Realization of the pascal based on argon using a Fabry-Perot refractometer.

Based on a recent experimental determination of the static polarizability and a first-principle calculation of the frequency-dependent dipole polarizability of argon, this work presents, by using a Fabry-Perot refractometer operated at 1550 nm, a realization of the SI unit of pressure, the pascal, for pressures up to 100 kPa, with an uncertainty of [(1.0 mPa)2 + (5.8 × 10-6P)2 + (26 × 10-12P2)2]1/2. The work also presents a value of the molar polarizability of N2 at 1550 nm and 302.9146 K of 4.396572(26) × 10-6 m3/mol, which agrees well with previously determined ones.

EXPRESS: Landmark Publications in Analytical Atomic Spectrometry: Fundamentals and Instrumentation Development.

The almost-two-centuries history of spectrochemical analysis has generated a body of literature so vast that it has become nearly intractable for experts, much less for those wishing to enter the field. Authoritative, focused reviews help to address this problem but become so granular that the overall directions of the field are lost. This broader perspective can be provided partially by general overviews but then the thinking, experimental details, theoretical underpinnings and instrumental innovations of the original work must be sacrificed. In the present compilation, this dilemma is overcome by assembling the most impactful publications in the area of analytical atomic spectrometry. Each entry was proposed by at least one current expert in the field and supported by a narrative that justifies its inclusion. The entries were then assembled into a coherent sequence and returned to contributors for a round-robin review.

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.

Sub-Doppler optical-optical double-resonance spectroscopy using a cavity-enhanced frequency comb probe.

Accurate parameters of molecular hot-band transitions, i.e., those starting from vibrationally excited levels, are needed to accurately model high-temperature spectra in astrophysics and combustion, yet laboratory spectra measured at high temperatures are often unresolved and difficult to assign. Optical-optical double-resonance (OODR) spectroscopy allows the measurement and assignment of individual hot-band transitions from selectively pumped energy levels without the need to heat the sample. However, previous demonstrations lacked either sufficient resolution, spectral coverage, absorption sensitivity, or frequency accuracy. Here we demonstrate OODR spectroscopy using a cavity-enhanced frequency comb probe that combines all these advantages. We detect and assign sub-Doppler transitions in the spectral range of the 3ν3 ← ν3 resonance of methane with frequency precision and sensitivity more than an order of magnitude better than before. This technique will provide high-accuracy data about excited states of a wide range of molecules that is urgently needed for theoretical modeling of high-temperature data and cannot be obtained using other methods.

Self-calibrated NICE-OHMS based on an asymmetric signal: theoretical analysis and experimental validation.

As an ultra-sensitive detection technique, the noise-immune cavity enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) technique has great potential for assessment of the concentration of trace gases. To determine gas concentrations at the ppt or lower level with high accuracy, it is desirable that the technique exhibits self-calibration (or calibration-free) capabilities. Although being sensitive, NICE-OHMS has so far not demonstrated any such ability. To remedy this, this paper provides a self-calibrated realization of NICE-OHMS that is based on a switching of the feedback target of the DeVoe-Brewer (DVB) locking procedure from the modulation frequency of the frequency modulation spectroscopy (FMS) to the cavity length, which creates an asymmetrical signal whose form and size can be used to unambiguously assess the gas concentration. A comprehensive theoretical model for self-calibrated NICE-OHMS is established by analyzing the shift of cavity modes caused by intracavity absorption, demonstrating that gas absorption information can be encoded in both the laser frequency and the NICE-OHMS signal. To experimentally verify the methodology, we measure a series of dispersion signals under different levels of absorbance using a built experimental setup. An instrument factor and the partial pressure are obtained by fitting the measured signal through theoretical expressions. Our results demonstrate that fitted values are more accurate for higher partial pressures than for lower. To improve on the accuracy at low partial pressures, it is shown that the instrument factor obtained by fitting the signal at large partial pressures (in this case, above 7.8 µTorr) can be set to a fixed value for all fits. By this, the partial pressures can be assessed with a relative error below 0.65%. This technique has the potential to enable calibration-free ultra-sensitive gas detection.

Demonstration of a Transportable Fabry-Pérot Refractometer by a Ring-Type Comparison of Dead-Weight Pressure Balances at Four European National Metrology Institutes.

Fabry-Pérot-based refractometry has demonstrated the ability to assess gas pressure with high accuracy and has been prophesized to be able to realize the SI unit for pressure, the pascal, based on quantum calculations of the molar polarizabilities of gases. So far, the technology has mostly been limited to well-controlled laboratories. However, recently, an easy-to-use transportable refractometer has been constructed. Although its performance has previously been assessed under well-controlled laboratory conditions, to assess its ability to serve as an actually transportable system, a ring-type comparison addressing various well-characterized pressure balances in the 10-90 kPa range at several European national metrology institutes is presented in this work. It was found that the transportable refractometer is capable of being transported and swiftly set up to be operational with retained performance in a variety of environments. The system could also verify that the pressure balances used within the ring-type comparison agree with each other. These results constitute an important step toward broadening the application areas of FP-based refractometry technology and bringing it within reach of various types of stakeholders, not least within industry.

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).

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.

Sub-Doppler Double-Resonance Spectroscopy of Methane Using a Frequency Comb Probe.

We report the first measurement of sub-Doppler molecular response using a frequency comb by employing the comb as a probe in optical-optical double-resonance spectroscopy. We use a 3.3 µm continuous wave pump and a 1.67 µm comb probe to detect sub-Doppler transitions to the 2ν_{3} and 3ν_{3} bands of methane with ∼1.7 MHz center frequency accuracy. These measurements provide the first verification of the accuracy of theoretical predictions from highly vibrationally excited states, needed to model the high-temperature spectra of exoplanets. Transition frequencies to the 3ν_{3} band show good agreement with the TheoReTS line list.

Sensitive and broadband measurement of dispersion in a cavity using a Fourier transform spectrometer with kHz resolution: erratum.

We correct the values of the group delay dispersion of the cavity mirrors and N2, as well as the concentration of CO2, obtained from the measurement of the center frequencies of cavity modes using a comb-based Fourier transform spectrometer. The corrected values of group delay dispersion are a factor of 3 higher, which implies that the precision and accuracy of the dispersion measurements is 0.3 fs2 and 3 fs2, respectively.

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 s1/2. 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-resolution trace gas detection by sub-Doppler noise-immune cavity-enhanced optical heterodyne molecular spectrometry: application to detection of acetylene in human breath.

A sensitive high-resolution sub-Doppler detecting spectrometer, based on noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS), for trace gas detection of species whose transitions have severe spectral overlap with abundant concomitant species is presented. It is designed around a NICE-OHMS instrumentation utilizing balanced detection that provides shot-noise limited Doppler-broadened (Db) detection. By synchronous dithering the positions of the two cavity mirrors, the effect of residual etalons between the cavity and other surfaces in the system could be reduced. An Allan deviation of the absorption coefficient of 2.2 × 10-13 cm-1 at 60 s, which, for the targeted transition in C2H2, corresponds to a 3σ detection sensitivity of 130 ppt, is demonstrated. It is shown that despite significant spectral interference from CO2 at the targeted transition, which precludes Db detection of C2H2, acetylene could be detected in exhaled breath of healthy smokers.

A novel methodology to directly pre-determine the relative wavelength response of DFB laser in wavelength modulation spectroscopy.

A novel methodology to directly pre-determine the relative wavelength response (RWR) of a DFB laser, in terms of a combined current linearly scanned wavelength response and current modulated wavelength response (CMWR), in wavelength modulation spectroscopy (WMS) is presented. It is shown that the assessed RWR can be used to mimic the measured response with standard deviation of discriminations that are below 3.4 × 10-3cm-1 under a variety of conditions. It is also shown that its performance supersedes two commonly used assessment models of the CMWR but is slightly worse than that of the third model, however with the benefit of solely using a single fitting parameter (the concentration) instead of more. When the novel method is applied to the assessment of CO2 concentration in a Herriot-type multipass cell by using the technique of calibration-free WMS, the results show that there is virtually no difference compared to that by use of the best of the other methods. It is concluded that the novel method is more robust and simplifies the retrieval process of gas concentration.

Broadband calibration-free cavity-enhanced complex refractive index spectroscopy using a frequency comb.

We present broadband cavity-enhanced complex refractive index spectroscopy (CE-CRIS), a technique for calibration-free determination of the complex refractive index of entire molecular bands via direct measurement of transmission modes of a Fabry-Perot cavity filled with the sample. The measurement of the cavity transmission spectrum is done using an optical frequency comb and a mechanical Fourier transform spectrometer with sub-nominal resolution. Molecular absorption and dispersion spectra (corresponding to the imaginary and real parts of the refractive index) are obtained from the cavity mode broadening and shift retrieved from fits of Lorentzian profiles to the individual cavity modes. This method is calibration-free because the mode broadening and shift are independent of the cavity parameters such as the length and mirror reflectivity. In this first demonstration of broadband CE-CRIS we measure simultaneously the absorption and dispersion spectra of three combination bands of CO2 in the range between 1525 nm and 1620 nm and achieve good agreement with theoretical models. This opens up for precision spectroscopy of the complex refractive index of several molecular bands simultaneously.

Shot-noise-limited Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectrometry.

Shot-noise-limited Doppler-broadened (Db) noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS) has been realized by implementation of balanced detection. A characterization of the system based on Allan-Werle plots of the absorption coefficient, retrieved by fitting a model function to data, shows that the system has a white noise equivalent absorption per unit length per square root of bandwidth of 2.3×10-13 cm-1 Hz-1/2, solely 44% above the shot noise limit, and a detection sensitivity of 2.2×10-14 cm-1 over 200 s, both being unprecedented for Db NICE-OHMS. The white noise response follows the expected inverse square root dependence on power that is representative of a shot-noise-limited response, which confirms that the system is shot-noise-limited.

Sensitive and broadband measurement of dispersion in a cavity using a Fourier transform spectrometer with kHz resolution.

Optical cavities provide high sensitivity to dispersion since their resonance frequencies depend on the index of refraction. We present a direct, broadband, and accurate measurement of the modes of a high finesse cavity using an optical frequency comb and a mechanical Fourier transform spectrometer with a kHz-level resolution. We characterize 16000 longitudinal cavity modes spanning 16 THz of bandwidth in terms of center frequency, linewidth, and amplitude. Using the center frequencies we retrieve the group delay dispersion of the cavity mirror coatings and pure N2 with 0.1 fs2 precision and 1 fs2 accuracy, as well as the refractivity of the 3ν1 + ν3 absorption band of CO2 with 5 × 10-12 precision. This opens up for broadband refractive index metrology and calibration-free spectroscopy of entire molecular bands.

Whispering-gallery-mode laser-based noise-immune cavity-enhanced optical heterodyne molecular spectrometry.

The whispering-gallery-mode (WGM) laser is a type of laser that has an exceptionally narrow linewidth. Noise-immune cavity-enhanced optical heterodyne molecular spectrometry, which is a detection technique with extraordinary properties that benefit from narrow linewidth lasers, has been realized with a WGM laser. By locking to a cavity with a finesse of 55 000, acetylene and carbon dioxide could be simultaneously detected down to an unprecedented noise equivalent absorption per unit length of 6.6×10-14 cm-1 over 150 s, corresponding to 5 ppt of C2H2.

Intensity-Stabilized Fast-Scanned Direct Absorption Spectroscopy Instrumentation Based on a Distributed Feedback Laser with Detection Sensitivity down to 4 × 10-6.

A novel, intensity-stabilized, fast-scanned, direct absorption spectroscopy (IS-FS-DAS) instrumentation, based on a distributed feedback (DFB) diode laser, is developed. A fiber-coupled polarization rotator and a fiber-coupled polarizer are used to stabilize the intensity of the laser, which significantly reduces its relative intensity noise (RIN). The influence of white noise is reduced by fast scanning over the spectral feature (at 1 kHz), followed by averaging. By combining these two noise-reducing techniques, it is demonstrated that direct absorption spectroscopy (DAS) can be swiftly performed down to a limit of detection (LOD) (1σ) of 4 × 10-6, which opens up a number of new applications.

Wavelength-modulated tunable diode-laser absorption spectrometry for real-time monitoring of microbial growth.

It is important to monitor and assess the growth of micro-organisms under various conditions. Yet, thus far there has been no technique to do this with the required speed and accuracy. This work demonstrates swift and accurate assessment of the concentration of carbon dioxide that is produced by use of a wavelength-modulated tunable diode-laser based absorption spectroscopy (WM-TDLAS). It is shown by experiments on two types of bacteria, Staphylococcus aureus and Candida albicans, that the technique can produce high signal-to-noise-ratio data from bacteria grown in confined spaces and exposed to limited amounts of nutrients that can be used for extraction of growth parameters by fitting of the Gompertz model. By applying the technique to S. aureus bacteria at various temperatures (in the 25°C to 42°C range), it is specifically shown that both the maximum growth rate and the so-called lag time have a strong temperature dependence (under the specific conditions with a maximum of the former at 37°C) that matches conventional models well for bacterial growth. Hence, it is demonstrated that WM-TDLAS monitoring CO2 is a user-friendly, non-intrusive, and label-free technique that swiftly, and with high signal-to-noise-ratio, can be used for rapid (on the Hz scale) and accurate assessment of bacterial growth.

Calibration-free wavelength-modulation spectroscopy based on a swiftly determined wavelength-modulation frequency response function of a DFB laser.

A methodology for calibration-free wavelength modulation spectroscopy (CF-WMS) that is based upon an extensive empirical description of the wavelength-modulation frequency response (WMFR) of DFB laser is presented. An assessment of the WMFR of a DFB laser by the use of an etalon confirms that it consists of two parts: a 1st harmonic component with an amplitude that is linear with the sweep and a nonlinear 2nd harmonic component with a constant amplitude. Simulations show that, among the various factors that affect the line shape of a background-subtracted peak-normalized 2f signal, such as concentration, phase shifts between intensity modulation and frequency modulation, and WMFR, only the last factor has a decisive impact. Based on this and to avoid the impractical use of an etalon, a novel method to pre-determine the parameters of the WMFR by fitting to a background-subtracted peak-normalized 2f signal has been developed. The accuracy of the new scheme to determine the WMFR is demonstrated and compared with that of conventional methods in CF-WMS by detection of trace acetylene. The results show that the new method provides a four times smaller fitting error than the conventional methods and retrieves concentration more accurately.