute air refractometer

We present a real-time absolute air refractometer benefiting from the synthetic pseudo-wavelength (SPW) method. Based on laser heterodyne interferometry, the SPW method uses three vacuum cells with specific lengths to synthesize a set of synthetic pseudo-wavelengths, by combination of which the refractive index can be determined directly without ambiguity. In addition, owing to the parallel arrangement of the vacuum cells in the optical path, the measured data can be collected simultaneously so that one measurement process can be less than 2 ms. The real-time feature makes it possible for instantaneous compensation for laser interferometers.

Humidity and pressure sensor based on internal reflection

A low-cost humidity and pressure optical sensor, based on the internal reflection phenomenon, is presented. It takes advantage of the phase difference acquired by s- and p-polarized light undergoing internal reflection to generate an easily detectable minimum in the reflected profile, in a position corresponding to the critical angle. The apparatus presents good sensitivity to relative humidity changes above 70% and a response time below one second. The same device is also capable of measuring changes in pressure and can be used as a vacuum gauge between 1 and 1000 mbar.

Design and performance of an absolute gas refractometer based on a synthetic pseudo-wavelength method

We present a refractometer that is capable of measuring the refractive index of gases with an unambiguous range of 1.000395 and an uncertainty of 3.14×10(-8) at 633 nm. The measurement range was extended via the combination of the vacuum cells according to the proposed synthetic pseudo-wavelength (SPW) method. The basic principles of the SPW method and the design of the gas refractometer are presented in detail. The performance of the refractometer was verified in the measurements of dry air, nitrogen gas, and ambient air under different environmental conditions. No gas-filling or pumping processes were required during the measurements; so one measurement could be completed within 70 s. Compared with existing refractometers, the method reported here holds advantages in its large unambiguous measuring range, fast speed, high accuracy, and simple instrumentation design.